Translate the following inference to logic notation: For all x, x_5 is a bartender if and only if x_5 will sleep. For all x, if x_5 sleeps, then x_5 is playing a game. For all x, if x_5 drinks water, then x_5 is a bartender. For all x, x_5 will not play a game. Therefore for all x, x_5 will not drink water.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). forall x: ~R(x). Therefore forall x: ~S(x).