contradictory

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

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