# Equisatisfiability

A translation from propositional logic into propositional logic in which every binary disjunction ${\displaystyle a\vee b}$ is replaced by ${\displaystyle ((a\vee n)\wedge (\neg n\vee b))}$, where ${\displaystyle n}$ is a new variable (one for each replaced disjunction) is a transformation in which satisfiability is preserved: the original and resulting formulae are equisatisfiable. Note that these two formulae are not equivalent: the first formula has the model in which ${\displaystyle b}$ is true while ${\displaystyle a}$ and ${\displaystyle n}$ are false (the model's truth value for ${\displaystyle n}$ being irrelevant to the truth value of the formula), but this is not a model of the second formula, in which ${\displaystyle n}$ has to be true in this case.