Synonyms for Inconsistent (same or very similar meaning)
WordNet sense 1 (impossible to reconcile):
irreconcilable, unreconcilableWordNet sense 2 (not compatible with other facts):
discrepant, incompatibleWordNet sense 3 (in disagreement):
conflicting, contradictory, self-contradictoryWordNet sense 4 (lacking in harmony or compatibility or appropriateness):
incongruousFrom the ODE community, based on WordNetadd/edit