contradictory

from The American Heritage® Dictionary of the English Language, 5th Edition.

• adjective Involving, of the nature of, or being a contradiction: synonym: opposite.
• adjective Given to contradicting.
• noun Either of two propositions related in such a way that it is impossible for both to be true or both to be false.

from The Century Dictionary.

• Denying that something stated or approved is completely true; diametrically opposed.
• Inconsistent; logically antagonistic; incapable of being true together (though both may be false).
• Synonyms Contrary, Inconsistent, etc. See contrary.
• noun pl. contradictories (-riz). A proposition of a pair inconsistent with each other, or each of which precisely denies or falsifies the other.

from the GNU version of the Collaborative International Dictionary of English.

• adjective Affirming the contrary; implying a denial of what has been asserted; also, mutually contradicting; inconsistent.
• adjective Opposing or opposed; repugnant.
• noun A proposition or thing which denies or opposes another; contrariety.
• noun (Logic) propositions with the same terms, but opposed to each other both in quality and quantity.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• adjective That contradicts something, such as an argument.
• adjective That is itself a contradiction.
• adjective That is diametrically opposed to something.
• adjective Mutually exclusive.
• adjective Tending to contradict or oppose, contrarious
• noun logic Any of a pair of propositions, that cannot both be true or both be false.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• adjective in disagreement
• adjective that confounds or contradicts or confuses
• adjective unable to be both true at the same time
• adjective of words or propositions so related that both cannot be true and both cannot be false
• noun two propositions are contradictories if both cannot be true (or both cannot be false) at the same time