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. DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent

    Apr 29, 2026Youyuan Zhang, Jialiang Sun, Hangrui Bi +4Automated Theorem ProvingProgram Synthesis

    University of Toronto · UC Berkeley

  2. QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems

    Apr 27, 2026Chenyang An, Qihao Ye, Minghao Pan +1AI Agents for Scientific DiscoveryAutomated Theorem Proving

    University of California, San Diego, La Jolla, USA · California Institute of Technology, Pasadena, USA · Amazon Web Services

  3. OptProver: Bridging Olympiad and Optimization through Continual Training in Formal Theorem Proving

    Apr 26, 2026Chenyi Li, Yanchen Nie, Zhenyu Ming +3Continual Learning for LLMsAutomated Theorem Proving

    School of Mathematical Sciences, Peking University · 2Huawei Technologies · Center for Machine Learning Research, Peking University +1

  4. Benchmarking Testing in Automated Theorem Proving

    Apr 26, 2026Jongyoon Kim, Hojae Han, Seung-won HwangLLM EvaluationAutomated Theorem Proving

    Interdisciplinary Program in Artificial Intelligence, Seoul National University1 · Electronics and Telecommunications Research Institute2

  5. Scaling Self-Play with Self-Guidance

    Apr 22, 2026Luke Bailey, Kaiyue Wen, Kefan Dong +2Self-Play RLAutomated Theorem Proving

    Stanford University

  6. Yanasse: Finding New Proofs from Deep Vision's Analogies, Part 1

    Apr 19, 2026Alexandre LinharesAutomated Theorem ProvingAnalogical Reasoning

    Getulio Vargas Foundation · ARGO LABS

  7. Learning to Reason with Insight for Informal Theorem Proving

    Apr 17, 2026Yunhe Li, Hao Shi, Bowen Deng +8Automated Theorem ProvingRL for Language Model Reasoning

    City University of Hong Kong · Tsinghua University · Ke Holdings Inc. +2

  8. Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4

    Apr 17, 2026Chengwu Liu, Yichun Yin, Ye Yuan +7Automated Theorem ProvingLean Theorem Proving

    State Key Laboratory for Multimedia Information Processing, School of Computer Science, PKU-Anker LLM Lab, Peking University · Huawei Technologies Co., Ltd. · School of Software & Microelectronics, Peking University +1

  9. Awakening the Sleeping Agent: Lean-Specific Agentic Data Reactivates General Tool Use in Goedel Prover

    Apr 9, 2026Jui-Hui Chung, Hongzhou Lin, Lai Jiang +2LLM Tool UseLLM Post-Training

    Princeton Language and Intelligence · Amazon · Department of Computer Science, University of Illinois at Urbana-Champaign

  10. ProofSketcher: Hybrid LLM + Lightweight Proof Checker for Reliable Math/Logic Reasoning

    Apr 7, 2026Kranthi Kommuru, Kunal Khanvilkar, Gaurav ParekhLarge Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Automatic Data Processing, Inc Atlanta, USA · Amazon Web Services, Inc Banglore, India

  11. QED-Nano: Teaching a Tiny Model to Prove Hard Theorems

    Apr 6, 2026LM-Provers, Yuxiao Qu, Amrith Setlur +6Mathematical ReasoningLLM Mathematical Reasoning

    CMU · Hugging Face · ETH Zurich +1

  12. Automated Conjecture Resolution with Formal Verification

    Apr 4, 2026Haocheng Ju, Guoxiong Gao, Jiedong Jiang +13Automated Theorem ProvingLLM Mathematical Reasoning

    School of Mathematical Sciences, Peking University · IQuest Research · Westlake Institute for Advanced Study, Westlake University +8

  13. MechMath: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving

    Mar 25, 2026Ruichen Qiu, Yichuan Cao, Junqi Liu +4Automated Theorem ProvingLLM Mathematical Reasoning

    SKLMS, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, China · School of Advanced Interdisciplinary Sciences, UCAS, Beijing, 101408, China · School of Mathematical Science, UCAS, Beijing, 101408, China

  14. LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning

    Mar 22, 2026Jianing Wang, Jianfei Zhang, Qi Guo +24Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Meituan LongCat Team

  15. Putnam 2025 Problems in Rocq using Opus 4.6 and Rocq-MCP

    Mar 20, 2026Guillaume Baudart, Marc Lelarge, Tristan Stérin +1Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    IRIF, Université Paris Cité, Inria, CNRS · DI ENS, PSL University, Inria · PRGM DEV

