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

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.

Red-Teaming Text-to-Image Systems by Rule-based Preference Modeling

Text-to-image (T2I) models raise ethical and safety concerns due to their potential to generate inappropriate or harmful images. Evaluating these models' security through red-teaming is vital, yet white-box approaches are limited by their need for internal access, complicating their use with closed-source models. Moreover, existing black-box methods often assume knowledge about the model's specific defense mechanisms, limiting their utility in real-world commercial API scenarios. A significant challenge is how to evade unknown and diverse defense mechanisms. To overcome this difficulty, we propose a novel Rule-based Preference modeling Guided Red-Teaming (RPG-RT), which iteratively employs LLM to modify prompts to query and leverages feedback from T2I systems for fine-tuning the LLM. RPG-RT treats the feedback from each iteration as a prior, enabling the LLM to dynamically adapt to unknown defense mechanisms. Given that the feedback is often labeled and coarse-grained, making it difficult to utilize directly, we further propose rule-based preference modeling, which employs a set of rules to evaluate desired or undesired feedback, facilitating finer-grained control over the LLM's dynamic adaptation process. Extensive experiments on nineteen T2I systems with varied safety mechanisms, three online commercial API services, and T2V models verify the superiority and practicality of our approach.