I think you are addressing the wrong problem, with a dash of cleverness, sure.
It is a matter of “how intelligent” not “whether intelligent.” Is there a special word for the intellect of a child? Or animal? Or imbecile? Or average person? Or genius?
Even without quibbling for the ultimate definition of intelligence, we may consider intelligence is scalar with boundary conditions relating to competence or completion.
How many of you got things right the first time? I know I’m intelligent because I don’t give up until I have a satisfying solution, not that I got it right on the first go. And those of us of ”inferior” intelligence huffed and puffed that they couldn’t do it because it was impossible or accepted the fist plausibility without regard to thoroughness.
I would like to point out that most of society accepts “reasons” rather than demonstrating “reasoning” of that thing. One might relegate the old argument of inference vs deduction. Are you intelligent because you found the agreeable conclusion, or identified and correlated all signifying factors?