Translate the following inference to logic notation: For all x, x_12 is a cashier. There is at least one x for which if x_12 were a cashier, then x_12 is playing squash. For all x, x_12 is fast. For all x, if x_12 plays squash, then x_12 is a bartender. Therefore there is at least one x for which x_12 is fast.
forall x: P(x). exists x: P(x) -> Q(x). forall x: R(x). forall x: Q(x) -> S(x). Therefore exists x: R(x).