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First page of MATP-BENCH: Can MLLM Be a Good Automated Theorem Prover for Multimodal Problems?

MATP-BENCH: Can MLLM Be a Good Automated Theorem Prover for Multimodal Problems?

Zhitao He, Zongwei Lyu, Dazhong Chen, Dadi Guo, Yi R. Fung

cs.CL Jun 6, 2025 · v1
Introduces MATP-BENCH whose 1056 multimodal theorems are formalized in Lean 4 (alongside Coq and Isabelle) to evaluate MLLM provers.
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in solving a wide range of mathematical problems. However, the potential of MLLMs as Automated Theorem Provers (ATPs), specifically in the multimodal domain, remains underexplored. In this paper, we introduce the Multimodal Automated Theorem Proving benchmark (MATP-BENCH), a new Multimodal, Multi-level, and Multi-language benchmark designed to evaluate MLLMs in this role as multimodal automated theorem provers. MATP-BENCH consists of 1056 multimodal theorems drawn from high school, university, and competition-level mathematics. All these multimodal problems are accompanied by formalizations in Lean 4, Coq and Isabelle, thus making the benchmark compatible with a wide range of theorem-proving frameworks. MATP-BENCH requires models to integrate sophisticated visual understanding with mastery of a broad spectrum of mathematical knowledge and rigorous symbolic reasoning to generate formal proofs. We use MATP-BENCH to evaluate a variety of advanced multimodal language models. Existing methods can only solve a limited number of the MATP-BENCH problems, indicating that this benchmark poses an open challenge for research on automated theorem proving.

Multimodal theorems (e.g., geometry problems with diagrams) require visual reasoning for proof, but the potential of multimodal LLMs as automated theorem provers in formal languages has not been evaluated.

The authors introduce MATP-BENCH, a benchmark of 1056 multimodal theorems from high school, university, and competition-level mathematics. All problems include formalizations in Lean 4, Coq, and Isabelle. The benchmark requires models to integrate visual understanding of diagrams with formal proof generation, testing both theorem proving and theorem formalization capabilities.

Existing methods solve only a limited portion of MATP-BENCH problems. On Lean 4 theorem proving (pass@10), the best model achieves 9.32% on high school, 2.99% on university, and 0.86% on competition problems. Theorem formalization rates are higher (up to 61.28% at university level) but still leave substantial room for improvement.

MethodHigh SchoolUniversityCompetition
OpenAI-o17.20%3.85%0.86%
Claude-3.7-Sonnet8.47%2.14%0.00%
Gemini-2.0-flash-thinking9.32%2.99%0.86%
GPT-4.12.12%1.50%0.00%
Theorem proving performance on MATP-BENCH (Lean 4, pass@10)