Prover Agent: An Agent-based Framework for Formal Mathematical Proofs

2025-06-24

AI Summary

To address the low proof success rate and high sample complexity of small language models (SLMs) in automated theorem proving, this paper proposes a multi-module agent framework that synergistically integrates an informal-reasoning large language model, a formal-proving SLM, and the Lean proof assistant. The framework employs closed-loop feedback to dynamically generate critical auxiliary lemmas, thereby guiding efficient proof-strategy search. Its key innovation lies in using an SLM as the core reasoning engine for lemma-driven proving, significantly reducing sampling requirements. Evaluated on the MiniF2F benchmark, the approach achieves an 86.1% proof success rate—the highest reported for SLM-based methods. Ablation studies and case analyses confirm that auxiliary lemma generation is the central mechanism driving both search efficiency and proof success.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and feedback from Lean while also generating auxiliary lemmas to assist in discovering the overall proof strategy. It achieves an 86.1% success rate on the MiniF2F benchmark, establishing a new state-of-the-art among methods using small language models (SLMs) with a much lower sample budget than previous approaches. We also present case studies illustrating how these generated lemmas contribute to solving challenging problems.

Problem

• Integrates LLMs with Lean for automated theorem proving
• Achieves high success rate on MiniF2F benchmark efficiently
• Generates auxiliary lemmas to aid proof strategy discovery

Innovation

• Integrates LLMs with Lean proof assistant
• Coordinates informal and formal reasoning models
• Generates auxiliary lemmas for proof strategy