A formula $\phi$ of the language of pure (or narrow) predicate calculus that is false in all models of this language. A formula $\phi$ is a contradiction if and only if $\neg\phi$ is derivable in pure predicate calculus.
Contradiction (inconsistency). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Contradiction_(inconsistency)&oldid=31391