Translate the following inference to logic notation: For all x, if x_17 writes a letter, then x_17 is cooking. For all x, if x_17 cooks, then x_17 is a janitor. For all x, if x_17 drives a car, then x_17 is writing a letter. There is at least one x for which x_17 is not a janitor. For all x, if x_17 were a janitor, then x_17 is cooking. Therefore there is at least one x for which x_17 will not drive a car.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). exists x: ~R(x). forall x: R(x) -> Q(x). Therefore exists x: ~S(x).