Translate the following inference to logic notation: For all x, if x_9 goes running, then x_9 is an astronaut. For all x, if x_9 climbs a mountain, then x_9 is running. For all x, x_9 will play a game or x_9 is not a carpenter. For all x, if x_9 plays a game, then x_9 is climbing a mountain. Therefore for all x, if x_9 were a carpenter, then x_9 is an astronaut.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) or ~T(x). forall x: S(x) -> R(x). Therefore forall x: T(x) -> Q(x).