  16. Neuro-Symbolic Proof Generation for Scaling Systems Software Verification

    Mar 20, 2026Baoding He, Zenan Li, Wei Sun +4Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Computer Science, Nanjing University, China · Department of Computer Science, ETH Zurich, Switzerland +1

  17. Can LLMs Prove Robotic Path Planning Optimality? A Benchmark for Research-Level Algorithm Verification

    Mar 19, 2026Zhengbang Yang, Md. Tasin Tazwar, Minghan Wei +1Mathematical Reasoning BenchmarksAutomated Theorem Proving

    George Mason University · Florida Atlantic University

  18. Goedel-Code-Prover: Hierarchical Proof Search for Open State-of-the-Art Code Verification

    Mar 18, 2026Zenan Li, Ziran Yang, Deyuan He +7Formal VerificationAutomated Theorem Proving

    ETH Zürich · Princeton Language and Intelligence · Department of Computer Science, Princeton University +1

  19. Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium

    Mar 16, 2026Vasily IlinAutoformalizationFormal Verification

    University of Washington

  20. s2n-bignum-bench: A practical benchmark for evaluating low-level code reasoning of LLMs

    Mar 15, 2026Balaji Rao, John Harrison, Soonho Kong +2Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Stevens Institute of Technology Hoboken, NJ 07030 · Amazon Web Services Seattle, WA 98101

  21. Executable Archaeology: Reanimating the Logic Theorist from its IPL-V Source

    Mar 13, 2026Jeff ShragerAutomated Theorem Proving

    Bennu Climate, Inc.

  22. Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning

    Mar 13, 2026Yang Xu, Jun Liu, Shuwei Chen +2Neuro-Symbolic ReasoningExplainable Artificial Intelligence

    School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China · National–Local Joint Engineering Laboratory of System Credibility Automatic Verification, Southwest Jiaotong University, Chengdu 611756, Sichuan, China · School of Computing, Ulster University, Belfast, Northern Ireland, UK

  23. TaoBench: Do Automated Theorem Prover LLMs Generalize Beyond MathLib?

    Mar 13, 2026Alexander K Taylor, Junyi Zhang, Ethan Ji +10Automated Theorem ProvingMathematical Reasoning Benchmarks

    University of California, Los Angeles · University of California, Santa Barbara

  24. Compile to Compress: Boosting Formal Theorem Provers by Compiler Outputs

    Mar 13, 2026Guchan Li, Rui Tian, Hongning WangAutomated Theorem ProvingEfficient Language Model Reasoning

    Department of Computer Science and Technology, Tsinghua University, Beijing, China.

  25. Twitch: Learning Abstractions for Equational Theorem Proving

    Mar 6, 2026Guy Axelrod, Moa Johansson, Nicholas SmallboneAutomated Theorem ProvingAutomated Heuristic Design

    Chalmers University, of Technology, Gothenburg, Sweden · University of Gothenburg, Gothenburg, Sweden

  26. Non-Parametric Structural Priors for Geometry Theorem Prediction

    Mar 5, 2026Junbo Zhao, Ting Zhang, Can Li +3Mathematical ReasoningAutomated Theorem Proving

    School of Artificial Intelligence, Beijing Normal University, Beijing, China · Engineering Research Center of Intelligent Technology and Educational Application, Ministry of Education, Beijing, China · Beijing Key Laboratory of Artificial Intelligence for Education, Beijing, China +1

  27. Can LLM Aid in Solving Constraints with Inductive Definitions?

    Mar 4, 2026Weizhi Feng, Shidong Shen, Jiaxiang Liu +3Automated Theorem ProvingNeuro-Symbolic Reasoning

    Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Birkbeck, University of London, United Kingdom +1

  28. SorryDB: Can AI Provers Complete Real-World Lean Theorems?

    Mar 3, 2026Austin Letson, Leopoldo Sarra, Auguste Poiroux +9Automated Theorem ProvingLean Theorem Proving

    Axiomatic AI · Math, Inc. · EPFL +8

  29. A Minimal Agent for Automated Theorem Proving

    Feb 27, 2026Borja Requena, Austin Letson, Krystian Nowakowski +2Large Language Model-Guided Theorem ProvingAutomated Theorem Proving

    Axiomatic AI, Barcelona, Spain.

  30. LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics

    Feb 27, 2026Antoine Peyronnet, Fabian Gloeckle, Amaury HayatMathematical Reasoning BenchmarksAutomated Theorem Proving

    1Ecole Normale Superieure de Rennes · 2Ecole des Ponts Paris · 3Korean Institute for Advanced Study