Proof Artifact Co-training for Theorem Proving with Language Models
University of Pittsburgh（匹兹堡大学）；OpenAI；IBM Research（IBM研究院）；Google Research（谷歌研究院）；Stanford University（斯坦福大学）；Carnegie Mellon University（卡内基梅隆大学）；CIBO Technologies（CIBO科技）；University of Toronto（多伦多大学）；University of Cambridge（剑桥大学）
Jesse Michael Han, Jason Rute, Yuhuai Wu, Edward W. Ayers, Stanislas Polu
Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32\% to 48\%.
Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
D-CHAB, ETH Zurich, Zurich, Switzerland.；D-INFK, ETH Zurich, Zurich, Switzerland.；ETH AI Center, Zurich, Switzerland.；University of Pennsylvania, PA, USA.；Independent Researcher.
CD Tools -- Condensed Detachment and Structure Generating Theorem Proving (System Description)
University of Potsdam（波茨坦大学）
CD Tools是一个Prolog库，用于在一阶ATP中试验凝聚分离，它将最近围绕证明结构的正式观点付诸实践。从一阶ATP的观点来看，凝聚分离提供了一个相对简单但具有基本特征和重要应用的环境，使其成为开发和评估新技术的基础。CD Tools包含基于枚举证明结构的专用证明器。我们在这里集中在其中之一，SGCD，它允许混合目标和公理驱动的证明搜索特别灵活的方式。在纯目标驱动的配置中，它的作用类似于子句表或连接方法家族的证明者。在混合配置中，它的性能要强得多，接近最先进的证明器，同时发出相对较短的证明。实验表明了该证明器实现的结构生成方法的特点和应用的可能性。对于ATP中经常研究的一个历史性问题，它产生了一个新的证明，比任何已知的证明都要短得多。
Learning to Reason with Insight for Informal Theorem Proving
City University of Hong Kong（香港城市大学）；Tsinghua University（清华大学）；Ke Holdings Inc.（Ke控股公司）；Shenzhen University of Advanced Technology（深圳先进技术大学）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement
College of Computer Science and Technology Zhejiang University（浙江大学计算机科学与技术学院）；Siebel Center for Computer Science University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校计算机科学中心）
Sun Yat-sen University（中山大学）；University of Edinburgh（爱丁堡大学）；City University of Hong Kong（香港城市大学）；HKU（香港大学）；HKUST (Guangzhou)（香港科技大学（广州））；HKUST（香港科技大学）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）
AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language
Nanyang Technological University Singapore（南洋理工大学新加坡分校）；Imperial College London London, UK（伦敦帝国理工学院伦敦分校）；University of Edinburgh Edinburgh, UK（爱丁堡大学爱丁堡分校）
LLM-based Automated Theorem Proving Hinges on Scalable Synthetic Data Generation
State Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术全国重点实验室）；School of Computing and Mathematical Sciences, Birkbeck, University of London（伦敦大学伯贝克学院计算与数学科学学院）
FormalRewardBench: A Benchmark for Formal Theorem Proving Reward Models
Koç University, Department of Computer Science and Engineering（科克大学计算机科学与工程系）；Codeway Studios（Codeway工作室）；Boğaziçi University, Department of Computer Engineering（博雅奇大学计算机工程系）；Friedrich-Alexander-Universität Erlangen-Nürnberg, Intelligent Language Systems（埃尔兰根-纽伦堡弗里德里希-亚历山大大学智能语言系统）
Neural Theorem Proving for Verification Conditions: A Real-World Benchmark
Nanyang Technological University（南洋理工大学）；Peking University（北京大学）；MBZUAI；Imperial College London（帝国理工学院）；East China Normal University（华东师范大学）；University of Edinburgh（爱丁堡大学）
Proof-Refactor: Refactoring Generated Formal Proofs into Modular Artifacts
Department of Mathematics, Southern University of Science and Technology（南方科技大学数学系）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）
