The Collaborative International Dictionary of English v.0.48:

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.]
   [1913 Webster]
   1. Not soluble; in capable or difficult of being dissolved,
      as by a liquid; as, chalk is insoluble in water.
      [1913 Webster]

   2. Not to be solved or explained; insolvable; as, an
      insoluble doubt, question, or difficulty.
      [1913 Webster]

   3. Strong. "An insoluble wall." [Obs.] --Holland
      [1913 Webster]

WordNet (r) 3.0 (2006):

insoluble
    adj 1: (of a substance) incapable of being dissolved [syn:
           insoluble, indissoluble] [ant: soluble]
    2: admitting of no solution or explanation; "an insoluble doubt"
       [ant: soluble]
    3: without hope of solution; "an insoluble problem"

Moby Thesaurus II by Grady Ward, 1.0:

24 Moby Thesaurus words for "insoluble":
   coherent, cohesive, enwrapped in mystery, impartible, indefinable,
   indiscerptible, indissoluble, indissolvable, indivisible,
   inexplicable, inextricable, infrangible, infusible, inseparable,
   insolvable, mysterious, mystic, unaccountable, undefinable,
   undividable, unexplainable, unified, uninterpretable, unsolvable