Translate the following inference to logic notation: For all x, x_9 is not a soldier. For all x, if x_9 were a soldier, then x_9 is a poet. There is at least one x for which if x_9 were a poet, then x_9 is a soldier. For all x, if x_9 listens to a song, then x_9 is a poet. Therefore there is at least one x for which x_9 will not listen to a song.
forall x: ~P(x). forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: R(x) -> Q(x). Therefore exists x: ~R(x).