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.