contradictory

of words or propositions so related that both cannot be true and both cannot be false; "`perfect'' and `imperfect'' are contradictory terms"

that confounds or contradicts or confuses

in disagreement; "the figures are at odds with our findings"; "contradictory attributes of unjust justice and loving vindictiveness"- John Morley

unable to be both true at the same time

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