Translate the following inference to logic notation: For all x, x_12 will take a plane. For all x, if x_12 sleeps, then x_12 is a sailor. There is at least one x for which x_12 will sleep or x_12 is a bartender. For all x, x_12 is a bartender if and only if x_12 is a sailor. Therefore there is at least one x for which x_12 is a sailor and x_12 will take a plane.
forall x: P(x). forall x: Q(x) -> R(x). exists x: Q(x) or S(x). forall x: S(x) <-> R(x). Therefore exists x: R(x) and P(x).