Translate the following inference to logic notation: For all x, x_4 will not listen to a song. There is at least one x for which if x_4 listens to a song, then x_4 is a poet. For all x, if x_4 were a server, then x_4 is listening to a song. For all x, if x_4 were a poet, then x_4 is a server. Therefore there is at least one x for which x_4 is not a server.
forall x: ~P(x). exists x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: ~R(x).