Translate the following inference to logic notation: There is at least one x for which if x_1 were a nurse, then x_1 is a doctor. For all x, if x_1 were a taxi driver, then x_1 is a doctor. For all x, x_1 will not sleep or x_1 is a nurse. For all x, x_1 will sleep or x_1 is a taxi driver. Therefore there is at least one x for which x_1 is a doctor.
exists x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: ~S(x) or P(x). forall x: S(x) or R(x). Therefore exists x: Q(x).