Translate the following inference to logic notation: For all x, if x_9 were a carpenter, then x_9 is excited. For all x, x_9 is not a carpenter. For all x, if x_9 were excited, then x_9 is a carpenter. For all x, if x_9 sleeps, then x_9 is a cashier. For all x, if x_9 were a cashier, then x_9 is excited. Therefore for all x, x_9 will not sleep.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: Q(x) -> P(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore forall x: ~R(x).