What reason is there to expect such a thing?
(Not to mention that, proverbs notwithstanding, humans can and do kill cockroaches easily; I wouldn't want the tables to be reversed.)
Reason: Cockroaches and the behavior of humans. We can and do kill individuals and specific groups of individuals. We can't kill all of them, however. If humans can get into space, the lightspeed barrier might let far-flung tribes of "human fundamentalists," to borrow a term from Charles Stross, to survive, though individuals would often be killed and would never stand a chance in a direct conflict with a super AI.
From the last thread:
Meta: