Fang Pu

Chendong Song, Zihan Wang, Frederick Pu et al.

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

Yuming Feng, Frederick Pu, One An et al.

Auto-formalization is critical for scalable formal verification, but existing progress largely focuses on isolated statements, while theory-scale auto-formalization, which coherently translates hundreds of interdependent definitions, lemmas, and theorems, remains open due to challenges in consistency, faithfulness, scalability, and correctness. In this paper, we introduce LCS-Bench, a stand-alone, theory-scale benchmark based on Logics for Computer Science. LCS-Bench is built through a novel semi-automated agentic pipeline that leverages concept graphs, formal signature planning, issue tracking, sorry-filling with counter-example search, complemented by faithfulness review from human experts. The resulting artifact covers 327 textbook items, over 4,076 Lean declarations, and more than 85K lines of Lean code. The dataset supports broad evaluation through a data engine that automatically derives five tracks of evaluation benchmarks, measuring different aspects of auto-formalization and theorem-proving capabilities. We also introduce a novel evaluation protocol featuring definitional equivalence checkers, enabling more fine-grained and faithful assessment. Through extensive evaluation on 14 models, we demonstrate that (1) LCS-Bench is of high quality, consistent, and faithful; (2) the benchmark is challenging, with state-of-the-art models achieving only 20.1% on auto-formalization tasks; and (3) our analysis reveals key findings regarding theory-scale auto-formalization and suggests promising directions for future work.