automated reasoning tool developers

Abstract: Lean verifies that a formal proof establishes its stated proposition under declared assumptions, but does not check whether that proposition faithfully expresses the mathematical claim in a manuscript. Assessing this correspondence requires interpreting the main theorem through its project dependencies, which may be scattered throughout a large development. We introduce MechAlign, a framework for project-level semantic alignment review that combines formal dependency extraction with LLM-based assessment. Its extraction tool, LeanTrace, constructs a statement dependency graph from elaborated declarations, retaining definition bodies and structure constraints while excluding proof bodies and stopping at an explicit library boundary. The reviewer uses this context to investigate alignment and report discrepancies with localized evidence. We conduct a preliminary review of 201 main results from 173 OpenAI Math projects, using supplied informal descriptions and available paper context. A hyperbolic-group case illustrates how dependency inspection localizes a missing dimensional constraint relative to the manuscript, consistent with the upstream declaration of formalization scope. We also construct LeanReviewBench, comprising 501 fixed claim-statement-context triples from OpenAI Math, Fermat's Last Theorem, and Kakeya, with description provenance recorded. The resource supports controlled comparisons of more project-level semantic alignment evaluations.

Abstract: The Minimum Equivalent Expression problem (MEE) asks, given a propositional formula $φ$ and an integer $k$, whether $φ$ is equivalent to a formula with at most $k$ occurrences of propositional variables. While the problem is clearly in $Σ_2^p$, its completeness under polynomial-time many-one reductions has remained open since at least 1979. Buchfuhrer and Umans showed in 2008 that it is $Σ_2^p$-complete under polynomial-time Turing reductions. In this note, we present a proof discovered by GPT-Sol-6.1 which establishes that MEE is $Σ_2^p$-complete also under polynomial-time many-one reductions.

Abstract: We introduce the formalism of non-wellfounded and cyclic linear nested sequent calculi, developing concrete systems for linear temporal logic (LTL). The paper addresses two central problems, which we call "cycle recognition" and "unraveling." Cycle recognition concerns identifying cycles in non-wellfounded proofs in order to extract corresponding cyclic proofs, while unraveling studies the converse transformation, from cyclic proofs to non-wellfounded ones. Although these processes are well understood for Gentzen sequents, they have received little attention for more expressive sequent formalisms and become more challenging in the linear nested sequent setting. To address cycle recognition, we show the completeness of non-wellfounded proofs relative to a particular normal form exhibiting a property we call "saturation recurrence," which enables the systematic extraction of cyclic proofs. To address unraveling, we introduce a specialized procedure that shifts rule applications forward along linear nested sequents, allowing non-wellfounded proofs to be reconstructed from cyclic ones. Overall, our work provides new proof-theoretic techniques for cycle recognition and unraveling in expressive multisequent formalisms.

Abstract: We introduce Sequent-Prover, a family of verifier-using language-model agents, and the post-training framework that produces them. Agents reason in an executable SMT-LIB scratchpad: they write complete SMT-LIB programs, query Z3 across turns, inspect solver feedback, repair formalizations, and terminate with an explicit answer. Our recipe, verifier-conditioned trajectory distillation, bootstraps from a noisy teacher proposal policy by sampling multi-turn trajectories, retaining the successful tail that is correct, non-trivial, grounded, and executable, then applying supervised fine-tuning and trajectory-level preference optimization. Because solver success alone does not guarantee semantic faithfulness, we evaluate task accuracy, k-sample reliability, and SMT program quality. Across 37 benchmarks and 7,254 problems per model family, post-training raises the 4B model's per-attempt accuracy from 85.6% to 97.0% and four-sample all-correct reliability (pass^4}) from 64.1% to 91.7%. It also reduces average SMT calls from 4.10 to 2.52 and tokens per attempt from 18.97k to 12.72k. Sequent-Prover agents give answers backed by executable formal artifacts.