Sequent-Prover: Training Agents for Formal, Checkable SMT-based Reasoning

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.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic in Computer Science (cs.LO)

arXiv:2610.15258 [cs.CL]

(or arXiv:2610.15258v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.15258 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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