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Model: introvoyz041/Goedel-Prover-V2-32B Source: Original Platform
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README.md
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---
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base_model:
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- Qwen/Qwen3-32B
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license: apache-2.0
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pipeline_tag: text-generation
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library_name: transformers
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---
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<div align="center">
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<h1> <a href="http://blog.goedel-prover.com"> <strong>Goedel-Prover-V2: The Strongest Open-Source Theorem Prover to Date</strong></a></h1>
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</div>
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<div align="center">
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[](http://blog.goedel-prover.com)
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[](https://github.com/Goedel-LM/Goedel-Prover-V2)
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[](https://huggingface.co/Goedel-LM/Goedel-Prover-V2-32B)
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[](https://arxiv.org/abs/2508.03613)
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[](https://opensource.org/licenses/Apache-2.0)
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</div>
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## 1. Introduction
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We introduce Goedel-Prover-V2, an open-source language model series that sets a new state-of-the-art in automated formal proof generation. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) <strong>Scaffolded data synthesis</strong>: We generate synthetic proof tasks of increasing difficulty to progressively train the model, enabling it to master increasingly complex theorems; (2) <strong>Verifier-guided self-correction</strong>: The model learns to iteratively revise its own proofs by leveraging feedback from Lean’s compiler, closely mimicking how humans refine their work; (3) <strong>Model averaging</strong>: We combine multiple model checkpoints to improve robustness and overall performance.
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Our small model, Goedel-Prover-V2-8B, reaches 84.6% on MiniF2F test set at Pass@32, matching the performance of prior state-of-the-art DeepSeek-Prover-V2-671B while being nearly 100 times smaller in model size. Our flagship model, Goedel-Prover-V2-32B, achieves 88.0% on MiniF2F at Pass@32 on standard mode and 90.4% on self-correction mode, outperforming prior SOTA DeepSeek-Prover-V2-671B and concurrent work Kimina-Prover-72B by a large margin. Additionaly, our flagship model with self-correction solves 64 problems on PutnamBench at Pass@64, securing the 1st on the leaderboard surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by Pass@1024.
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## 2. Benchmark Performance
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<strong>Self-correction mode</strong>: Our model improves proof quality by first generating an initial candidate and then using Lean compiler feedback to iteratively revise it. We perform two rounds of self-correction, which remain computationally efficient—the total output length (including the initial proof and two revisions) increases only modestly from the standard 32K to 40K tokens.
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<style>
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.fig-row {
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display: flex;
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justify-content: space-between; /* spread them out */
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align-items: flex-start; /* align tops */
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figure {
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margin: 0;
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}
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figure figcaption {
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text-align: center;
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font-size: 0.9em;
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margin-top: 0.75rem;
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color: #555;
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figure figcaption strong {
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font-weight: bold;
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}
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/* Italicize the rest of the caption */
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figure figcaption em {
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font-style: italic;
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</style>
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<figure>
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<div class="fig-row">
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<div class="panel panel-1" style="width:100%;">
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<img src="https://github.com/Goedel-LM/Goedel-Prover-V2/blob/main/assets/combined_performance_plots_varied_width.png?raw=true" alt="…">
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</div>
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</div>
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<figcaption>
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<strong>Figure 1</strong>: <em>Pass@32 performance on MiniF2F, PutnamBench, and our new MathOlympiadBench containing 360 IMO-level problems.</em>
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</figcaption>
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</figure>
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The charts above demonstrate the state-of-the-art performance of Goedel-Prover-V2. We report all numbers at Pass@32: (1) Across all three datasets, our flagship 32B model, in both standard and self-correction mode, significantly outperforms prior state-of-the-art DeepSeek-Prover-V2-671B and Kimina-Prover-72B; (2) on miniF2F, our 8B model matches the performance of DeepSeek-Prover-V2-671B while being 100 times smaller in model size.
