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Such a set is easily recognizable as satisfiable or unsatisfiable with respect to the semantics of the logic in question. en.wikipedia.org

Put another way, is satisfiable if and only if is invalid. en.wikipedia.org

An unsatisfiable core is called a "minimal unsatisfiable core", if every proper subset (allowing removal of any arbitrary clause or clauses) of it is satisfiable. en.wikipedia.org

If is satisfiable, then there exists a proof (a truly satisfying assignment) that the system will always accept. en.wikipedia.org

If one of these two tests returns that the smaller instance is satisfiable, continue solving that instance until a complete solution has been derived. en.wikipedia.org

A tableau checks whether a given set of formulae is satisfiable or not. en.wikipedia.org

The resulting instance is satisfiable if and only if no domain or constraint is made empty. en.wikipedia.org

Graphs that can not be simplified beyond a certain point are analogues of the satisfiable formulas of first-order logic. en.wikipedia.org

An initial problem is solved by reducing it to a satisfiable conjunction of constraints. en.wikipedia.org

They may find a solution of a problem, but they may fail even if the problem is satisfiable. en.wikipedia.org

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