Translate the following inference to logic notation: For all x, if x_5 listens to a song, then x_5 is a doctor. For all x, if x_5 were a scientist, then x_5 is sleeping. For all x, if x_5 were a doctor, then x_5 is a scientist. There is at least one x for which if x_5 sleeps, then x_5 is a server. Therefore there is at least one x for which if x_5 listens to a song, then x_5 is a server.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). exists x: S(x) -> T(x). Therefore exists x: P(x) -> T(x).