Translate the following inference to logic notation: For all x, x_9 is excited if and only if x_9 is a server. There is at least one x for which if x_9 were a server, then x_9 is a lawyer. For all x, x_9 will sleep if and only if x_9 is excited. For all x, x_9 is not a lawyer. Therefore there is at least one x for which x_9 will not sleep.
forall x: P(x) <-> Q(x). exists x: Q(x) -> R(x). forall x: S(x) <-> P(x). forall x: ~R(x). Therefore exists x: ~S(x).