If someone built a gravity-defying flying saucer and said he doesn’t know how he did it, we might consider him a genius but not “intelligent.” The criteria by which we determine someone to be “intelligent” is use of logic. Use of logic is “intelligent” not because we can prove this claim, but because we defined “intelligence” as such.
In the split between the mind and the body, the former is seen as the intelligent part and the latter the dumb part, but the truly intelligent part is actually the body. It can convert matters into energy. It can move fluidly and efficiently. It can heal itself from cuts, bruises, and scrapes. It can fight pathogens. And, it can reproduce itself. The mind can comprehend only a fraction of what the body can do.