AI & ML Paradigm Shift

Introduces a 'sorry-driven' formal decomposition that allows LLM agents to solve complex proofs by isolating and independently verifying subgoals.

March 26, 2026

Original Paper

Mechanic: Sorrifier-Driven Formal Decomposition Workflow for Automated Theorem Proving

Ruichen Qiu, Yichuan Cao, Junqi Liu, Dakai Guo, Xiao-Shan Gao, Lihong Zhi, Ruyong Feng

arXiv · 2603.24465

The Takeaway

Standard automated theorem proving struggles with context length degradation during repeated repairs. By using the Lean 'sorry' placeholder to create clean, modular subproblems, Mechanic achieves much higher efficiency and success rates on elite competition benchmarks like IMO and Putnam 2025.

From the 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,