Automated Theorem Proving

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Overview

Automated theorem proving studies how to turn goals and assumptions into proofs that trusted checkers can validate, supporting dependable mathematics and software verification. Approaches range from symbolic search, resolution, tableaux, SAT/SMT solving, and tactics to language models that retrieve lemmas, decompose goals, learn from proof traces, and use Lean, Rocq, Isabelle, or Dafny feedback. Evaluation spans contest benchmarks such as miniF2F and PutnamBench, large proof libraries, code-verification tasks, and research-level problems. A central challenge is moving from benchmark success to robust, economical proofs whose formal statements faithfully capture the intended mathematics or specifications; autoformalization and semantic verification remain difficult.

Latest papers

CardsList

160 papers29 papers in the last four weeks, up 142% on the four weeks before. 0.2% of all new papers.

  1. Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMs

    Oct 27, 2026Azim Ospanov, Zijin Feng, Ding Ding +5Automated GradingLanguage Model Reasoning Evaluation

    Huawei Foundation Model Department · The Chinese University of Hong Kong · The Hong Kong University of Science and Technology

  2. KAPPA: Checking the Proofs in Statistics Papers with Lean 4 and Language Model Agents

    Oct 26, 2026Zihua She, Xiao WangLarge Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Department of Statistics, Purdue University, West Lafayette, IN 47907, USA

  3. Efficient Proof Generation for Lean Statements with Multiple Candidate Answers

    Oct 25, 2026Pengzhen Lin, Ke Zhang, Maziar Raissi +1Automated Theorem ProvingLLM Mathematical Reasoning

    University of California, Riverside

  4. h1: A Taste of the Bitter Lesson in Automated Theorem Proving

    Oct 25, 2026Skander Moalla, Ahmad Rammal, Niket Patel +2Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    FAIR at Meta · EPFL · CERMICS, ENPC, Institut Polytechnique de Paris +1

  5. PACE: Research Proving Agent for Adaptive Conjecture Exploration

    Oct 24, 2026Shu Miao, Feiming Wang, Wentao Long +3AI-Assisted Mathematical DiscoveryAutonomous Research Agents

    Peking University · Nankai University · Fudan University

  6. ReuF2F: Benchmarking Coding Agents on Formalized Undergraduate Research Problems

    Oct 19, 2026Zeyu Zheng, Yiyang Liu, Yuyang Zhao +20Coding Agent BenchmarksMathematical Reasoning Benchmarks

    Carnegie Mellon University · Chinese University of Hong Kong, Shenzhen · Shenzhen Loop Area Institute +3

  7. Fix, Not Just Resample: Bounded Compiler-Guided Repair in Lean 4

    Oct 18, 2026Haotian Deng, Chris Farber, Sonal Narasimha +2Automated Theorem ProvingLarge Language Model-Guided Theorem Proving

    Purdue University

  8. Repair, Retry, and the Cost of Hindsight: Verifier Feedback in Formal Theorem Proving

    Oct 15, 2026Jack Li, Sophia LiLLM Self-CorrectionLarge Language Model-Guided Theorem Proving

    Department of Computer Science, Stanford University

  9. Lean Graph Search for Formal Theorem Proving

    Oct 15, 2026Yihan Xu, Jia-Chen Gu, Junyi Zhang +7Graph-Based RetrievalLean Theorem Proving

    University of California, Los Angeles

  10. Learning Lean Feedback for Efficient Proof-Candidate Evaluation on GPUs

    Oct 15, 2026Lazar Milikic, Etienne Bamas, Emmanuel Abbe +1Automated Theorem ProvingReinforcement Learning with Verifiable Rewards

    EPFL, Lausanne, Switzerland

  11. Reset Early, Reset Often, Eliminate Models

    Oct 13, 2026Martin S. Fixman, Fredrik Rømming, Sean B. HoldenAutomated Theorem Proving

    University of Cambridge, United Kingdom

  12. Do Theorem Provers Need Theorem-Proving Agents? mini-Lean-agent: A Coding-Agent Baseline for Lean

    Oct 12, 2026Tomas Ortega, Simon Park, Ayush Khaitan +3Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Princeton Language and Intelligence Princeton University Princeton, NJ 08540 · Department of Mathematics Rutgers University Piscataway, NJ 08854

  13. TLA-Verus: Generating and Solving Temporal Proof Obligations with LLM Agents

    Oct 10, 2026Kseniia Strelbytska, Balázs Szilágyi, Anna Mészáros +1Formal VerificationAutomated Theorem Proving

    Stephen Perse Cambridge, UK · University of Cambridge, UK · Reasonable

  14. SqueezeBench: Saturation-Resilient Evaluation of Mathematical Capability

    Oct 9, 2026Pablo Manrique, Hai Xia, Stefan SzeiderMathematical Reasoning BenchmarksBenchmark Design

