Translate the following inference to logic notation: For all x, if x_8 were a cashier, then x_8 is an office clerk. For all x, x_8 is not a cashier. For all x, if x_8 plays tennis, then x_8 is a cashier. For all x, if x_8 climbs a mountain, then x_8 is playing tennis. There is at least one x for which if x_8 were an office clerk, then x_8 is climbing a mountain. Therefore there is at least one x for which x_8 will not climb a mountain.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: R(x) -> P(x). forall x: S(x) -> R(x). exists x: Q(x) -> S(x). Therefore exists x: ~S(x).