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inutility (n.)

"quality of being useless or unprofitable," 1590s, from French inutilité (15c.), from Latin inutilitas "uselessness," from inutilis "useless, unprofitable," from in- "not" (see in- (1)) + utilis "useful, beneficial, profitable," from uti "make use of, profit by, take advantage of" (see use (v.)).

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Definitions of inutility from WordNet

inutility (n.)
the quality of having no practical use;
Synonyms: uselessness / unusefulness
From wordnet.princeton.edu