Paper
Mechanic: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving
Authors
Ruichen Qiu, Yichuan Cao, Junqi Liu, Dakai Guo, Xiao-Shan Gao, Lihong Zhi, Ruyong Feng
Abstract
Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems requiring complex mathematical reasoning, current systems rarely succeed on the first try and must repeatedly modify their proof strategies. Existing approaches for handling failed attempts typically either discard the entire proof and regenerate it from scratch or iteratively fix errors within the proof. The former is inefficient, as it may abandon mostly correct reasoning due to localized errors, while the latter, although preserving prior progress, leads to progressively longer contexts which progressively degrades the model's ability to attend to the remaining unresolved subproblems. To address this dilemma, we propose Mechanic, a novel agent system that employs a sorry-driven formal decomposition strategy. By leveraging the sorry placeholder in Lean to precisely isolate unresolved subgoals while preserving the surrounding verified proof structure, Mechanic extracts each failed subproblem into a clean, self-contained context and resolves it independently. This avoids both the waste of full regeneration and the excessive context length induced by repeated repairs. Experimental results on challenging mathematical competition benchmarks, including IMO 2025 and Putnam 2025, demonstrate that our agent achieves significant advantages in proving efficiency.
Metadata
Related papers
Vibe Coding XR: Accelerating AI + XR Prototyping with XR Blocks and Gemini
Ruofei Du, Benjamin Hersh, David Li, Nels Numan, Xun Qian, Yanhe Chen, Zhongy... • 2026-03-25
Comparing Developer and LLM Biases in Code Evaluation
Aditya Mittal, Ryan Shar, Zichu Wu, Shyam Agarwal, Tongshuang Wu, Chris Donah... • 2026-03-25
The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence
Biplab Pal, Santanu Bhattacharya • 2026-03-25
Retrieval Improvements Do Not Guarantee Better Answers: A Study of RAG for AI Policy QA
Saahil Mathur, Ryan David Rittner, Vedant Ajit Thakur, Daniel Stuart Schiff, ... • 2026-03-25
MARCH: Multi-Agent Reinforced Self-Check for LLM Hallucination
Zhuo Li, Yupeng Zhang, Pengyu Cheng, Jiajun Song, Mengyu Zhou, Hao Li, Shujie... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.24465v1</id>\n <title>Mechanic: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving</title>\n <updated>2026-03-25T16:12:08Z</updated>\n <link href='https://arxiv.org/abs/2603.24465v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.24465v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Recent advances in large language models (LLMs) and LLM-based agents have substantially improved the capabilities of automated theorem proving. However, for problems requiring complex mathematical reasoning, current systems rarely succeed on the first try and must repeatedly modify their proof strategies. Existing approaches for handling failed attempts typically either discard the entire proof and regenerate it from scratch or iteratively fix errors within the proof. The former is inefficient, as it may abandon mostly correct reasoning due to localized errors, while the latter, although preserving prior progress, leads to progressively longer contexts which progressively degrades the model's ability to attend to the remaining unresolved subproblems. To address this dilemma, we propose Mechanic, a novel agent system that employs a sorry-driven formal decomposition strategy. By leveraging the sorry placeholder in Lean to precisely isolate unresolved subgoals while preserving the surrounding verified proof structure, Mechanic extracts each failed subproblem into a clean, self-contained context and resolves it independently. This avoids both the waste of full regeneration and the excessive context length induced by repeated repairs. Experimental results on challenging mathematical competition benchmarks, including IMO 2025 and Putnam 2025, demonstrate that our agent achieves significant advantages in proving efficiency.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CL'/>\n <published>2026-03-25T16:12:08Z</published>\n <arxiv:primary_category term='cs.CL'/>\n <author>\n <name>Ruichen Qiu</name>\n </author>\n <author>\n <name>Yichuan Cao</name>\n </author>\n <author>\n <name>Junqi Liu</name>\n </author>\n <author>\n <name>Dakai Guo</name>\n </author>\n <author>\n <name>Xiao-Shan Gao</name>\n </author>\n <author>\n <name>Lihong Zhi</name>\n </author>\n <author>\n <name>Ruyong Feng</name>\n </author>\n </entry>"
}