    Algorithms and Complexity Group TU Wien, Vienna, Austria

  15. LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs

    Oct 8, 2026Nihal Jain, Shuangjie Yao, Begum Cicekdag +2Automated Theorem ProvingInference-Time Search

    Columbia University

  16. NanoProof: Open and Efficient Automated Theorem Proving in Lean 4

    Oct 8, 2026Matěj Kripner, Milan StrakaAutomated Theorem ProvingLean Theorem Proving

    Institute of Formal and Applied Linguistics, Faculty of Mathematics and Physics, Charles University Prague, Czech Republic

  17. Bolzano: From Expert-Guided Proof Search to Automated Open-Problem Solving

    Oct 7, 2026Adrián Zámečník, Matěj Kripner, Martin Koutecký +5Automated Theorem ProvingAI Agents for Scientific Discovery

    Computer Science Institute, Charles University · Institute of Formal and Applied Linguistics, Charles University · Department of Applied Mathematics, Charles University +1

  18. Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification

    Oct 7, 2026Shuangjie Yao, Nikolaus Holzer, Mark Paul Santolucito +3Automated Theorem ProvingFormal Verification

    Columbia University · The Hong Kong University of Science and Technology · Barnard College, Columbia University

  19. Let the Library Speak: Self-Advertised Method Selection for Formal Proving

    Oct 7, 2026Xiaopeng Yuan, Suijin Wang, Yanli Wang +5Automated Theorem ProvingLLM Mathematical Reasoning

    University of Illinois at Urbana-Champaign · Tsinghua University · Imperial College London +1

  20. SCOPE: Certified Theorem Proving with a Language Model as the Policy Planner

    Oct 6, 2026Hanchao Zhou, Jialei LiLarge Language Model-Guided Theorem ProvingAutomated Theorem Proving

  21. AIProver: Agentic Auto-Formalization of Mathematical Research via Certificate-Driven Evolving Harness

    Oct 4, 2026Prithwish Jana, Viet Bach Hoang, Logan Luna +9Mathematical Reasoning BenchmarksAutomated Theorem Proving

    Georgia Institute of Technology, USA · University of Pennsylvania, USA · Foothill College, USA +3

  22. Viva La Vida: Verification and Accumulation Failures in Multi-Agent Proof Search

    Oct 4, 2026Benji Xu, Ken Zheng, Noah HanLLM Agent VerificationLLM Agent Reliability

    University of California, Berkeley

  23. Dense Neuro-Symbolic Reasoning in a Unified Geometry State

    Oct 3, 2026Ruoran Xu, Wending Gao, Haoyu Cheng +2Mathematical ReasoningNeuro-Symbolic Reasoning

    Xi’an Jiaotong-Liverpool University

  24. Solving VeriContest with a Lean-Backed Rust Verifier

    Oct 2, 2026Traian Serbanuta, Jun Xu, Andrei Stefanescu +1Large Language Model-Guided Theorem ProvingFormal Verification

    Asymptotic

  25. ProsaBuddy: Assisting Mechanized Real-Time Schedulability Analysis with LLM-based Agents

    Oct 1, 2026Junyi Liu, Tianchi Ren, Fei Guan +4Automated Theorem ProvingReal-Time Scheduling

    City University of Hong Kong · Northeastern University (China) · Northeast Forestry University +3

  26. Cogentic: Multi-Agent Orchestration for Automated Proof Discovery

    Sep 30, 2026Yang Cai, Vineet Gupta, Yanchen Jiang +4Multi-Agent LLM SystemsAI Agents for Scientific Discovery

    Google Research · Yale University · Google DeepMind

  27. Growing an Agent/Prover Interface: Evolutionary Tool Design for Cost-Efficient Theorem Proving in Rocq and Lean

    Sep 30, 2026Jules Viennot, Guillaume Baudart, Marc LelargeAutomated Theorem ProvingEvolutionary Optimization

    IRIF, Universit´e Paris Cit´e, Inria, CNRS · DI ENS, PSL University, Inria

  28. Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization

    Sep 30, 2026Wei Zhao, Yangshuo Zou, Chengxiang Ding +5Automated Theorem ProvingHuman-in-the-Loop AI

    School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China · University of California, Berkeley, CA 94720, USA · Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China +4

  29. TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science

    Sep 28, 2026Chutong Yang, Xiyuan Zhang, Yu Huang +7Mathematical Reasoning BenchmarksAutomated Theorem Proving

    Department of Computer Science, The University of Texas at Austin · Amazon · Department of Statistics and Data Science, The Wharton School, University of Pennsylvania

  30. ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization

    Sep 28, 2026Feiming Wang, Daibo Li, Kun YuanStochastic OptimizationLarge Language Model-Guided Theorem Proving

    Nankai University · Peking University