---
license: mit
configs:
- config_name: default
  data_files:
  - split: test
    path: data/test-*
  - split: test_with_solution
    path: data/test_with_solution-*
dataset_info:
  features:
  - name: theorem_name
    dtype: string
  - name: natural_language
    dtype: string
  - name: answer
    sequence: string
  - name: source
    dtype: string
  - name: tag
    dtype: string
  - name: formal_statement
    dtype: string
  splits:
  - name: test
    num_bytes: 104379
    num_examples: 100
  - name: test_with_solution
    num_bytes: 102493
    num_examples: 100
  download_size: 110307
  dataset_size: 206872
size_categories:
- n<1K
---

# CombiBench

<p align="center">
    <a href="https://github.com/MoonshotAI/CombiBench/"><img src="https://img.shields.io/badge/🚀-github-black"</a>
</p>

##

CombiBench is the first benchmark focused on combinatorial problems, based on the formal language Lean 4. CombiBench is a manually produced benchmark, including 100 combinatorial mathematics problems of varying difficulty and knowledge levels. It aims to provide a benchmark for evaluating the combinatorial mathematics capabilities of automated theorem proving systems to advance the field. For problems that require providing a solution first and then proving its correctness, we have referred to the style of [PutnamBench](https://github.com/trishullab/PutnamBench).

We are hosting a [**leaderboard**](https://moonshotai.github.io/CombiBench/leaderboard.html) and will readily receive evaluation results which are accompanied by a preprint or publication. Please reach out privately at `liujunqi@amss.ac.cn` with any requests for additions to the leaderboard. 

## Statistics 

We collected all combinatorics problems from the official IMO problems since 2000, except for one problem that relies on a figure. And We selected problems through random sampling from 14 chapters in the book, choosing 3 problems from each chapter, ensuring that the 42 problems are evenly distributed across all 14 chapters. We randomly selected 10 simple combinatorics problems at the middle school level from a mathematics problem collection website [hackmath](https://www.hackmath.net/). Then, we randomly collected 12 problems from other mathematics competitions.

| Source           | Count          | 
| ---------------- | -------------- | 
| Hackmath         | 10             |
| Brualdi's book   | 42             |
| IMO              | 36             |
| APMO             | 2              |
| Balticway        | 1              |
| EGMO             | 1              |
| IMO-Shortlist    | 4              |
| IZHO             | 2              |
| BXMO             | 1              |
| USAMO            | 1              |


Note : The complete proofs of Problem 3 and Problem 5 from IMO 2024 have already been formalized in [mathlib4/Archive/Imo2024Q3](https://leanprover-community.github.io/mathlib4_docs/Archive/Imo/Imo2024Q3.html) and [mathlib4/Archive/Imo2024Q5](https://leanprover-community.github.io/mathlib4_docs/Archive/Imo/Imo2024Q5.html). Therefore, we directly refer to the statements of these problems, along with the necessary definitions used in the statements. We are very grateful to Joseph Myers, the author of these two problems. We also appreciate his suggestions on the formalization of our problems.

## Evaluation

Our evaluation code is released at [https://github.com/MoonshotAI/CombiBench](https://github.com/MoonshotAI/CombiBench)

## 🙌 Contributing

Contributions are welcome! If anyone notices any mistakes, please raise an issue on the repository and we will address it.

## 📝 License

This project is licensed under the MIT License. See the [LICENSE](./LICENSE) file for full details.