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