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Model: m-a-p/OProver-8B-Round2
Source: Original Platform

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README.md

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+---
+license: apache-2.0
+language:
+  - en
+library_name: transformers
+pipeline_tag: text-generation
+tags:
+  - lean4
+  - theorem-proving
+  - formal-mathematics
+  - agentic
+  - retrieval-augmented
+datasets:
+  - m-a-p/OProofs
+---
+
+# OProver
+
+> A unified framework for **agentic formal theorem proving** in Lean 4.
+
+- 📄 Paper: [OProver: A Unified Framework for Agentic Formal Theorem Proving](https://huggingface.co/papers/2605.17283) ([arXiv](https://arxiv.org/abs/2605.17283))
+- 📚 Collection: [m-a-p/OProver](https://huggingface.co/collections/m-a-p/oprover)
+- 📦 Dataset: [m-a-p/OProofs](https://huggingface.co/datasets/m-a-p/OProofs)
+
+OProver treats theorem proving as a multi-round refinement loop. Given a target
+theorem, the prover retrieves top-k compiler-verified proofs from a memory of
+prior proofs, generates a proof attempt, runs the Lean 4 compiler, and—on
+failure—revises the attempt using the compiler feedback in the next round.
+The same retrieval and feedback signals are baked into training, so the
+training-time interface matches the proving-time interaction.
+
+## Highlights
+
+- **State-of-the-art among open-weight whole-proof provers.** OProver-32B
+  attains the best Pass@32 on MiniF2F (93.3), ProverBench (58.2), and
+  PutnamBench (11.3), and the second-best on MathOlympiad (22.8) and
+  ProofNet (33.2). Even OProver-8B beats Goedel-Prover-V2-32B on all five
+  benchmarks despite having 4× fewer parameters.
+- **Agentic proving is in the policy, not bolted on.** Retrieval, multi-turn
+  compiler feedback, and iterative repair are all part of the trained policy.
+  Ablations show feedback is the dominant driver: removing it costs OProver-32B
+  4.9–7.4 Pass@32 points across benchmarks; removing retrieval on top adds
+  0.5–1.7 more.
+- **Co-evolving prover and corpus.** Each post-training iteration runs agentic
+  rollouts; verified proofs are added to OProofs and re-indexed for retrieval,
+  repair trajectories become SFT data, and unresolved hard cases provide RL
+  signal. MiniF2F-Test Pass@32 grows monotonically: OProver-8B 79.5 → 86.2 →
+  87.0 → 91.8 across rounds; OProver-32B 84.7 → 88.1 → 93.3.
+
+## What's in this release
+
+The OProver collection ([m-a-p/OProver](https://huggingface.co/collections/m-a-p/oprover)) bundles the paper,
+the corpus, and seven model checkpoints covering both training stages and
+both model sizes:
+
+| Repo | Stage | Size | Note |
+|---|---|---|---|
+| [OProver-8B-Base](https://huggingface.co/m-a-p/OProver-8B-Base) | Continued pretraining only | 8B | Domain-adapted base; before SFT/RL |
+| [OProver-32B-Base](https://huggingface.co/m-a-p/OProver-32B-Base) | Continued pretraining only | 32B | Domain-adapted base; before SFT/RL |
+| [OProver-8B-Round1](https://huggingface.co/m-a-p/OProver-8B-Round1) | Post-training Round 1 | 8B | After first SFT+RL iteration |
+| [OProver-8B-Round2](https://huggingface.co/m-a-p/OProver-8B-Round2) | Post-training Round 2 | 8B | After second SFT+RL iteration |
+| [OProver-32B-Round1](https://huggingface.co/m-a-p/OProver-32B-Round1) | Post-training Round 1 | 32B | After first SFT+RL iteration |
+| **[OProver-8B](https://huggingface.co/m-a-p/OProver-8B)** | Final | 8B | The 8B prover reported in the paper (Round 3) |
+| **[OProver-32B](https://huggingface.co/m-a-p/OProver-32B)** | Final | 32B | The 32B prover reported in the paper (Round 2) |
+| [OProofs](https://huggingface.co/datasets/m-a-p/OProofs) | Dataset | 6.86M proofs | Lean 4 corpus used for CPT, SFT, and the retrieval memory |
+
+Use **OProver-8B** or **OProver-32B** for proving. The Base / Round-N
+checkpoints are released for reproducibility and ablation studies.
