Source : Webster's Revised Unabridged Dictionary (1913)

Irreconcilable \Ir*rec"on*ci`la*ble\ (?; 277), a. [Pref. ir- not
   + reconcilable: cf. F. irr['e]conciliable.]
   Not reconcilable; implacable; incompatible; inconsistent;
   disagreeing; as, irreconcilable enemies, statements. --
   {Ir*rec"on*ci`la*ble*ness}, n. -- {Ir*rec"on*ci`la*bly}, adv.

Source : WordNet®

irreconcilable
     adj : impossible to reconcile; "irreconcilable differences" [syn:
           {unreconcilable}] [ant: {reconcilable}]