Translate the following inference to logic notation: For all x, if x_8 were fast, then x_8 is an astronaut. For all x, x_8 will play a game. For all x, if x_8 plays a game, then x_8 is a carpenter. For all x, x_8 is sad or x_8 is fast. For all x, if x_8 were sad, then x_8 is an astronaut. Therefore for all x, x_8 is a carpenter and x_8 is an astronaut.
forall x: P(x) -> Q(x). forall x: R(x). forall x: R(x) -> S(x). forall x: T(x) or P(x). forall x: T(x) -> Q(x). Therefore forall x: S(x) and Q(x).