[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82259-en":3,"doc-seo-82259-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82259,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","OpenProver: Agentic and Interactive Theorem Proving with Lean 4","OpenProver is an open-source, LLM-driven automated theorem proving (ATP) system integrating Lean 4 formal verification. The system uses a Planner-Worker-Verifier architecture inspired by agentic ATP approaches: a Planner maintains a compact Whiteboard scratchpad plus an unbounded repository of intermediate findings, decomposing proof work into parallel Workers. Verifiers independently check each Worker contribution, enabling reproducible evaluation. OpenProver also supports an interactive terminal interface that lets humans monitor and steer proof search.","arXiv :2607 .092 17v 1 [ cs .AI] 10 Jul 2026  \nOpenProver: Agentic and Interactive Theorem Proving with Lean 4  \nMatěj Kripner [0009−0006−9530−3670] and Milan Straka [0000−0003−3295−5576]  \nCharles University, Faculty of Mathematics and Physics, Prague, Czech Republic {kripner,[straka}@ufal.mff.cuni.cz](straka}@ufal.mff.cuni.cz)  \nAbstract. In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification. OpenProver integrates a PlannerWorker-Verifier architecture inspired by recent ATP agentic systems such as Aletheia. A Planner agent maintains a compact Whiteboard scratchpad and an unbounded Repository of intermediate findings, and decomposes mathematical work into parallel Workers.  \nOpenProver is fully open-source, offers reproducible evaluation through automatic formal verification of generated proofs, and provides an interactive terminal interface for human-guided proof search. In interactive mode, OpenProver allows the human operator to monitor and steer the proof search process, motivated by the established human-AI synergy in interactive code generation.  \nTo showcase the potential for quantitative ablation experiments enabled by automatic formal verification, we evaluate OpenProver on ProofNet and compare it with a simple baseline. OpenProver is publicly available at [github.com/kripner/OpenProver](github.com/kripner/OpenProver).  \nKeywords: Automated Theorem Proving · Lean 4 · Agentic LLMs  \n1 Introduction  \nAutomated Theorem Proving (ATP) has seen a significant rise in capabilities with the integration of Large Language Models (LLMs) trained using Reinforcement Learning from Verifiable Rewards (RLVR) [13] . Beyond tackling some of the hardest problems in competition mathematics, we are now seeing sparks of usefulness of ATP systems in frontier mathematical research.  \nExisting ATP systems can be roughly divided into two categories. First, fully autonomous theorem provers attempt end-to-end proof generation without human intervention, enabling reproducibility across runs. An example of such a system is Aletheia [3] .  \nSecond, interactive theorem provers (ITPs) enable the user to monitor and intervene in the proof search process, following the observation that while autonomous AI systems do not yet match expert human performance, the integration of both can greatly accelerate research. For example, a mathematician can formulate several potential approaches to completing a certain proof, receive worked-out counterexamples and observations from an AI assistant, and use these to iteratively adjust the high-level plan. With a human operator in the loop, ITP approaches require careful design of the visual user interface. Concurrent to our work, several agentic LLM-based ITP tools have been released, including OpenGauss [6] .  \n2 M. Kripner and M. Straka  \nWe present OpenProver, an automated theorem prover that bridges the gap between reproducible ATP research and interactive mathematical tooling. OpenProver extends Aletheia, most notably by integrating formal verification capabilities of Lean 4 [8] . To showcase the automatic evaluation enabled by Lean, we present quantitative measurements of OpenProver performance on ProofNet [2], compared to a simple linear Chain-of-Thought baseline. We hope that our work advances progress towards ATP systems that are both useful in frontier mathematical research and whose performance can be rigorously measured.  \n2 System Description  \nFig. 1. Overview of the OpenProver proof search loop. Planner iterates on the highlevel plan, manages persistent state, and delegates mathematical work to Workers. A Verifier provides independent feedback to each Worker contribution.  \nOpenProver is an automated theorem prover utilizing a reasoning LLM executed in an agentic scaffolding, with integration of the Lean 4 formal verifier. The system operates in an iterative loop composed of three types of agents illu","cbCaiaqCvU0KXbI8","https://ap.wps.com/l/cbCaiaqCvU0KXbI8","pdf",433132,2,1,7,"English","en",105,"# Introduction\n# System Description\n## Architecture","[{\"question\":\"What is OpenProver and what problem does it target?\",\"answer\":\"OpenProver is an open-source LLM-driven automated theorem proving system that bridges reproducible ATP research with interactive mathematical tooling by integrating Lean 4 formal verification.\"},{\"question\":\"How does OpenProver’s Planner-Worker-Verifier architecture work?\",\"answer\":\"A Planner maintains global proof state (Whiteboard and a repository), decomposes tasks, and delegates work to parallel Workers. Independent Verifiers then check each Worker’s output to provide feedback to the Planner.\"},{\"question\":\"How does OpenProver enable evaluation and human interaction?\",\"answer\":\"Automatic formal verification of generated proofs enables reproducible quantitative evaluation (e.g., on ProofNet). An interactive terminal mode allows a human operator to monitor and steer the proof search process.\"}]",1784179209,18,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"openprover-agentic-and-interactive-theorem-proving-with-lean-4","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/openprover-agentic-and-interactive-theorem-proving-with-lean-4/82259/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is OpenProver and what problem does it target?","Question",{"text":75,"@type":76},"OpenProver is an open-source LLM-driven automated theorem proving system that bridges reproducible ATP research with interactive mathematical tooling by integrating Lean 4 formal verification.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does OpenProver’s Planner-Worker-Verifier architecture work?",{"text":80,"@type":76},"A Planner maintains global proof state (Whiteboard and a repository), decomposes tasks, and delegates work to parallel Workers. Independent Verifiers then check each Worker’s output to provide feedback to the Planner.",{"name":82,"@type":73,"acceptedAnswer":83},"How does OpenProver enable evaluation and human interaction?",{"text":84,"@type":76},"Automatic formal verification of generated proofs enables reproducible quantitative evaluation (e.g., on ProofNet). An interactive terminal mode allows a human operator to monitor and steer the proof search process.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]