I think the human/computer dichotomy you set up should be extended to a human/mathematician/computer trichotomy, just because a substantial portion of "mathematical maturity" is about learning to think like a computer, in your sense.

Anyway I've just put that in place to try and shore up my example. It seems that humans read "let's say we have X and Y..." and automatically take the extra step of assuming X and Y are unequal. Computers wouldn't bother to take this extra step. Mathematicians, or at least I myself, split into the X=Y and X$\neq $Y cases but try to obviate that split when writing down a proof.