Translate the following inference to logic notation: For all x, if x_11 were a doctor, then x_11 is working. For all x, if x_11 works, then x_11 is a police officer. For all x, x_11 is excited or x_11 is not a police officer. There is at least one x for which if x_11 were a janitor, then x_11 is a doctor. Therefore there is at least one x for which if x_11 were a janitor, then x_11 is excited.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) or ~R(x). exists x: T(x) -> P(x). Therefore exists x: T(x) -> S(x).