Translate the following inference to logic notation: For all x, x_9 is excited if and only if x_9 will listen to a song. For all x, x_9 is excited. There is at least one x for which x_9 will not listen to a song. Therefore there is at least one x for which x_9 is a server.
forall x: P(x) <-> Q(x). forall x: P(x). exists x: ~Q(x). Therefore exists x: R(x).