arXiv:2607. 21199v1 Announce Type: cross Abstract: Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution.
By Daimy Van Caudenberg, Alexander Ek, Carlos Cantero, Bart Bogaerts
The paper introduces a new calculus that integrates ground instantiations, CDCL(T)-style rules, and non‑ground conflict analysis for SMT solving. By performing resolution on the original non‑ground clauses, the solver learns more general, often non‑redundant clauses, potentially yielding exponentially shorter proofs. The approach also incorporates chronological backtracking and is shown to simulate several existing solving frameworks, including CDCL, SCL(FOL), SCL(T), and Resolution.
By Yasmine Briefs, Christoph Weidenbach
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.
By Hironao Nakamura
arXiv:2608. 09190v1 Announce Type: new Abstract: GK is a query-directed first-order prover that extends ordinary resolution-based proof search with explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions.
By Tanel Tammet
arXiv:2608. 19009v2 Announce Type: replace Abstract: Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors.
By Yajie Yin
FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
By Ziyu Wang, Qiming Dai, Yishan Wu, Zaiwen Wen