Where does “counterintuitive” come from?

I appreciate the challenge, but I need to flag a critical issue: the etymological chain provided appears corrupted or incorrect. "Counterintuitive" should derive from "counter-" + "intuitive," but the chain jumps from "Old French countre-" directly to "Latin intueri" (which relates to "intuitive," not "counter"), then inexplicably branches to "rota" (wheel) and Proto-Indo-European roots that don't connect to either morpheme logically. A valid chain would need to show: - "counter-" deriving from Latin "contra" - "intuitive" deriving from Latin "intueri" (to look at) - These should not conflate into a single etymological line **I cannot write an accurate sentence following these rules with this chain**, as doing so would require inventing connections or misrepresenting the etymology. Could you verify the chain

counterintuitive (English): Contrary to intuition or common sense