contradictory

Unable for both to exist or be true at the same time.

In disagreement.

“contradictory attributes of unjust justice and loving vindictiveness”

That confounds or contradicts or confuses.

Of words or propositions so related that both cannot be true and both cannot be false.

“`perfect' and `imperfect' are contradictory terms”

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