Translate the following inference to logic notation: For all x, x_9 will not go running. For all x, x_9 is a janitor. There is at least one x for which x_9 will go running if and only if x_9 is a janitor. Therefore there is at least one x for which x_9 is fast.
forall x: ~P(x). forall x: Q(x). exists x: P(x) <-> Q(x). Therefore exists x: R(x).