Transfer of Best-First Search Superiority to Factorized Search with a Trained Critic

Determine whether the observed ability of simple best-first search to outperform Monte Carlo tree search-style search in linear execution-guided theorem proving carries over to factorized proof search with a trained critic.

Background

The paper compares NanoProof with linear execution-guided provers such as BFS-Prover, which perform best-first search over monolithic Lean proof states, and with factorized systems such as NanoProof that independently search decomposed proof goals. It notes that BFS-Prover reports that, when using a large pretrained policy and no learned critic, simple best-first search can outperform Monte Carlo tree search-style search.

The paper explicitly leaves unresolved whether that result generalizes to the different setting of factorized search combined with a trained critic. Because NanoProof releases its implementation and supporting artifacts, the authors identify this as an experimentally testable question rather than a result established in the paper.

References

BFS-Prover also argues that, in its setting of a large pretrained policy and no learned critic, simple best-first search can outperform MCTS-style search; whether this carries over to factorized search with a trained critic is an open question that our release makes testable.

— NanoProof: Open and Efficient Automated Theorem Proving in Lean 4  (2610.11605 - Kripner et al., 8 Oct 2026) in Section 2, Related Work, subsection “Execution-Guided ATP”