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<div align="center">
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<table style="margin: 0 auto;">
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<thead>
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<tr>
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<th>#</th>
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<th>Model</th>
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<th>num‑solved</th>
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<th>compute</th>
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</tr>
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</thead>
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<tbody>
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<tr><td>1</td><td><strong>Goedel-Prover-V2-32B (self-correction mode)</strong></td><td><strong>86</strong></td><td><strong>Pass@192</strong></td></tr>
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<tr><td>1</td><td><strong>Goedel-Prover-V2-32B (self-correction mode)</strong></td><td><strong>57</strong></td><td><strong>Pass@32</strong></td></tr>
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<tr><td>1</td><td><strong>Goedel-Prover-V2-32B</strong></td><td><strong>43</strong></td><td><strong>Pass@32</strong></td></tr>
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<tr><td>2</td><td>DeepSeek‑Prover‑V2-671B</td><td>47</td><td>Pass@1024</td></tr>
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<tr><td>2</td><td>DeepSeek‑Prover‑V2-671B</td><td>22</td><td>Pass@32</td></tr>
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<tr><td>3</td><td>DSP+</td><td>23</td><td>Pass@128</td></tr>
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<tr><td>4</td><td>Kimina‑Prover‑7B‑Distill</td><td>10</td><td>Pass@192</td></tr>
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<tr><td>5</td><td>Self-play Theorem Prover</td><td>8</td><td>Pass@3200</td></tr>
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<tr><td>6</td><td>Goedel-Prover-V1</td><td>7</td><td>Pass@512</td></tr>
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</tbody>
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</table>
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<!-- table caption -->
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<caption align="bottom"><strong>Table 1</strong>: <em>PutnamBench leaderboard. Goedel-Prover-V2-32B secures the top rank with significantly less compute (pass number) than the previous state-of-the-art.</em>
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</div>
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## 3. Compelling Scaling Performance
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<style>
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.fig-row {
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display: flex;
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justify-content: space-between; /* spread them out */
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align-items: flex-start; /* align tops */
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gap: 1rem; /* space between images */
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}
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display: block;
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width: 100%;
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height: auto;
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}
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.fig-row .panel {
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/* override per‐panel width as needed */
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/* e.g. .panel-1 { width:25%; } .panel-2 { width:40%; } etc. */
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}
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figure {
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margin: 0;
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}
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figure figcaption {
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text-align: center;
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font-size: 0.9em;
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margin-top: 0.75rem;
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color: #555;
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}
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figure figcaption strong {
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font-weight: bold;
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}
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/* Italicize the rest of the caption */
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figure figcaption em {
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font-style: italic;
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</style>
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<figure>
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<div class="fig-row">
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<div class="panel panel-1" style="width:80%;">
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<img src="https://github.com/Goedel-LM/Goedel-Prover-V2/blob/main/assets/inference_scale_performance.png?raw=true" alt="…">
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</div>
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</div>
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<figcaption>
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<strong>Figure 2</strong>: <em>Performance on MiniF2F test set under different sample budgets.</em>
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</figcaption>
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</figure>
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The scaling curves above show that our 32B model consistently outperforms all prior state-of-the-art models across the entire range of inference-time compute budgets.
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## 4. Model & Dataset Downloads
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We release our Goedel-Prover-V2 models and the new MathOlympiadBench benchmark to foster future research.
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<div align="center">
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| Model | Download |
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| -------- | -------- |
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| Goedel-Prover-V2-32B | [🤗Download](https://huggingface.co/Goedel-LM/Goedel-Prover-V2-32B) |
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| Goedel-Prover-V2-8B | [🤗Download](https://huggingface.co/Goedel-LM/Goedel-Prover-V2-8B) |
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</div>
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<div align="center">
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| Dataset | Download |
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| -------- | -------- |
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| MathOlympiadBench | [🤗Download](https://huggingface.co/datasets/Goedel-LM/MathOlympiadBench) |
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</div>
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<strong>MathOlympiadBench</strong> (Math Olympiad Bench) comprises human-verified formalizations of Olympiad-level mathematical competition problems, sourced from [Compfiles](https://dwrensha.github.io/compfiles/imo.html) and [IMOSLLean4 repository](https://github.com/mortarsanjaya/IMOSLLean4). MathOlympiadBench contains 360 problems, including 158 IMO problems from 1959 to 2024, 131 IMO shortlist problems covering 2006 to 2023, 68 regional mathematical Olympiad problems, and 3 additional mathematical puzzles.
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This model is being released to aid other open-source projects, including those geared towards the upcoming IMO competition. A full paper with all details will be released in the coming weeks.
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## 5. Quick Start
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You can directly use [Huggingface's Transformers](https://github.com/huggingface/transformers) for model inference.
