arXiv:2509. 14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving.
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.
arXiv:2506. 17104v2 Announce Type: replace Abstract: Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas.
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.
MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.
RePro is a framework that rewrites benchmark problems for large language models (LLMs) in mathematical problem solving, ensuring that the rewritten problems and their answers are valid and correct through Lean-verified proofs. It integrates Lean-oriented neural automated theorem provers (ATPs) to regenerate answers, achieving 100% well-definedness, feasibility, and answer correctness on GSM8K and MATH datasets. Experiments show that models’ performance drops on these proof‑verified rewritten benchmarks, indicating sensitivity to surface‑level and structural variations and potential memorization effects.
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.
The paper introduces a compiler-guided adaptive proof search framework for Lean 4 theorem proving, addressing the challenge of context-dependent proofs in real-world projects. It balances exploration and exploitation by generating diverse starting points via dual-model generation and resampling when stagnation occurs, while refining promising states using compiler-grounded pairwise comparison. Experiments on seven Lean 4 projects from miniCTX‑v2 demonstrate that the method improves average pass rates by 12.8 percentage points within a pass@32 budget and reduces LLM calls by 21.9 % compared to pass@k baselines.
arXiv:2602.18307v2 Announce Type: replace-cross Abstract: Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-b...
We introduce TCS-Bench, a benchmark for evaluating Large Language Models (LLMs) on research-level Theoretical Computer Science (TCS) proof generation. TCS-Bench consists of theorem-proving tasks from papers published at top theoretical computer science venues (STOC, FOCS, and SODA).
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.