inutility (n.)

"quality of being useless or unprofitable," 1590s, from Middle 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.)).