Translate the following inference to logic notation: For all x, if x_5 were excited, then x_5 is a carpenter. For all x, if x_5 plays a game, then x_5 is a musician. For all x, if x_5 were a musician, then x_5 is excited. There is at least one x for which if x_5 were a carpenter, then x_5 is an astronaut. Therefore there is at least one x for which if x_5 plays a game, then x_5 is an astronaut.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). exists x: Q(x) -> T(x). Therefore exists x: R(x) -> T(x).