# A Combinatorial Identities Benchmark for Theorem Proving via Automated Theorem Generation

arXiv: https://arxiv.org/abs/2502.17840 · HTML: https://mlsanity.com/paper/2502.17840/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics](https://mlsanity.com/paper/2505.03171/) (2025)
- [FATE: A Formal Benchmark Series for Frontier Algebra of Multiple Difficulty Levels](https://mlsanity.com/paper/2511.02872/) (2025)
- [Autoformalization in the Era of Large Language Models: A Survey](https://mlsanity.com/paper/2505.23486/) (2025)
- [Automated Formal Proofs of Combinatorial Identities via Wilf-Zeilberger Guidance and LLMs](https://mlsanity.com/paper/2605.04472/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have significantly advanced formal theorem proving, yet the scarcity of high-quality training data constrains their capabilities in complex mathematical domains. Combinatorics, a cornerstone of mathematics, provides essential tools for analyzing discrete structures and solving optimization problems. However, its inherent complexity makes it particularly challenging for automated theorem proving (ATP) for combinatorial identities. To address this, we manually construct LeanComb, combinatorial identities benchmark in Lean, which is, to our knowledge, the first formalized theorem proving benchmark built for combinatorial identities. We develop an Automated Theorem Generator for Combinatorial Identities, ATG4CI, which combines candidate tactics suggested by a self-improving large language model with a Reinforcement Learning Tree Search approach for tactic prediction. By utilizing ATG4CI, we generate a LeanComb-Enhanced dataset comprising 260K combinatorial identities theorems, each with a complete formal proof in Lean, and experimental evaluations demonstrate that models trained on this dataset can generate more effective tactics, thereby improving success rates in automated theorem proving for combinatorial identities.