Translate the following inference to logic notation: For all x, x_12 is fast if and only if x_12 will play squash. For all x, if x_12 were an astronaut, then x_12 is listening to a song. For all x, if x_12 were fast, then x_12 is an astronaut. For all x, x_12 will play squash. Therefore for all x, x_12 will listen to a song.
forall x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: P(x) -> R(x). forall x: Q(x). Therefore forall x: S(x).