xiaoxuezhu/PSR_Selected_Isabelle_Proof_Dataset

PSR-Selected Isabelle Proof Dataset

This dataset contains a compact, high-quality collection of Isabelle/HOL theorem-proof pairs for neural theorem proving. It is constructed from a larger raw corpus of approximately 200,000 Isabelle/HOL and Archive of Formal Proofs (AFP) examples, using the PSR data selection criterion proposed in our paper.

PSR selects training examples from three complementary perspectives:

• Proof Complexity: keeps proofs with useful, moderate reasoning structure while filtering overly trivial or excessively long examples.
• Semantic Coverage: improves coverage across different theorem domains and problem types.
• Reasoning Diversity: encourages diverse Isabelle tactics and proof strategies.

The released dataset contains 4,271 theorem-proof pairs and is intended for supervised fine-tuning of language models for Isabelle proof generation.

Dataset Contents

Each example consists of an Isabelle theorem statement and its corresponding formal proof. A typical sample contains:

{
  "instruct":"...",
  "input": "...",
  "output": "..."
}

The dataset can be used to train models that generate Isabelle proofs from formal theorem statements.

Intended Use

This dataset is designed for research on:

• neural theorem proving;
• Isabelle/HOL proof generation;
• formal mathematical reasoning;
• data-centric training for theorem-proving language models;
• supervised fine-tuning of proof-generation models.

In our experiments, fine-tuning DeepSeek-Math-7B-Base with LoRA on this dataset achieved strong performance on the Isabelle portion of miniF2F, despite using far fewer examples than the full raw corpus.

Source and Construction

The dataset is selected from a raw Isabelle proof corpus collected from Isabelle/HOL and AFP. We apply a PSR-guided pipeline that combines:

1. complexity-based filtering;
2. TF-IDF + K-Means semantic clustering;
3. entropy-based reasoning diversity estimation;
4. constrained sampling to reduce template-like one-shot proofs.

The final subset is intended to preserve useful proof structure, semantic breadth, and tactic-level diversity.

Limitations

This dataset focuses on Isabelle/HOL theorem proving. It may not directly transfer to other proof assistants such as Lean or Coq without additional conversion or adaptation. Users should also verify compatibility with their Isabelle version and downstream proof-checking environment.

Citation

If you use this dataset, please cite:

@inproceedings{zhu2026enhancing,
  title={Enhancing Neural Theorem Proving via High-Quality Data Selection and Verifier Feedback},
  author={Zhu, Xiaoxue and Hu, Jilin and Zhang, Fuyuan and Zhang, Jianyu and Zhao, Yongwang},
  booktitle={Proceedings of the 43rd International Conference on Machine Learning},
  year={2026}
}