What is "equisatisfiability"

In logic, two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or both are not. Two equisatisfiable formulae may have different models, provided they both have some or both have none. As a result, equisatisfiability is different from logical equivalence, as two equivalent formulae always have the same models.

Equisatisfiability is generally used in the context of translating formulae, so that one can define a translation to be correct if the original and resulting formulae are equisatisfiable. Examples of translations involving this concept are Skolemization and some translations into conjunctive normal form.