Translate the following inference to logic notation: For all x, if x_11 sleeps, then x_11 is a doctor. For all x, if x_11 works, then x_11 is sleeping. For all x, if x_11 were a nurse, then x_11 is working. There is at least one x for which x_11 is a nurse or x_11 is a doctor. For all x, x_11 will sleep or x_11 is not a doctor. Therefore there is at least one x for which x_11 will sleep.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) -> R(x). exists x: S(x) or Q(x). forall x: P(x) or ~Q(x). Therefore exists x: P(x).