Translate the following inference to logic notation: For all x, if x_9 were a bartender, then x_9 is a soldier. For all x, if x_9 drinks water, then x_9 is a bartender. For all x, x_9 is a police officer or x_9 will drink water. There is at least one x for which x_9 is a soldier if and only if x_9 is a police officer. Therefore there is at least one x for which x_9 is a soldier.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) or R(x). exists x: Q(x) <-> S(x). Therefore exists x: Q(x).