| --- |
| license: apache-2.0 |
| task_categories: |
| - text-generation |
| pretty_name: Formal Problem-Solving Benchmarks |
| size_categories: |
| - 1K<n<10K |
| --- |
| |
| # Dataset Card for Formal Problem-Solving Benchmarks |
|
|
| This dataset is part of the official implementation of _Beyond Theorem Proving: Formulation, Framework and Benchmark for Formal Problem-Solving_, accepted as an **ICML 2026 Spotlight** paper. |
|
|
| Links: |
|
|
| - Paper: https://openreview.net/forum?id=hgMZraPlSv |
| - Project: https://github.com/Purewhite2019/formal_problem_solving_main |
| |
| ## Overview |
| |
| The benchmark supports three evaluation settings: |
| |
| - **Formal Problem-Solving (FPS)**: Given a formal problem, generate a formal solution. The formal solution should solve all goals and provide a direct answer. |
| - **Deductive Formal Problem-Solving (D-FPS)**: Given a formal problem, generate a forward solution and, optionally, a backward proof. The forward solution should derive a direct answer and prove its completeness; the backward proof should prove the answer's soundness. |
| - **Formal Theorem Proving (FTP)**: Given a formal problem and its ground-truth answer, generate a formal proof of the ground-truth answer's correctness. |
| |
| ## Benchmarks |
| |
| | JSONL File | Benchmark | Size | |
| | --- | --- | ---: | |
| | `formal_math500.jsonl` | FormalMath500 | 387 | |
| | `minif2f_solving.jsonl` | MiniF2F-Solving | 375 | |
| | `putnam_solving.jsonl` | PutnamBench-Solving | 324 | |
|
|
| **FormalMath500** is a formalized subset of MATH500 with 387 samples covering Algebra, Intermediate Algebra, Number Theory, Prealgebra, and Precalculus. |
|
|
| **MiniF2F-Solving** refactors MiniF2F propositions into problem-solving instances with detached direct answers. It contains 375 samples from AIME, MATH-Algebra, AMC, IMO, and MATH-Number Theory. |
|
|
| **PutnamBench-Solving** refactors a subset of PutnamBench into 324 undergraduate-level problem-solving instances across algebra, analysis, number theory, geometry, linear algebra, combinatorics, abstract algebra, probability, and set theory. |
|
|
| ## Dataset Structure |
|
|
| Each JSONL record contains the following core fields: |
|
|
| - `informal_problem`: The natural-language problem statement, including LaTeX when applicable. |
| - `informal_answer`: The natural-language ground-truth answer, including LaTeX when applicable. |
| - `header`: Lean openings/options used before the formal problem. |
| - `independent_variables`: Problem-level independent variables. |
| - `hypotheses`: Assumptions rendered in the Lean `s.t.` / `iff` block before the conclusion. |
| - `conclusions`: Lean propositions that the queried answer must satisfy. |
| - `formal_answer`: The formal ground-truth answer predicate in Lean 4. |
| - `formal_answer_type`: The Lean type of the direct answer. |
| - `metainfo`: Benchmark name and sample index. |
|
|
| The released JSONL files intentionally omit empty draft fields and Lean-only export override fields. The structured JSONL files can be exported to the Lean benchmark project with `common/export_fps_benchmark.py` in the code repository. |
|
|
| ## License |
|
|
| This dataset is released under the Apache 2.0 license. |
|
|
| ## Citation |
|
|
| If you find this dataset useful, please cite: |
|
|
| ```bibtex |
| @inproceedings{ |
| liu2026beyond, |
| title={Beyond Theorem Proving: Formulation, Framework and Benchmark for Formal Problem-Solving}, |
| author={Qi Liu and Xinhao Zheng and Renqiu Xia and Xingzhi Qi and Qinxiang Cao and Junchi Yan}, |
| booktitle={Forty-third International Conference on Machine Learning}, |
| year={2026}, |
| url={https://openreview.net/forum?id=hgMZraPlSv} |
| } |
| ``` |
|
|
