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]

WordNet (r) 3.0 (2006):

irreconcilable
    adj 1: impossible to reconcile; "irreconcilable differences"
           [syn: irreconcilable, unreconcilable] [ant:
           reconcilable]

Moby Thesaurus II by Grady Ward, 1.0:

143 Moby Thesaurus words for "irreconcilable":
   abnormal, absurd, adamant, adamantine, alienated, anomalous,
   assorted, at odds, at variance, avenging, bitter-ender, brawler,
   cast-iron, contrary, contrasted, contrasting, defendant, departing,
   deviating, deviative, diehard, different, differentiated,
   differing, disaccordant, disaffected, disagreeing, discordant,
   discrepant, discrete, discriminated, disjoined, disparate,
   disproportionate, disputant, dissentient, dissident, dissimilar,
   dissonant, distinct, distinguished, disunited, divergent,
   diverging, divers, diverse, diversified, divided, dour, estranged,
   firm, flinty, grim, grudgeful, hard, hard-core, heterogeneous,
   immovable, immutable, implacable, impliable, in disagreement,
   inaccordant, incoherent, incommensurable, incommensurate,
   incompatible, incongruent, incongruous, inconsequent, inconsistent,
   inconsonant, inelastic, inexorable, inflexible, inharmonious,
   intransigent, iron, last-ditcher, litigant, many, motley,
   multifarious, naysayer, negativist, noncooperator, objector,
   obstructionist, obstructive, opposer, oppositionist,
   out of proportion, oxymoronic, paradoxical, plaintiff, poles apart,
   poles asunder, protester, punitive, punitory, quarreler, rancorous,
   relentless, resister, retaliatory, revanchist, revengeful, rigid,
   rigorous, rock-ribbed, scrapper, self-contradictory, separate,
   separated, several, steely, stern, stiff, torn, unaffected,
   unalterable, unappeasable, unbending, unchangeable, uncompromising,
   unconformable, unequal, ungiving, unlike, unmoved, unrelenting,
   unyielding, variant, varied, variegated, various, varying,
   vengeful, vindicatory, vindictive, widely apart, worlds apart,
   wrangler