The official implementation of "Self-play LLM Theorem Provers with Iterative Conjecturing and Proving"

This is an official implementation of the Self-play Theorem Prover as described in the paper https://arxiv.org/abs/2502.00212. The code is based on levanter, DeepSeek-Prover-V1.5, and LeanDojo. Please cite the paper and star this repo if you find STP useful. Thank you!

@article{dong2025beyond,
  title={Beyond Limited Data: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving},
  author={Dong, Kefan and Ma, Tengyu},
  journal={arXiv preprint arXiv:2502.00212},
  year={2025}
}

News

• [2025/03] We scaled STP’s training compute by 2x, and achieved new SoTA for whole-proof generation methods on miniF2F, ProofNet, and LeanWorkbook!
• [2025/02] Code, data, and models of STP are released.

1. Evaluation Results

The table below compares the pass@3200 performance of STP (our model) and DeepSeek-Prover-V1.5 on miniF2F-test and ProofNet-test.

	miniF2F-test	ProofNet-test
DeepSeek-Prover-V1.5-SFT	53.3% ± 0.5%	21.0% ± 0.9%
DeepSeek-Prover-V1.5-RL	54.9% ± 0.7%	22.0% ± 0.5%
STP	65.0% ± 0.5%	23.9% ± 0.6%

2. Model and Dataset

Our final model can be downloaded here.

We also release the dataset here, which contains:

• Extracted examples from mathlib4,
• Generated correct proofs of statements in LeanWorkbook,
• Generated correct proofs of conjectures proposed by our model during self-play training.

Our final model is finetuned from DeepSeek-Prover-V1.5-SFT with this dataset for 1 epoch.

3. Setup Environment

Our experiments are mostly run on TPU VMs. You can find a quick overview of TPU VMs here, and please follow the instructions to setup Google Cloud.

3.1. Request a TPU VM

Pease first modify the environment variables in the last few lines of levanter/infra/helpers/setup-tpu-vm.sh to provide the path to your Google Cloud buckets, WandB access token, and Hugging Face access token.

Use the following commands to request an instance with 256 TPU-v4 cores (please replace STP-train and us-central2-b with your TPU name and zone):

cd levanter
eval $(ssh-agent -s) bash infra/spin-up-vm.sh STP-train -z us-central2-b -t v4-256

This will automatically install the dependencies specified in this setup file, such as Levanter, vLLM, Lean4, and mathlib4, and sync the environment variables to all TPU nodes.

3.2. Reproduce Test Results

Use the following commands to connect to the TPU VM, and then generate and test proofs on miniF2F-test and ProofNet-test.

gcloud compute tpus tpu-vm ssh STP-train --zone us-central2-b --worker=0
source ~/venv_vllm/bin/activate
cd ~/STP/RL
source .bash_alias.sh
bash run_generation_and_test.sh kfdong/STP_model_Lean_0320 $STORAGE/STP/benchmark_results
python summary.py --log_path $STORAGE/STP/benchmark_results/generated_proofs_tests.jsonl.gz --split miniF2F --max_iter 3200
python summary.py --log_path $STORAGE/STP/benchmark_results/generated_proofs_tests.jsonl.gz --split proofnet --max_iter 3200

3.3. Prepare Datasets

On the TPU VM, use the following commands to prepare SFT datasets:

cd ~/STP/RL
source ~/venv_vllm/bin/activate
source .bash_alias.sh
python prepare_datasets.py

This script will generate three .json files in your Google Cloud storage bucket ($STORAGE/data/SFT/), corresponding to the SFT dataset, mathlib4 eval examples, and mathlib4 training examples, respectively.

3.4. STP

The Self-play Theorem Prover (STP) involves three training stages:

Stage 1: Model initialization. Use the following commands to finetune the DeepSeek-Prover-V1.5-SFT model on the SFT dataset:

gcloud compute tpus tpu-vm ssh STP-train --zone us-central2-b --worker=0
cd ~/STP/RL
bash run_SFT.sh

A Hugging Face compatible model checkpoint will be saved at $STORAGE/SFT/<wandb run id>/step-114.

Stage 2: Self-play training. On the TPU VM node (worker=0), update the the model checkpoint path in the RL/run_RL_steps.sh script. Then, use the following command to run the self-play training. Adjust TOTAL_ROUNDS to change the number of iterations of self-play training:

bash run_RL_steps.sh

Stage 3: Final re-training. After the self-play training, use the following command to

• create a dataset that contains the correct proofs to the statements in the training dataset and the correct proofs to the generated conjectures,
• re-train a model checkpoint.

bash run_RL_train.sh

In our experiments, we alternate between Stage 2 and Stage 3 to stabilize the training. That is, we periodically restart self-play training (Stage 2) with the re-trained model checkpoint (Stage 3).

3.5. GPU Support

This codebase does not directly support GPUs. However, both the training and inference frameworks (Levanter and vLLM) support GPUs. Therefore, the required changes should be somewhat manageable. Below is a (possibly incomplete) list of platform-specific code changes needed:

1. We use ray to manage the TPU and CPU resources on multiple nodes. Please modify the function init_ray_cluster in RL/utils/model_utils.py to start the ray cluster.
2. Please modify the execute_on_all_workers function in RL/utils/gcloud_utils.py to execute bash commands on all nodes. This function is used to (a) copy model checkpoints to local disk, and (b) cleanup the CPU resources used by Lean verifier.

License

• Code: This project is licensed under the MIT License. However, the code in the levanter/ directory is licensed under the Apache License 2.0.

• Model: The model is derived from DeepSeek and is licensed under the DeepSeek License Agreement. The use of the model and its derivatives must comply with the use-based restrictions outlined in the DeepSeek License Agreement.