arXiv:2606. 04877v1 Announce Type: cross Abstract: Proof assistants based on expressive logics suffer limited automation for proof search, raising the cost of formal verification based on proof assistants.
arXiv:2604. 15713v2 Announce Type: replace-cross Abstract: Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference.
HybridProver is a unified framework that combines whole-proof synthesis and tactic-based generation using proof sketches as an intermediate representation. Implemented in Isabelle/HOL, it employs two 7B-scale LLMs trained on optimized Isabelle datasets. On the miniF2F Isabelle benchmark, HybridProver achieved a 73.8% success rate, surpassing the previous state of the art of 61.9%, and ablation studies examined the effects of dataset quality, training settings, and sampling strategies.
arXiv:2512. 10187v3 Announce Type: replace Abstract: LLMs excel at reasoning, but validating their steps remains challenging.
arXiv:2607. 07779v1 Announce Type: cross Abstract: Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages.
arXiv:2605. 20531v2 Announce Type: replace-cross Abstract: Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning.
arXiv:2606. 19197v1 Announce Type: cross Abstract: Abduction is a central approach to explain missing entailments from a knowledge base by providing a hypothesis, that would, if added to the knowledge base, make the missing entailment become true.
arXiv:2607. 21191v1 Announce Type: cross Abstract: Event-B is a formal method rooted in predicate logic and set theory.
arXiv:2606. 18098v1 Announce Type: new Abstract: Advances in Artificial Intelligence (AI) have led AI for Theorem Proving to become a promising means of formally verifying computer systems.
arXiv:2607. 01585v1 Announce Type: cross Abstract: Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP).
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.
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.