Translate the following inference to logic notation: For all x, if x_5 works, then x_5 is taking a plane. For all x, if x_5 takes a plane, then x_5 is climbing a mountain. For all x, x_5 will not climb a mountain. There is at least one x for which x_5 will write a letter if and only if x_5 will work. Therefore there is at least one x for which x_5 will not write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: ~R(x). exists x: S(x) <-> P(x). Therefore exists x: ~S(x).