Conjunction of Clauses and Well-Formed Formulas Here is a theorem in my notes: > If $\phi$ is any wff such that $\neg \phi$ is not a tautology, then $\phi$ is tautologically equivalent to a conjunction of clauses. My question is that...can this theorem hold if $\phi$ is not a tautology and so $\neg \phi$ is tautologically equivalent to a conjunction of clauses?

_Short answer._ Yes, it does.

_Long answer._ The statement:

> If $\varphi$ is any wff such that $\varphi$ is not a tautology, then $\lnot \varphi$ is tautologically equivalent to a conjunction of clauses.

is a corollary of the theorem stated in your question. Indeed, if $\varphi$ is any wff such that $\varphi$ is not a tautology, then $\lnot \varphi$ is a wff and $\lnot \lnot \varphi$ (which is equivalent to $\varphi$) is not a tautology. According to the theorem stated in your question (applied to $\lnot \varphi$), $\lnot \varphi$ is tautologically equivalent to a conjunction of clauses.