The Collaborative International Dictionary of English v.0.48:

Inutility \In`u*til"i*ty\, n. [L. inutilitas: cf. F.
   inutilit['e].]
   Uselessness; the quality of being unprofitable;
   unprofitableness; as, the inutility of vain speculations and
   visionary projects.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inutility
    n 1: the quality of having no practical use [syn: inutility,
         uselessness, unusefulness] [ant: usefulness,
         utility]