+
+## Dataset: OProofs
+
+OProofs is a large-scale Lean 4 corpus that doubles as the retrieval memory at
+proving time. It is built from three sources: public Lean resources
+(NuminaMath-LEAN, Lean-Workbook, Leanabell-FormalStmt, Goedel-Pset, …),
+large-scale autoformalization + agentic proof synthesis from informal math
+mined on Common Crawl and GitHub, and traces from OProver's own agentic
+proving runs.
+
+![OProofs Lean 4 corpus statistics](./assets/oproofs.png)
+
+## Training
+
+Two stages, both anchored on OProofs.
+
+**1. Continued pretraining (one-time).** A 65B-token mixture of formal
+Lean (≈30%, from OProofs), code (≈20%, OpenCoder), mathematics (≈40%,
+Nemotron-Math-4-Plus), and long-CoT (≈10%, ProLong-64K). AdamW, peak LR
+5e-5, cosine with 3% warmup, batch 512, sequence length 8192. Output:
+`OProver-{8B,32B}-Base`.
+
+**2. Iterative post-training.** Each round runs:
+
+1. Agentic proving with the current prover on a theorem pool, producing
+   multi-round rollouts conditioned on retrieved proofs and Lean feedback.
+2. **SFT** on round-level repair examples `(s, R, p_{t-1}, f_{t-1}) → p_t`,
+   with cross-entropy loss only on the new attempt.
+3. **GSPO RL** on hard cases (groups with non-trivial pass-rate). Per-round
+   reward `r = 0.8 + 0.2·1[format ok]` if Lean-verified, else 0; advantages
+   are pooled across the n×R rounds for the same theorem.
+4. Newly verified proofs and repair trajectories are folded back into OProofs
+   and re-indexed into the retrieval memory for the next round.
+
+## Results
+
+Pass@32 (n=64) across five Lean 4 benchmarks. **Bold** is best, _underlined_
+is second-best.
+
+![Main results: Pass@32 across five Lean 4 benchmarks](./assets/main_results.png)
+
+OProver-32B reaches three best and two second-best across five benchmarks —
+the most top placements of any model in the comparison, despite being a
+32B dense model versus a 560B MoE or a 671B dense competitor.
+
+## Loading
+
+```python
+from transformers import AutoModelForCausalLM, AutoTokenizer
+
+# Pick any of: OProver-8B, OProver-32B, *-Base, *-Round1, *-Round2
+name = "m-a-p/OProver-8B"
+tok = AutoTokenizer.from_pretrained(name)
+model = AutoModelForCausalLM.from_pretrained(name, torch_dtype="bfloat16", device_map="auto")
+```
+
+```python
+from datasets import load_dataset
+ds = load_dataset("m-a-p/OProofs", split="train")
+```
+
+OProver is trained against a multi-round agentic interface: at each round the
+input includes the target Lean statement, top-k retrieved verified proofs, the
+prior proof attempt, and the Lean compiler feedback. See the paper §2.1 for
+the prompt template, and Appendix B for serialization details.
