Correctness of the remaining solver-model refinements

Prove the correctness of the remaining refinements from the ideal solver model to the implementable solver models for E-matching generation accounting, including the stated confluence and simulation properties.

Background

The paper presents a sequence of solver models that refine an ideal, solver-agnostic model into increasingly efficient implementations. The paper gives proof sketches for the refinements and fully formalizes only some of the associated arguments in the appendix.

The authors explicitly state that the correctness of the remaining refinements is conjectural. Thus, completing rigorous proofs of those refinements is an unresolved problem concerning the formal soundness of the proposed generation-accounting approach.

References

In this work-in-progress paper, we present proof sketches for the refinements , , and , aiming to convey the underlying intuition rather than full rigor. We present some of the fully formalized proofs in the appendix; the correctness of the remaining refinements is conjectured, supported by the proof sketches.

— A Deeper Look at Depth: Stable Generation Accounting for Quantifier Reasoning  (2609.26345 - Cebeci et al., 22 Sep 2026) in Section 1, Introduction