Create README.md

README.md

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+---
+pipeline_tag: text-generation
+license: other
+language:
+- en
+tags:
+- math
+datasets:
+- internlm/Lean-Workbook
+- internlm/Lean-Github
+---
+
+# InternLM2.5-Step-Prover
+
+<div align="center">
+
+<img src="https://raw.githubusercontent.com/InternLM/InternLM/main/assets/logo.svg" width="200"/>
+  <div> </div>
+  <div align="center">
+    <b><font size="5">InternLM-Math</font></b>
+    <sup>
+      <a href="https://internlm.intern-ai.org.cn/">
+        <i><font size="4">HOT</font></i>
+      </a>
+    </sup>
+    <div> </div>
+  </div>
+
+A state-of-the-art LEAN4 step prover.
+
+[💻 Github](https://github.com/InternLM/InternLM-Math) [📊Dataset](https://huggingface.co/datasets/internlm/Lean-Github) [📖 Paper](https://arxiv.org/abs/2410.15700)
+</div>
+
+InternLM2.5-Step-Prover is a 7B language model which 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 template
+f"---\nNAME: {theorem.full_name}\n\n"
+f"---\nPROOF_BEFORE: {proof_before}\n\n"
+f"---\nSTATE_BEFORE: {state}\n\n"
+f"---\nTACTIC: "
+### Input example
+---
+NAME: square_sub_one_divisible_eight
+---
+PROOF_BEFORE: rw [h, pow_two]
+---
+STATE_BEFORE: m n : N
+h : n = 2 * m + 1
+⊢ 8 | (2 * m + 1) * (2 * m + 1) - 1
+---
+TACTIC:
+### Output example
+rw [← Nat.mod_add_div (2 * m + 1) 8]
+```
+If you want to use critic model, please refer critic's model page.
+
+# 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%* |
+| DeepSeek-Prover-1.5 | 7B | 32 | - | 63.5% |
+| 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% |
+| InternLM2.5-Step-Prover | 7B | 1 | 55.4% | 47.3% |
+| InternLM2.5-Step-Prover+Critic | 7B | 256 | **69.6%** | **65.9%** |
+
+
+## Proofnet & Putnam
+| Method | Model size | Pass | result |
+|--------|------------|------|--------|
+| **ProofNet benchmark** |
+| ReProver | 229M | 1 | 13.8% |
+| InternLM2-Step-Prover | 7B | 1 | 18.1% |
+| InternLM2.5-Step-Prover | 7B | 256 | **27.0%** |
+| **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 |
+| InternLM2.5-Step-Prover | 7B | 1 | **6/640** |
+
+
+# Citation and Tech Report
+```
+@misc{wu2024internlm25stepproveradvancingautomatedtheorem,
+      title={InternLM2.5-StepProver: Advancing Automated Theorem Proving via Expert Iteration on Large-Scale LEAN Problems}, 
+      author={Zijian Wu and Suozhi Huang and Zhejian Zhou and Huaiyuan Ying and Jiayu Wang and Dahua Lin and Kai Chen},
+      year={2024},
+      eprint={2410.15700},
+      archivePrefix={arXiv},
+      primaryClass={cs.AI},
+      url={https://arxiv.org/abs/2410.15700}, 
+}
+```