Translate the following inference to logic notation: For all x, if x_9 were a bartender, then x_9 is an office clerk. For all x, x_9 is not an astronaut. There is at least one x for which x_9 is an office clerk if and only if x_9 is an astronaut. Therefore there is at least one x for which x_9 is not a bartender.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: Q(x) <-> R(x). Therefore exists x: ~P(x).