Conclusive
late 16th century (in the sense ‘summing up’): from late Latin conclusivus, from Latin conclus- ‘closed up’, from the verb concludere (see conclusion).
wiktionary
French conclusif, from Late Latin conclusivus, from Latin conclūsīvē(“conclusively”), from past participle of concludere
etymonline
conclusive (adj.)
1610s, "occurring at the end," from French conclusif, from Late Latin conclusivus, from conclus-, past participle stem of Latin concludere "to shut up, enclose," from assimilated form of com "together" (see con-) + -cludere, combining form of claudere "to shut" (see close (v.)). Meaning "definitive, decisive, convincing, being so forcible as not to admit of contradiction" (on the notion of "leading to a logical conclusion," and thus putting an end to debate) is from 1640s. Related: Conclusiveness.