Editing First-order logic (section)

===Resolution===

{{Main|Resolution (logic)}}

The [[resolution (logic)|resolution rule]] is a single rule of inference that, together with [[Unification (computing)#Definition of unification for first-order logic|unification]], is sound and complete for first-order logic. As with the tableaux method, a formula is proved by showing that the negation of the formula is unsatisfiable. Resolution is commonly used in automated theorem proving.

The resolution method works only with formulas that are disjunctions of atomic formulas; arbitrary formulas must first be converted to this form through [[Skolemization]]. The resolution rule states that from the hypotheses <math>A_1 \lor\cdots\lor A_k \lor C</math> and <math>B_1\lor\cdots\lor B_l\lor\lnot C</math>, the conclusion <math>A_1\lor\cdots\lor A_k\lor B_1\lor\cdots\lor B_l</math> can be obtained.