Nouns

(n)contradictorytwo propositions are contradictories if both cannot be true (or both cannot be false) at the same time

Adjectives

(s)contradictoryof words or propositions so related that both cannot be true and both cannot be false“`perfect' and `imperfect' are contradictory terms”
(s)confounding, contradictorythat confounds or contradicts or confuses
(s)at odds, conflicting, contradictory, self-contradictoryin disagreement“the figures are at odds with our findings”, “contradictory attributes of unjust justice and loving vindictiveness” (John Morley)
(s)contradictory, mutually exclusiveunable for both to exist or be true at the same time