Translate the following inference to logic notation: For all x, if x_16 climbs a mountain, then x_16 is a nurse. For all x, if x_16 listens to a song, then x_16 is poor. There is at least one x for which x_16 will listen to a song if and only if x_16 is a nurse. For all x, if x_16 were poor, then x_16 is climbing a mountain. Therefore there is at least one x for which if x_16 were poor, then x_16 is a nurse.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: R(x) <-> Q(x). forall x: S(x) -> P(x). Therefore exists x: S(x) -> Q(x).