Translate the following inference to logic notation: For all x, if x_9 climbs a mountain, then x_9 is writing a letter. For all x, x_9 will write a letter or x_9 will drive a car. For all x, if x_9 drives a car, then x_9 is climbing a mountain. For all x, if x_9 writes a letter, then x_9 is climbing a mountain. There is at least one x for which if x_9 were a carpenter, then x_9 is not climbing a mountain. Therefore there is at least one x for which x_9 is not a carpenter.
forall x: P(x) -> Q(x). forall x: Q(x) or R(x). forall x: R(x) -> P(x). forall x: Q(x) -> P(x). exists x: S(x) -> ~P(x). Therefore exists x: ~S(x).