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4 lines
642 B
4 lines
642 B
Two propositional formulas $\varphi$ and $\psi$ are \emph{equisatisfiable} if and only if
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either \emph{both are satisfiable} or \emph{both are unsatisfiable}.
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When checking whether two formulas $\varphi_1$ and $\varphi_2$ are equivalent we check whether $\varphi = \varphi_1 \oplus \varphi_2$ is satisfiable. If $\varphi$ is \textit{SAT} we know that there is a model such that one of the input formulas evaluated to true, while the other evaluated to false. The equisatisfiable formula $CNF(\varphi)$ is satisfiable if and only if $\varphi$ is satisfiable and therefore answers our question of whether the two input formulas are equivalent.
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