On Reasoning-Centric LLM-based Automated Theorem Proving

2026-04-21

AI Summary

This work addresses the limitations of existing large language model (LLM)-driven automated theorem proving systems, which often lack high-level strategic planning and self-correction capabilities, relying excessively on locally generated tactics. To overcome these shortcomings, the authors propose ReCent-Prover, a reasoning-centric proof agent for Coq that incorporates a reflection-based verification mechanism to synthesize failure summaries and filter out ineffective tactics. Furthermore, it innovatively integrates LLM-generated proof plans to guide premise retrieval, aligning evidence selection more closely with the overarching proof objective. Evaluated on the CoqStoq benchmark under identical model invocation budgets, ReCent-Prover achieves a 22.58% improvement in theorem-proving success rate over the current state-of-the-art approach.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they inadequately leverage reasoning capabilities of modern LLMs in high-level planning and self-critique. We argue that proof agents should not merely generate tactics but also reason strategically about proof plans and critically evaluate their own proposals. This paper introduces ReCent-Prover, a reasoning-centric LLM-based proof agent for Rocq that addresses two critical limitations in current systems. First, we present validation with reflection, enabling LLMs to scrutinize their generated tactics and synthesize failure summaries when reflection identifies potential errors, filtering out potentially misapplied tactics earlier. Second, we propose retrieval with planning, which conditions retrieval on LLM-generated proof plans rather than subgoal similarity, retrieving lemmas and proofs that align with the anticipated proof strategy. Both techniques increase the number of invocations of LLMs. However, when evaluated on the CoqStoq benchmark, even under the same budget of LLM invocations, ReCent-Prover achieves a 22.58% relative improvement in the number of proved theorems over the previous state-of-the-art, demonstrating that our reasoning-centric design significantly enhances automated theorem proving capabilities.

Problem

• automated theorem proving
• large language models
• reasoning
• proof planning
• self-critique

Innovation

• reasoning-centric
• validation with reflection
• retrieval with planning
• automated theorem proving
• large language models