purewhite42/putnambench_solving

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:

@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}
}