# Does NP-Complete imply non-satisfiability?

I've seen a lot of text concerning the first NP-Complete problem, Boolean Satisfiability. I guess I'm confused concerning the language.

It sounds to me as though the problem could be difficult to compute (hence the NP-complete), however it still might be satisfiable. As in, there exists a satisfying mapping of literals. We can't necessarily compute it easily, but it's out there.

In fact, I would guess that the two adjectives really have no relation to each other. But, when working with problems, I am often asked to see whether a set of clauses is satisfiable. Does that mean, Can we compute a satisfying mapping? And by extension, does NP-complete imply that a given CNF setup is unsatisfiable?

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