Translate the following inference to logic notation: There is at least one x for which if x_12 plays tennis, then x_12 is working. For all x, if x_12 writes a letter, then x_12 is climbing a mountain. For all x, if x_12 works, then x_12 is writing a letter. For all x, if x_12 writes a letter, then x_12 is playing tennis. For all x, if x_12 climbs a mountain, then x_12 is writing a letter. For all x, x_12 will not climb a mountain. Therefore there is at least one x for which x_12 will not work.
exists x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). forall x: S(x) -> R(x). forall x: ~S(x). Therefore exists x: ~Q(x).