Translate the following inference to logic notation: For all x, if x_11 were a bartender, then x_11 is an astronaut. There is at least one x for which if x_11 drinks water, then x_11 is an astronaut. For all x, if x_11 were rich, then x_11 is a bartender. For all x, x_11 is a bartender or x_11 will work. For all x, if x_11 were an astronaut, then x_11 is rich. For all x, if x_11 works, then x_11 is drinking water. Therefore there is at least one x for which x_11 is an astronaut.
forall x: P(x) -> Q(x). exists x: R(x) -> Q(x). forall x: S(x) -> P(x). forall x: P(x) or T(x). forall x: Q(x) -> S(x). forall x: T(x) -> R(x). Therefore exists x: Q(x).