Translate the following inference to logic notation: For all x, if x_1 listens to a song, then x_1 is playing a game. For all x, x_1 is not an artist. There is at least one x for which if x_1 plays a game, then x_1 is an artist. Therefore there is at least one x for which x_1 will not listen to a song.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: Q(x) -> R(x). Therefore exists x: ~P(x).