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