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We present a systematic study of LLMs on 2-SAT and 3-SAT, together with two canonical reductions, Vertex Cover and discrete 3D packing, to probe representation-invariant reasoning. We first evaluate models using conventional metrics, including accuracy, precision, recall, and F1, as well as the SAT phase-transition setting. We find that these metrics can be misleading: many models obtain high scores by over-predicting satisfiable formulas, fail to reproduce the classical easy-hard-easy signature around the 3-SAT threshold, and degrade sharply as the number of variables grows.\n  To address this problem, we introduce a paired-formula protocol based on minimally different satisfiable and unsatisfiable instances, together with Accurate Differentiation Rate (ADR), which requir","title":"Satisfiability Solving with LLMs: A Matched-Pair Evaluation of Reasoning Capability","url":"https://arxiv.org/abs/2605.28602","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.28602v1 Announce Type: new \nAbstract: Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with two canonical reductions, Vertex Cover and discrete 3D packing, to probe representation-invariant reasoning. We first evaluate models using conventional metrics, including accuracy, precision, recall, and F1, as well as the SAT phase-transition setting. 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