Translate the following inference to logic notation: For all x, x_13 will not sleep. For all x, if x_13 were a soldier, then x_13 is a janitor. For all x, x_13 will play a game if and only if x_13 is a janitor. For all x, if x_13 sleeps, then x_13 is playing a game. For all x, if x_13 plays a game, then x_13 is sleeping. