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1510s, "refuse, reject," from Middle French réfuter (16c.) and directly from Latin refutare "drive back; rebut, disprove; repress, repel, resist, oppose," from re- "back" (see re-) + -futare "to beat," probably from PIE root *bhau- "to strike down" (see bat (n.1)).
Meaning "prove wrong" dates from 1540s. Since c.1964 linguists have frowned on the subtle shift in meaning towards "to deny," as it is used in connection with allegation. Related: Refuted; refuting.