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The Collaborative International Dictionary of English v.0.48:

Irresoluble \Ir*res"o*lu*ble\, a. [L. irresolubilis: cf. F. irr['e]soluble. See Resoluble, and cf. Irresolvable.] [1913 Webster] 1. Incapable of being dissolved or resolved into parts; insoluble. --Boyle. [1913 Webster] 2. Incapable of being relieved or assisted. [Obs.] [1913 Webster] The second is in the irresoluble condition of our souls after a known sin committed. --Bp. Hall. [1913 Webster]