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.
By Jilin Hu, Jianyu Zhang, Yongwang Zhao, Talia Ringer
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.
By QuocViet Pham, Elvir Karimov, Andrey Galichin, Ivan Oseledets
arXiv:2606. 03743v1 Announce Type: new Abstract: While Large Language Models (LLMs) have shown strong performance in generating formal proofs, their outputs often remain less readable, modular, maintainable, and reusable than proofs in mature formal mathematics libraries.
By Yiming Fu, Peixuan Liu, Zichen Wang, Kun yuan
LEVER is a new proof‑search algorithm that lets users program the objective over correct proofs and optimizes it during search. It scores partial proofs on an AND/OR graph, combining achieved objective values with predictions for open subgoals, so the objective guides search before a proof is complete. On the PutnamBench in Lean 4, LEVER reduces computational cost by 34 % and raises the solve rate from 80 % to 96 %, while also improving topical impurity and approaching refactoring for proof length.
By Nihal Jain, Shuangjie Yao, Begum Cicekdag, Zhuo Zhang, Suman Jana
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...
By Bodla Krishna Vamshi, Haizhao Yang
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.
By Xiyuan Zhou, Zhuoqi Li, Xinlei Wang, Yirui He, Yuhao Wu, Yuheng Cheng, Yan Xu, Junhua Zhao, Jinjin Gu
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.
By Joshua Ong Jun Leang, Zheng Zhao, Mihaela C\u{a}t\u{a}lina Stoian, Qiyuan Xu, Haonan Li, Wenda Li, Shay B. Cohen, Eleonora Giunchiglia
The paper presents a bounded, online step-level repair module for Lean 4 that uses compiler error messages to fix rejected tactics instead of discarding them. By sampling up to $K$ candidate tactics and allowing at most $R$ repairs per step, the method improves solve rates over a sampling-only baseline, achieving up to a 32% relative gain and solving 82 additional theorems on a 1,990-theorem subset of the LeanDojo benchmark. The approach trades extra runtime for reachable proofs, with most benefit coming from early repair attempts and shallow tactic failures, and it successfully replicates on the Lean Workbook benchmark, nearly doubling its solve rate without regressions.
By Haotian Deng, Chris Farber, Sonal Narasimha, Samskrithi Sivakumar, Yexiang Xue
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...
By Yutong Xin, Qiaochu Chen, Greg Durrett, I\c{s}il Dillig
arXiv:2509. 14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving.
By Kazumi Kasaura, Naoto Onda, Yuta Oriike, Masaya Taniguchi, Akiyoshi Sannai, Sho Sonoda
arXiv:2608. 09277v1 Announce Type: new Abstract: Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction.
By Zenan Li, Ziran Yang, Peiyang Song, Zhaoyu Li, Kaiyu Yang