Translate the following inference to logic notation: For all x, if x_8 climbs a mountain, then x_8 is an astronaut. For all x, if x_8 were an astronaut, then x_8 is working. There is at least one x for which x_8 will climb a mountain. For all x, x_8 will work or x_8 is not fast. Therefore there is at least one x for which x_8 will work.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: P(x). forall x: R(x) or ~S(x). Therefore exists x: R(x).