Translate the following inference to logic notation: For all x, y will not listen to a song. For all x, if y were a server, then y is playing a game. For all x, if y listens to a song, then y is a server. There is at least one x for which if y plays a game, then y is listening to a song. Therefore there is at least one x for which y is not a server.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: P(x) -> Q(x). exists x: R(x) -> P(x). Therefore exists x: ~Q(x).