irreconcilable (adj.) Look up irreconcilable at Dictionary.com
1590s, from assimilated form of in- (1) "not, opposite of" + reconcilable, if that word is so old. Or perhaps from French irréconcilable (16c.). Related: Irreconcilably. As a noun, "one who refuses reconciliation or compromise" (especially in politics), from 1748.