Go to ACL ARR 2026 January homepagePhysProver: Advancing Automatic Theorem Proving for Physics
Keywords: Formal Theorem Proving, Lean4, Physics Theorem Proving
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. To train our model, we leverage an open-source state-of-the-art mathematical theorem prover and apply Reinforcement Learning with Verifiable Rewards (RLVR) to train **PhysProver**. Comprehensive experiments demonstrate that, using only 5,000 training samples, **PhysProver** achieves a consistent **2.4%** improvement across multiple sub-domains, including difficult Quantum Field Theory problems. Furthermore, after formal physics training, we observed **1%** gains on the MiniF2F-Test benchmark, which indicates Physics domain training can, on the other hand, enhance formal math capability. The results highlight the efficiency and efficacy of our approach. To foster further research, we will release both our dataset and model to the community.
Paper Type: Long
Research Area: NLP Applications
Research Area Keywords: mathematical NLP, logical reasoning, reasoning
Contribution Types: NLP engineering experiment, Data resources
Languages Studied: English, Lean4
Submission Number: 9274
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