Translate the following inference to logic notation: For all x, if x_12 goes running, then x_12 is rich. There is at least one x for which x_12 will climb a mountain. For all x, if x_12 climbs a mountain, then x_12 is running. For all x, if x_12 were a police officer, then x_12 is not rich. Therefore there is at least one x for which x_12 is not a police officer.
forall x: P(x) -> Q(x). exists x: R(x). forall x: R(x) -> P(x). forall x: S(x) -> ~Q(x). Therefore exists x: ~S(x).