OpenProver: Agentic and Interactive Theorem Proving with Lean 4

2026-07-10

AI Summary

This work proposes a large language model–driven automated theorem proving system that enables human–machine collaborative formal verification. The system employs a Planner–Worker–Verifier multi-agent architecture to decompose proof tasks into parallel subgoals, integrates Lean 4 for automatic formal verification, and manages intermediate reasoning through a shared whiteboard and knowledge base. Innovatively combining agent-based automated proving with interactive user guidance within an open-source framework, it provides a terminal interface to support reproducible collaborative exploration. Experimental results on the ProofNet benchmark demonstrate that the approach significantly outperforms simple baselines. The system is fully open-sourced and designed for reproducible evaluation.

Abstract

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 Planner-Worker-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. OpenProver 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. To 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 https://github.com/kripner/OpenProver.

Problem

• automated theorem proving
• Lean 4
• large language models
• interactive proof
• formal verification

Innovation

• agentic theorem proving
• Lean 4 integration
• Planner-Worker-Verifier architecture
• interactive proof search
• formal verification