I suppose John just missed these two entries on the page to which he linked:
4. ( tr ) to be inconsistent with (a proposition, theory, etc): the facts contradicted his theory
5. ( intr ) (of two or more facts, principles, etc) to be at variance; be in contradiction
4. ( tr ) to be inconsistent with (a proposition, theory, etc): the facts contradicted his theory
5. ( intr ) (of two or more facts, principles, etc) to be at variance; be in contradiction
