irreconciliation (n.)

mid-14c., reconciliacioun, "renewal of friendship after disagreement or enmity, action of reaching accord with an adversary or one estranged" (originally especially of God and sinners), from Old French reconciliacion (14c.) and directly from Latin reconciliationem (nominative reconciliatio) "a re-establishing, a reconciling," noun of action from past-participle stem of reconciliare (see reconcile).

From 1729 as "act of harmonizing or making consistent." Other early noun forms included reconcilement (mid-15c.), reconciling (late 14c.).