Testing LLM reasoning abilities with SAT is not an original idea; there is a recent research that did a thorough testing with models such as GPT-4o and found that for hard enough problems, every model degrades to random guessing. But I couldn't find any research that used newer models like I used. It would be nice to see a more thorough testing done again with newer models.
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For UNSAT problems with 10 variables and 200 clauses, it had the same issue as Gemini 3 Pro of making up assignments.