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arXiv · 2510.26094

Lean4Physics: Comprehensive Reasoning Framework for College-level Physics in Lean4

Yuxin Li·Minghao Liu·Ruida Wang·Wenzhao Ji·Zhitao He·Rui Pan·Junming Huang·Tong Zhang·Yi R. Fung
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Abstract

We present **Lean4PHYS**, a comprehensive reasoning framework for college-level physics problems in Lean4. **Lean4PHYS** includes *LeanPhysBench*, a college-level benchmark for formal physics reasoning in Lean4, which contains 200 hand-crafted and peer-reviewed statements derived from university textbooks and physics competition problems. To establish a solid foundation for formal reasoning in physics, we also introduce *PhysLib*, a community-driven repository containing fundamental unit systems and theorems essential for formal physics reasoning. Based on the benchmark and Lean4 repository we composed in **Lean4PHYS**, we report baseline results using major expert Math Lean4 provers and state-of-the-art closed-source models, with the best performance of DeepSeek-Prover-V2-7B achieving only 16% and Claude-Sonnet-4 achieving 35%. We also conduct a detailed analysis showing that our *PhysLib* can achieve an average improvement of 11.75% in model performance. This demonstrates the challenging nature of our *LeanPhysBench* and the effectiveness of *PhysLib*. To the best of our knowledge, this is the first study to provide a physics benchmark in Lean4.

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Yuxin Li, Minghao Liu, Ruida Wang, Wenzhao Ji, Zhitao He, Rui Pan, Junming Huang, Tong Zhang, Yi R. Fung. 2025-10-30. Lean4Physics: Comprehensive Reasoning Framework for College-level Physics in Lean4. https://arxiv.org/abs/2510.26094

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