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Adjective: unresolvable  ,ún-ri'zól-vu-bul
  1. Admitting of no solution or explanation
    "an unresolvable doubt";
    - insoluble, insolvable [rare], unsoluble [rare], unsolvable
     
  2. Not capable of being resolved
    "unresolvable confusion"

See also: incomprehensible, inexplicable, inextricable

Encyclopedia: Unresolvable