Translate the following inference to logic notation: For all x, if x_6 were a doctor, then x_6 is climbing a mountain. There is at least one x for which if x_6 goes running, then x_6 is not climbing a mountain. For all x, x_6 is a doctor. For all x, x_6 is a musician. Therefore there is at least one x for which x_6 will not go running.
forall x: P(x) -> Q(x). exists x: R(x) -> ~Q(x). forall x: P(x). forall x: S(x). Therefore exists x: ~R(x).