Before HAL starts killing the crew, he seems to visibly cheat at chess when playing against Frank Poole. Why does he do so? If he has been programmed not to lie, this should be impossible.
Frank: Anyway, Queen takes Pawn. Uh... okay.
HAL: Bishop takes Knight's Pawn.
Frank: Uh, lovely move. Uh... Rook to King one.
HAL: I'm sorry, Frank. I think you missed it. Queen to Bishop three, Bishop takes Queen, Knight takes Bishop. Mate.
Frank: Uh... yeah. It looks like you're right. I resign.
HAL: Thank you for a very enjoyable game.
Frank: Yeah, thank you.
But the moves HAL suggests will mate Frank are actually wrong. HAL should have said “Queen to Bishop six”.