Translate the following inference to logic notation: For all x, x_13 is not a politician. For all x, if x_13 were fast, then x_13 is a politician. For all x, if x_13 were a politician, then x_13 is climbing a mountain. There is at least one x for which if x_13 climbs a mountain, then x_13 is a doctor. For all x, if x_13 were a doctor, then x_13 is fast. Therefore there is at least one x for which x_13 is not a doctor.
forall x: ~P(x). forall x: Q(x) -> P(x). forall x: P(x) -> R(x). exists x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: ~S(x).