There is a joke in science fiction about defeating an evil AI with some sort of paradox, but there has to be a reason for this. I'm aware the the I, Robot series had a story where a rival company's computers were melted down by a paradox, but what's the earliest example in fiction of a rogue intelligence (robot, computer, hologram) being defeated or disabled by a paradox?
I believe the earliest such story was "Liar!" by Isaac Asimov, circa 1941. In the story a mind-reading robot had been created and its unique ability produced unforeseen and unfortunate consequences. Susan Calvin drove the robot insane at the end of the story by forcing the robot to confront an inescapable First Law paradox.
“You can’t tell them,” droned the psychologist slowly, “because that would hurt and you mustn’t hurt. But if you don’t tell them, you hurt, so you must tell them. And if you do, you will hurt and you mustn’t, so you can’t tell them; but if you don’t, you hurt, so you must; but if you do, you hurt, so you mustn’t; but if you don’t, you hurt, so you must; but if you do, you—”
Herbie was up against the wall, and here he dropped to his knees. “Stop!” he shrieked.