+
+## Citation
+
+```bibtex
+@article{ma2026oprover,
+  title   = {OProver: A Unified Framework for Agentic Formal Theorem Proving},
+  author  = {David Ma and Kaijing Ma and Shawn Guo and Yunfeng Shi and Enduo Zhao and Jiajun Shi and Zhaoxiang Zhang and Gavin Cheung and Jiaheng Liu and Zili Wang},
+  journal = {arXiv preprint arXiv:2605.17283},
+  year    = {2026}
+}
+```

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+      "special": false
+    },
+    "151667": {
+      "content": "<think>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151668": {
+      "content": "</think>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": false
+    },
+    "151669": {
+      "content": "<|EOT|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151670": {
+      "content": "<|BOT|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151671": {
+      "content": "<|CALL_START|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151672": {
+      "content": "<|CALL_END|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151673": {
+      "content": "<|THINK_START|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151674": {
+      "content": "<|THINK_END|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151675": {
+      "content": "<|IMG_START|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151676": {
+      "content": "<|IMG_END|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151677": {
+      "content": "<|META_START|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151678": {
+      "content": "<|META_END|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151679": {
+      "content": "<im_patch>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151680": {
+      "content": "<im_start>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151681": {
+      "content": "<im_end>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151682": {
+      "content": "<dream>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151683": {
+      "content": "<dream_start>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151684": {
+      "content": "<dream_end>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151685": {
+      "content": "<|MASK_1e69f|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151686": {
+      "content": "<|UNMASK_1e69f|>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151687": {
+      "content": "<video_start>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151688": {
+      "content": "<video_end>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151689": {
+      "content": "<patch_start>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151690": {
+      "content": "<patch_end>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151691": {
+      "content": "<patch_newline>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151692": {
+      "content": "<｜begin▁of▁sentence｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151693": {
+      "content": "<｜begin▁of▁mask｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151694": {
+      "content": "<｜end▁of▁mask｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151695": {
+      "content": "<｜fim▁begin｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151696": {
+      "content": "<｜fim▁hole｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    },
+    "151697": {
+      "content": "<｜end▁of▁sentence｜>",
+      "lstrip": false,
+      "normalized": false,
+      "rstrip": false,
+      "single_word": false,
+      "special": true
+    }
+  },
+  "additional_special_tokens": [
+    "<|EOT|>",
+    "<|BOT|>",
+    "<|CALL_START|>",
+    "<|CALL_END|>",
+    "<|THINK_START|>",
+    "<|THINK_END|>",
+    "<|IMG_START|>",
+    "<|IMG_END|>",
+    "<|META_START|>",
+    "<|META_END|>",
+    "<im_patch>",
+    "<im_start>",
+    "<im_end>",
+    "<dream>",
+    "<dream_start>",
+    "<dream_end>",
+    "<|MASK_1e69f|>",
+    "<|UNMASK_1e69f|>",
+    "<video_start>",
+    "<video_end>",
+    "<patch_start>",
+    "<patch_end>",
+    "<patch_newline>",
+    "<｜begin▁of▁sentence｜>",
+    "<｜begin▁of▁mask｜>",
+    "<｜end▁of▁mask｜>",
+    "<｜fim▁begin｜>",
+    "<｜fim▁hole｜>",
+    "<｜end▁of▁sentence｜>"
+  ],
+  "bos_token": null,
+  "chat_template": "{%- if tools %}\n    {{- '<|im_start|>system\\n' }}\n    {%- if messages[0].role == 'system' %}\n        {{- messages[0].content + '\\n\\n' }}\n    {%- endif %}\n    {{- \"# Tools\\n\\nYou may call one or more functions to assist with the user query.\\n\\nYou are provided with function signatures within <tools></tools> XML tags:\\n<tools>\" }}\n    {%- for tool in tools %}\n        {{- \"\\n\" }}\n        {{- tool | tojson }}\n    {%- endfor %}\n    {{- \"\\n</tools>\\n\\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\\n<tool_call>\\n{\\\"name\\\": <function-name>, \\\"arguments\\\": <args-json-object>}\\n</tool_call><|im_end|>\\n\" }}\n{%- else %}\n    {%- if messages[0].role == 'system' %}\n        {{- '<|im_start|>system\\n' + messages[0].content + '<|im_end|>\\n' }}\n    {%- endif %}\n{%- endif %}\n{%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}\n{%- for message in messages[::-1] %}\n    {%- set index = (messages|length - 1) - loop.index0 %}\n    {%- if ns.multi_step_tool and message.role == \"user\" and message.content is string and not(message.content.startswith('<tool_response>') and message.content.endswith('</tool_response>')) %}\n        {%- set ns.multi_step_tool = false %}\n        {%- set ns.last_query_index = index %}\n    {%- endif %}\n{%- endfor %}\n{%- for message in messages %}\n    {%- if message.content is string %}\n        {%- set content = message.content %}\n    {%- else %}\n        {%- set content = '' %}\n    {%- endif %}\n    {%- if (message.role == \"user\") or (message.role == \"system\" and not loop.first) %}\n        {{- '<|im_start|>' + message.role + '\\n' + content + '<|im_end|>' + '\\n' }}\n    {%- elif message.role == \"assistant\" %}\n        {%- set reasoning_content = '' %}\n        {%- if message.reasoning_content is string %}\n            {%- set reasoning_content = message.reasoning_content %}\n        {%- else %}\n            {%- if '</think>' in content %}\n                {%- set reasoning_content = content.split('</think>')[0].rstrip('\\n').split('<think>')[-1].lstrip('\\n') %}\n                {%- set content = content.split('</think>')[-1].lstrip('\\n') %}\n            {%- endif %}\n        {%- endif %}\n        {%- if loop.index0 > ns.last_query_index %}\n            {%- if loop.last or (not loop.last and reasoning_content) %}\n                {{- '<|im_start|>' + message.role + '\\n<think>\\n' + reasoning_content.strip('\\n') + '\\n</think>\\n\\n' + content.lstrip('\\n') }}\n            {%- else %}\n                {{- '<|im_start|>' + message.role + '\\n' + content }}\n            {%- endif %}\n        {%- else %}\n            {{- '<|im_start|>' + message.role + '\\n' + content }}\n        {%- endif %}\n        {%- if message.tool_calls %}\n            {%- for tool_call in message.tool_calls %}\n                {%- if (loop.first and content) or (not loop.first) %}\n                    {{- '\\n' }}\n                {%- endif %}\n                {%- if tool_call.function %}\n                    {%- set tool_call = tool_call.function %}\n                {%- endif %}\n                {{- '<tool_call>\\n{\"name\": \"' }}\n                {{- tool_call.name }}\n                {{- '\", \"arguments\": ' }}\n                {%- if tool_call.arguments is string %}\n                    {{- tool_call.arguments }}\n                {%- else %}\n                    {{- tool_call.arguments | tojson }}\n                {%- endif %}\n                {{- '}\\n</tool_call>' }}\n            {%- endfor %}\n        {%- endif %}\n        {{- '<|im_end|>\\n' }}\n    {%- elif message.role == \"tool\" %}\n        {%- if loop.first or (messages[loop.index0 - 1].role != \"tool\") %}\n            {{- '<|im_start|>user' }}\n        {%- endif %}\n        {{- '\\n<tool_response>\\n' }}\n        {{- content }}\n        {{- '\\n</tool_response>' }}\n        {%- if loop.last or (messages[loop.index0 + 1].role != \"tool\") %}\n            {{- '<|im_end|>\\n' }}\n        {%- endif %}\n    {%- endif %}\n{%- endfor %}\n{%- if add_generation_prompt %}\n    {{- '<|im_start|>assistant\\n' }}\n    {%- if enable_thinking is defined and enable_thinking is false %}\n        {{- '<think>\\n\\n</think>\\n\\n' }}\n    {%- endif %}\n{%- endif %}",
+  "clean_up_tokenization_spaces": false,
+  "eos_token": "<|im_end|>",
+  "errors": "replace",
+  "extra_special_tokens": {},
+  "model_max_length": 131072,
+  "pad_token": "<|endoftext|>",
+  "split_special_tokens": false,
+  "tokenizer_class": "Qwen2Tokenizer",
+  "unk_token": null
+}