Translate the following inference to logic notation: If Susan were an astronaut, then it is cloudy. For all x, if z were an astronaut, then z is climbing a mountain. If it is cloudy, then Susan is an astronaut. For all x, z will not climb a mountain. Therefore it is not cloudy.
P(a) -> p. forall x: P(x) -> Q(x). p -> P(a). forall x: ~Q(x). Therefore ~p.