The important bit here is "in general". Most actual SAT instances can be solved much more efficiently. An that's what SAT solvers exploit.
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I'd say it depends. "SAT solving" is not by itself a specific algorithm, and modern SAT solvers are definitely not using brute force algos.
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On the other hand, you could obviously implement a SAT solver using brute force (enumerate and test valuations). Not that it's a good idea.
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Yap. Brute force implies searching all possible assignments in all dimensions. Metahuersitic local search is not brute force.
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