WordNet sense 1 (that confounds or contradicts or confuses):

confounding

WordNet sense 2 (not furnishing support or assistance):

unsupportive

WordNet sense 3 (in disagreement):

conflicting, self-contradictory, at odds

WordNet sense 4 (displaying a lack of consistency):

inconsistent

WordNet sense 5 (unable to be both true at the same time):

mutually exclusive

WordNet sense 6 (not compatible):

incompatible