Translate the following inference to logic notation: For all x, if x_9 writes a letter, then x_9 is climbing a mountain. For all x, if x_9 climbs a mountain, then x_9 is writing a letter. For all x, x_9 will climb a mountain or x_9 will make tea. For all x, if x_9 writes a letter, then x_9 is a janitor. For all x, if x_9 makes tea, then x_9 is writing a letter. Therefore for all x, x_9 is a janitor.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) or R(x). forall x: P(x) -> S(x). forall x: R(x) -> P(x). Therefore forall x: S(x).