Source : Webster's Revised Unabridged Dictionary (1913)

Insoluble \In*sol"u*ble\, a. [L. insolubilis indissoluble, that
   can not be loosed: cf. F. insoluble. See {In-} not, and
   {Soluble}, and cf. {Insolvable}.]
   1. Not soluble; in capable or difficult of being dissolved,
      as by a liquid; as, chalk is insoluble in water.

   2. Not to be solved or explained; insolvable; as, an
      insoluble doubt, question, or difficulty.

   3. Strong. ``An insoluble wall.'' [Obs.] --Holland

Source : WordNet®

insoluble
     adj 1: (of a substance) not easily dissolved [ant: {soluble}]
     2: admitting of no solution or explanation; "an insoluble
        doubt" [ant: {soluble}]
     3: without hope of solution; "an insoluble problem"