Discussion
Why can a local search satisfiability solver not prove unsatisfiability?
Answer: B
Failing to find a satisfying assignment establishes only that none was found, since the method samples rather than enumerates. Systematic solvers with learning can exhaust the space and produce a refutation proof. Clause evaluation and initialisation are unaffected. Knowing what may be concluded from a negative result decides which family a task requiring a proof must use, and it is the same consideration that arises in constraint satisfaction. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.
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