SemantEq introduces a principled method for verifying that formal statements faithfully translate natural‑language mathematics by requiring each statement to transform into the other through a chain of allowed logical steps, rather than relying on trivial logical equivalence. The system evaluates proofs using Lean’s proof terms, achieving 100 % precision and 65.6 % recall on the ProofNetVerif test split, outperforming prior methods. A complementary audit tool, SemantEq‑ProofAudit, further improves recall for equivalent pairs while rejecting all non‑equivalent pairs.
arXiv:2505. 18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs.
arXiv:2610.17358v1 Announce Type: cross Abstract: Formal verification proves that a program satisfies its specification, but says nothing about whether the specification captures what the author mean...
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.
The paper introduces a reference‑free proxy‑judge framework for autoformalization, separating correctness into grounding, statement faithfulness, coverage, and inference. It presents three theoretical results linking proxy error rates to pass‑but‑wrong rates, the impact of false rejections on refinement, and a decomposition of final pass rates. The framework is instantiated with eight proxies and evaluated on ProofNet, miniF2F, e‑SNLI, and ProntoQA, showing that the predictions hold and identifying failure routes.
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
arXiv:2608.28639v1 Announce Type: new Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existi...
arXiv:2608. 15432v1 Announce Type: new Abstract: In formal verification, both the autoformalization of statements and automated proof search have been studied extensively.
arXiv:2610.34490v1 Announce Type: cross Abstract: In formal systems such as Lean 4, efficiently finding answers to mathematical problems and generating verifiable proofs is an important task in autom...
arXiv:2608. 05420v1 Announce Type: cross Abstract: Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness.
arXiv:2607. 13069v1 Announce Type: new Abstract: Large language models produce chain-of-thought (CoT) reasoning that appears logically sound yet may not genuinely depend on its stated premises.
arXiv:2610.17697v1 Announce Type: cross Abstract: AI systems now write long and difficult mathematical proofs, and checking their step-by-step validity is becoming a bottleneck. A learned verifier co...