Translate the following inference to logic notation: For all x, x_3 will listen to a song if and only if x_3 is an artist. There is at least one x for which x_3 is an artist or x_3 is a server. For all x, x_3 will not listen to a song. Therefore there is at least one x for which x_3 is a server.
forall x: P(x) <-> Q(x). exists x: Q(x) or R(x). forall x: ~P(x). Therefore exists x: R(x).