Translate the following inference to logic notation: For all x, if x_6 writes a letter, then x_6 is a police officer. For all x, if x_6 were a police officer, then x_6 is sleeping. For all x, if x_6 sleeps, then x_6 is excited. For all x, if x_6 were excited, then x_6 is writing a letter. Therefore for all x, if x_6 writes a letter, then x_6 is excited.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). Therefore forall x: P(x) -> S(x).