Introduction
We introduce BFS-Prover-V2, the state-of-the-art open-source step-level theorem proving system for Lean4, designed to address the dual challenges of scaling both training and inference in neural theorem proving. BFS-Prover-V2 introduces novel solutions to overcome these limitations through:
-
Training-time scaling: A novel multi-stage expert iteration framework with adaptive tactic-level data filtering and periodic retraining to surmount the performance plateaus that typically curtail long-term post training
-
Inference-time scaling: A planner-enhanced multi-agent tree search system for hierarchical reasoning that scales performance at inference time
BFS-Prover-V2 achieves 95.08% and 41.4% on the miniF2F and ProofNet test sets respectively, setting a new state-of-the-art for step-level provers.
This repo contains the BFS-Prover-V2-7B model, with the following features:
- Base Model: Qwen2.5-Math-7B
- Training Approach: Multi-stage expert iteration with best-first tree search
- Training Data Sources:
- Mathlib (via LeanDojo)
- Lean-Github repositories
- Autoformalized NuminaMath datasets
- Goedel-Pset
Benchmark Performance
| Model | miniF2F-test | miniF2F-valid | ProofNet-test |
|---|---|---|---|
| 👉 BFS-Prover-V2-7B | 82.4% | - | - |
| BFS-Prover-V2-32B | 86.1% | 85.5% | 41.4% |
| BFS-Prover-V2-32B w/ Planner | 95.08% | 95.5% | - |
Usage
- The model expects input in the format
"{state}:::"where {state} is a Lean4 tactic 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.
# Example code for loading and using the tactic generator model
from transformers import AutoModelForCausalLM, AutoTokenizer
model = AutoModelForCausalLM.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
tokenizer = AutoTokenizer.from_pretrained("ByteDance-Seed/BFS-Prover-V2-7B")
# 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
@article{xin2025scaling,
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
This project is licensed under the Apache License 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)