Translate the following inference to logic notation: For all x, if x_5 were an astronaut, then x_5 is running. For all x, x_5 will listen to a song if and only if x_5 will write a letter. For all x, if x_5 writes a letter, then x_5 is an astronaut. For all x, x_5 will not go running. Therefore for all x, x_5 will not listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) <-> S(x). forall x: S(x) -> P(x). forall x: ~Q(x). Therefore forall x: ~R(x).