SATBench: Benchmarking LLMs' Logical Reasoning via Automated Puzzle Generation from SAT Formulas
This work addresses the need for better benchmarks to assess LLMs' search-based logical reasoning, though it is incremental as it builds on existing SAT problem frameworks.
The authors tackled the problem of evaluating logical reasoning in large language models (LLMs) by introducing SATBench, a benchmark of logical puzzles derived from Boolean satisfiability problems, and found that even top models like o4-mini achieved only 65.0% accuracy on hard UNSAT problems, close to random guessing.
We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a puzzle using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-based and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. Our error analysis reveals systematic failures such as satisfiability bias, context inconsistency, and condition omission, highlighting limitations of current LLMs in search-based logical reasoning. Our code and data are publicly available at https://github.com/Anjiang-Wei/SATBench