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```python
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from transformers import AutoModelForCausalLM, AutoTokenizer
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import torch
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torch.manual_seed(30)
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model_id = "Goedel-LM/Goedel-Prover-V2-32B"
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tokenizer = AutoTokenizer.from_pretrained(model_id)
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model = AutoModelForCausalLM.from_pretrained(model_id, device_map="auto", torch_dtype=torch.bfloat16, trust_remote_code=True)
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formal_statement = """
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import Mathlib
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import Aesop
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set_option maxHeartbeats 0
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open BigOperators Real Nat Topology Rat
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theorem square_equation_solution {x y : ℝ} (h : x^2 + y^2 = 2*x - 4*y - 5) : x + y = -1 := by
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sorry
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""".strip()
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prompt = """
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Complete the following Lean 4 code:
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```lean4
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{}```
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Before producing the Lean 4 code to formally prove the given theorem, provide a detailed proof plan outlining the main proof steps and strategies.
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The plan should highlight key ideas, intermediate lemmas, and proof structures that will guide the construction of the final formal proof.
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""".strip()
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chat = [
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{"role": "user", "content": prompt.format(formal_statement)},
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]
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inputs = tokenizer.apply_chat_template(chat, tokenize=True, add_generation_prompt=True, return_tensors="pt").to(model.device)
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import time
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start = time.time()
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outputs = model.generate(inputs, max_new_tokens=32768)
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print(tokenizer.batch_decode(outputs))
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print(time.time() - start)
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```
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### Cite
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```bibtex
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@article{lin2025goedelproverv2,
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title={Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction},
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author={Lin, Yong and Tang, Shange and Lyu, Bohan and Yang, Ziran and Chung, Jui-Hui and Zhao, Haoyu and Jiang, Lai and Geng, Yihan and Ge, Jiawei and Sun, Jingruo and others},
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journal={arXiv preprint arXiv:2508.03613},
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year={2025}
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}
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```
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{
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"architectures": [
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"Qwen3ForCausalLM"
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],
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"max_window_layers": 64,
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"model_type": "qwen3",
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"num_attention_heads": 64,
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"num_hidden_layers": 64,
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"num_key_value_heads": 8,
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"rms_norm_eps": 1e-06,
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"rope_scaling": null,
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"rope_theta": 1000000,
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"sliding_window": null,
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"tie_word_embeddings": false,
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"torch_dtype": "bfloat16",
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"transformers_version": "4.51.3",
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"use_cache": false,
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"use_sliding_window": false,
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"vocab_size": 151936
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}
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|
||||
"content": "<|box_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151649": {
|
||||
"content": "<|box_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151650": {
|
||||
"content": "<|quad_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151651": {
|
||||
"content": "<|quad_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151652": {
|
||||
"content": "<|vision_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151653": {
|
||||
"content": "<|vision_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151654": {
|
||||
"content": "<|vision_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151655": {
|
||||
"content": "<|image_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151656": {
|
||||
"content": "<|video_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151657": {
|
||||
"content": "<tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151658": {
|
||||
"content": "</tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151659": {
|
||||
"content": "<|fim_prefix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151660": {
|
||||
"content": "<|fim_middle|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151661": {
|
||||
"content": "<|fim_suffix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151662": {
|
||||
"content": "<|fim_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151663": {
|
||||
"content": "<|repo_name|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151664": {
|
||||
"content": "<|file_sep|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151665": {
|
||||
"content": "<tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151666": {
|
||||
"content": "</tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"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
|
||||
}
|
||||
},
|
||||
"additional_special_tokens": [
|
||||
"<|im_start|>",
|
||||
"<|im_end|>",
|
||||
"<|object_ref_start|>",
|
||||
"<|object_ref_end|>",
|
||||
"<|box_start|>",
|
||||
"<|box_end|>",
|
||||
"<|quad_start|>",
|
||||
"<|quad_end|>",
|
||||
"<|vision_start|>",
|
||||
"<|vision_end|>",
|
||||
"<|vision_pad|>",
|
||||
"<|image_pad|>",
|
||||
"<|video_pad|>"
|
||||
],
|
||||
"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|>",
|
||||
"padding_side": "right",
|
||||
"split_special_tokens": false,
|
||||
"tokenizer_class": "Qwen2Tokenizer",
|
||||
"unk_token": null
|
||||
}
|
||||
1
vocab.json
Normal file
1
vocab.json
Normal file
File diff suppressed because one or more lines are too long
Reference in New Issue
Block a user