Discussion
What does a solver report when a problem has no solution?
Answer: C
A complete solver that has explored the whole space, with propagation pruning the impossible, can assert unsatisfiability as a proved result rather than a failure to find anything. Timeouts, best efforts and explanations are all useful outputs but are different claims. Some systems can also produce a minimal unsatisfiable subset explaining why. Distinguishing a proof of absence from a failure to find is what makes a solver usable for verification rather than only for construction.
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