Translate the following inference to logic notation: For all x, x_13 will work or x_13 is not a doctor. There is at least one x for which if x_13 were a doctor, then x_13 is running. For all x, x_13 will not work. For all x, x_13 will go running if and only if x_13 is a doctor. Therefore there is at least one x for which x_13 will not go running.
forall x: P(x) or ~Q(x). exists x: Q(x) -> R(x). forall x: ~P(x). forall x: R(x) <-> Q(x). Therefore exists x: ~R(x).