1550s, from Late Latin indisputabilis, from in- "not, opposite of, without" (see in- (1)) + disputabilis, from Latin disputare "to weigh, examine, discuss, argue, explain" (see dispute (v.)). Related: Indisputably.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
c. 1300, "engage in argumentation or discussion," from Old French desputer (12c.) "dispute, fight over, contend for, discuss" and directly from Latin disputare "weigh, examine, discuss, argue, explain," from dis- "separately, apart" (see dis-) + putare "to count, consider," originally "to prune, make clean, clear up" (from PIE root *pau- (2) "to cut, strike, stamp").
The Latin word was used in Vulgate in sense of "to argue, contend with words." In English, transitive sense of "argue against, attempt to disprove, deny" is from 1510s. Related: Disputable; disputed; disputing.