---
license: apache-2.0
base_model:
- Qwen/Qwen2.5-Math-7B
pipeline_tag: text-generation
tags:
- lean4
- step-prover
---

<div align="center">
  <h1 style="font-size: 2.0em;">🚀 BFS-Prover-V2: Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers</h1>
  <div style="display: flex; justify-content: center; gap: 8px; flex-wrap: wrap;">
    <a href="https://arxiv.org/abs/2509.06493"><img src="https://img.shields.io/badge/arXiv-2509.06493-b31b1b.svg" alt="arXiv"></a>
    <a href="https://choosealicense.com/licenses/apache-2.0/"><img src="https://img.shields.io/badge/License-Apache%202.0-blue.svg" alt="License: Apache 2.0"></a>
    <a href="https://github.com/leanprover-community/mathlib4"><img src="https://img.shields.io/badge/Lean-4-orange" alt="Lean 4"></a>
  </div>
  <h2>State-of-the-art tactic generation model in Lean4</h2>
</div>
This repository contains the latest tactic generator model checkpoint from BFS-Prover-V2, a state-of-the-art step-level theorem proving system in Lean4. While the full BFS-Prover-V2 system integrates multiple components for scalable theorem proving, we are releasing the core tactic generation model here. Given a proof state in Lean4, the model generates a tactic that transforms the current proof state into a new state, progressively working towards completing the proof.

**📄 Paper: [Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers](https://arxiv.org/abs/2509.06493)**


## ✨ Model Details

- Base Model: Qwen2.5-32B
- Training Approach: Multi-stage expert iteration with best-first tree search
- Training Data Sources:
  - Mathlib (via LeanDojo)
  - Lean-Github repositories
  - Autoformalized NuminaMath datasets

## 📈 Performance
BFS-Prover-V2-32B achieves 95.08% on the miniF2F test, when integrated with the planner-based multi-agent tree search system, which significantly outperforms all previous step-provers.
Additionally, the model demonstrates strong generalization to undergraduate-level mathematics, independently attaining 41.4% on the ProofNet test without a planner.

## ⚙️ Usage
- The model expects Lean4 tactic states in the format `"{state}:::"`
- `:::` serves as a special indicator to signal the model to generate a tactic for the given state. 
- The model will echo back the input state followed by the generated tactic.


```python
# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-32B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-32B")

# imo_1964_p2 from miniF2F
state = """a b c : ℝ

    h₀ : 0 < a ∧ 0 < b ∧ 0 < c

    h₁ : c < a + b

    h₂ : b < a + c

    h₃ : a < b + c

    ⊢ a ^ 2 * (b + c - a) + b ^ 2 * (c + a - b) + c ^ 2 * (a + b - c) ≤ 3 * a * b * c"""

# Tactic generation
sep = ":::"
prompt = state + sep
inputs = tokenizer(prompt, return_tensors="pt")
outputs = model.generate(**inputs)
tactic = tokenizer.decode(outputs[0], skip_special_tokens=True).split(sep)[1]
print(tactic)

# Generated tactic: "nlinarith [sq_nonneg (a - b), sq_nonneg (c - a), sq_nonneg (b - c)]"
```

## 📚 Citation

If you use this model in your research, please cite our paper:

```bibtex
@article{xin2025bfsproverv2,
  title={Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers},
  author={Xin, Ran and Zheng, Zeyu and Nie, Yanchen and Yuan, Kun and Xiao, Xia},
  journal={arXiv preprint arXiv:2509.06493},
  year={2025}
}
```

## 📄 License

https://choosealicense.com/licenses/apache-2.0/

## 📧 Contact

For questions and feedback about the tactic generator model, please contact:
- Ran Xin (ran.xin@bytedance.com)
- Zeyu Zheng (zeyuzhen@andrew.cmu.edu)