Translate the following inference to logic notation: There is at least one x for which if x_5 listens to a song, then x_5 is playing squash. For all x, if x_5 goes running, then x_5 is excited. For all x, if x_5 were excited, then x_5 is listening to a song. For all x, x_5 will go running. Therefore there is at least one x for which x_5 will play squash.
exists x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). forall x: R(x). Therefore exists x: Q(x).