The Collaborative International Dictionary of English v.0.48:

Irreconcilable \Ir*rec"on*ci`la*ble\ (?; 277), a. [Pref. ir- not
   + reconcilable: cf. F. irr['e]conciliable.]
   Not reconcilable; not able to be reconciled or brought into
   accord; implacable; incompatible; inconsistent; disagreeing;
   as, irreconcilable enemies, statements. --
   Ir*rec"on*ci`la*ble*ness, n. -- Ir*rec"on*ci`la*bly, adv.
   [1913 Webster]