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.