PhysProver: Advancing Automatic Theorem Proving for Physics

TL;DR

This paper introduces PhysProver, a novel system that enhances formal physics theorem proving using a dedicated dataset, reinforcement learning, and a strong open-source prover, achieving notable improvements in physics and math reasoning.

Contribution

It presents the first approach to formal physics theorem proving, including a new dataset, training pipeline, and reinforcement learning method, demonstrating improved performance and generalization.

Findings

PhysProver achieves 2.4% improvement in physics sub-domains.

It gains 1.3% on MiniF2F-Test, indicating cross-domain generalization.

The approach is efficient, using only ~5K training samples.

Abstract

The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide foundation models and sophisticated agentic systems pushing the boundaries of formal mathematical reasoning to approach the natural language capability of LLMs. However, little attention has been given to the formal physics reasoning, which also heavily relies on similar problem-solving and theorem-proving frameworks. To solve this problem, this paper presents, to the best of our knowledge, the first approach to enhance formal theorem proving in the physics domain. We compose a dedicated dataset PhysLeanData for the task. It is composed of theorems sampled from PhysLean and data generated by a conjecture-based formal data generation pipeline. In the training pipeline, we leverage DeepSeek-Prover-V2-7B, a strong open-source mathematical theorem prover, and apply Reinforcement Learning with Verifiable Rewards (RLVR) to train our model PhysProver. Comprehensive experiments demonstrate that, using only $\sim$5K training samples, PhysProver achieves an overall 2.4\% improvement in multiple sub-domains. Furthermore, after formal physics training, we observe 1.3\% gains on the MiniF2F-Test benchmark, which indicates non-trivial generalization beyond physics domains and enhancement for formal math capability as well. The results highlight the effectiveness and efficiency of our approach, which provides a paradigm for extending formal provers outside mathematical domains. To foster further research, we will release both our dataset and model to the community.