contradictory

adj

1. That contradicts something, such as an argument.
2. That is itself a contradiction.

   “Our attitudes toward sharks are contradictory. We fear them and yet we seek them out.”

3. That is diametrically opposed to something.

   “Schemes […] contradictory to common sense.”

4. Mutually exclusive.

   “[White House deputy chief of policy Stephen] Miller has offered contradictory versions of Trump administration statements and court rulings.”

5. Tending to contradict or oppose, contrarious.

noun

1. Either of a pair of propositions, that cannot both be true or both be false.