inconsequent (adj.)

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.

late 14c., "logical inference, conclusion," from Old French consequence "result" (13c., Modern French conséquence), from Latin consequentia, abstract noun from present-participle stem of consequi "to follow after," from assimilated form of com "with, together" (see con-) + sequi "to follow" (from PIE root *sekw- (1) "to follow").

Meaning "that which follows from or grows out of any act or course" is from c. 1400. Sense of "importance, significance" (1590s) is from notion of being "full of consequences."