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.
By Wenqian Ye, Ziwei Guan, Eric Xie, Bohan Liu, Shivani Modi, Buyun Zhang, Ellie Dingqiao Wen, Henry Kautz, Aidong Zhang
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
By Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud, Md Kamrul Hasan
arXiv:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
By Tian-Shuo Liu, Shiyuan Zhang, Zijie Geng, Haoyu Liu, Runjie Xu, Pengyuan Wang, Lei Yuan, Yang Yu
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
arXiv:2608. 14221v1 Announce Type: new Abstract: Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4.
By Lushi Pu, Weiming Zhang, Xinheng Xie, Zixuan Fu, Bingxiang He, Hengyu Zhao, Hongya Lyu, Xin Li, Jie Zhou, Yudong Wang
arXiv:2608.18084v2 Announce Type: replace
Abstract: Theorem proving in real-world Lean 4 projects is challenging because proofs often depend on project-specific context. While iterative refinement ca...
By Zhuo Liu, Ding Yu, Hangfeng He
arXiv:2607. 19407v1 Announce Type: new Abstract: Formal theorem proving has emerged as a frontier challenge for machine learning, yet the ecosystem is fragmented: proofs remain siloed across incompatible systems, limiting both training data for learning-based provers and the portability of verified results.
By Jiayi Wu, Robert Joseph George, Anima Anandkumar
Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules. Whether such an output that appears creative is truly original and effective is hard to establis...
arXiv:2608. 15979v1 Announce Type: new Abstract: Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules.
By Eric Xie, Wenqian Ye, Aidong Zhang
arXiv:2510.11944v2 Announce Type: replace-cross
Abstract: Large Language Models (LLMs) excel at both informal and formal (e.g. Lean 4) mathematical reasoning but still struggle with autoformalisation...
By Yupei Li, Philipp Borchert, Gerasimos Lampouras
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
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.
By Jialiang Sun, Yuzhi Tang, Ao Li, Chris J. Maddison, Kuldeep S. Meel