In contrast to this, there is no a priori guarantee that classes such as \(\textbf{NP}\) defined in terms of non-deterministic models are closed under complementation. For consider a problem such as \(\sc{SAT}\) belonging to this class. \(\overline{\sc{SAT}}\) – i.e. the complement of \(\sc{SAT}\)– consists of the set of formulas for which there does not exist a satisfying valuation – i.e. the contradictory formulas of propositional logic. From this it follows that \(\phi \in \overline{\sc{SAT}}\) if and only if \(\neg \phi \in \sc{VALID}\) – i.e. the set of valid propositional formulas. As this observation provides an easy polynomial time reduction of \(\overline{\sc{SAT}}\) to \(\sc{VALID}\), the latter is thus not only a member of \(\textbf{coNP}\), but is also complete for this class.[23]