Translate the following inference to logic notation: For all x, x_7 will go running. For all x, if x_7 were fast, then x_7 is not running. There is at least one x for which x_7 is a bartender if and only if x_7 is fast. Therefore there is at least one x for which x_7 is not a bartender.
forall x: P(x). forall x: Q(x) -> ~P(x). exists x: R(x) <-> Q(x). Therefore exists x: ~R(x).