contradictory

Short definition from Wiktionary

Adjective

1. 1
   That contradicts something, such as an argument.
2. 2
   That is itself a contradiction.
3. 3
   That is diametrically opposed to something.
4. 4
   Mutually exclusive.
5. 5
   Tending to contradict or oppose, contrarious.

Noun

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