High Quality Content by WIKIPEDIA articles! Skolemization is a method for removing existential quantifiers from formal logic statements, often performed as the first step in an automated theorem prover. A formula of first-order logic is in Skolem normal form (named after Thoralf Skolem) if it is in conjunctive prenex normal form with only universal first-order quantifiers. Every first-order formula can be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization. The resulting formula is not necessarily equivalent to the original one, but is equisatisfiable with it: it is satisfiable if and only if the original one is. This equivalence is useful because the definition of first-order satisfiability implicitly existentially quantifies over the evaluation of function symbols. In particular, a first-order formula ? is satisfiable if there exists a model M and an evaluation ? of the free variables of the formula that evaluate the formula to true.

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