InternLM-Step-Prover is a 7B language model trained on Lean-Github and multiple sythesis datasets. InternLM-Step-Prover achieves state-of-the-art performances on MiniF2F, ProofNet, and Putnam math benchmarks, showing its formal math proving ability in multiple domains.

Dialogue Example

### Input Example
DECL MyNat.mul_pow
GOAL a b n : N
⊢ (a * b) ^ n = a ^ n * b ^ n
### Output Example
PROOFSTEP induction n with t Ht

Performance

MiniF2F

Method	Model size	Pass	miniF2F-valid	miniF2F-test
Whole-Proof Generation Methods
GPT-4-turbo 0409	-	64	25.4%	23.0%
DeepSeekMath-Base	7B	128	25.4%	27.5%
DeepSeek-Prover	7B	1	-	30.0%
		64	-	46.3%
		128	-	46.3%
		8192	-	48.8%
		65536	-	50.0%
		cumulative	60.2%	52.0%
TheoremLlama	-	cumulative	36.5%	33.6%
Tree Search Methods
COPRA (GPT-3.5)	-	1	-	9.0%
COPRA (GPT-4)	-	1	-	26.6%
DSP(Isabelle)	540B	100	42.6%	38.9%
Proof Artifact Co-Training	837M	1	23.9%	24.6%
		8	29.3%	29.2%
ReProver	229M	1	-	25.0%
Llemma	7B	1	26.2%	26.2%
Llemma	34B	1	27.9%	25.8%
Curriculum Learning	837M	1	33.6%	29.6%
		8	41.2%	34.5%
		64	47.3%	36.6%
Hypertree Proof Search	600M	cumulative	58.6%	-
		64	-	41.0%
Lean-STaR	7B	64	-	46.3%
InternLM2-Math	7B	1	29.9%	30.3%
InternLM2-Math-Plus	7B	1	-	43.4%
InternLM2-Step-Prover	7B	1	59.8%	48.8%
InternLM2-Step-Prover	7B	64	63.9%	54.5%

Proofnet & Putnam

Method	Model size	Pass	result
ProofNet benchmark
ReProver	229M	1	13.8%
InternLM2-Step-Prover	7B	1	18.1%
Putnam benchmark
GPT-4	-	10	1/640
COPRA (GPT-4)	-	10	1/640
DSP(Isabelle)	540B	10	4/640
ReProver	229M	1	0/640
InternLM2-Step-Prover	7B	1	5/640

Citation and Tech Report

@misc{wu2024leangithubcompilinggithublean,
      title={LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover}, 
      author={Zijian Wu and Jiayu Wang and Dahua Lin and Kai Chen},
      year={2024},
      eprint={2407.17227},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2407.17227}, 
}