 Endpoint-false disjunctive normal form

A propositional formula false on the all-true and all-false Boolean valuations has a disjunctive normal form in which every minterm contains a positive literal and a negative literal. Grouping the positive propositional variables into $C$ and the negated propositional variables into the negation of a logical disjunction $D$ writes each minterm as $\neg (C\to D)$. De Morgan's laws therefore give the negation of a logical conjunction of such logical implications. For a contradiction use $\neg (p\to p)$.