Translate the following inference to logic notation: For all x, x_6 will go running if and only if x_6 is happy. There is at least one x for which if x_6 goes running, then x_6 is happy. Therefore there is at least one x for which if x_6 were happy, then x_6 is running.
forall x: P(x) <-> Q(x). exists x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).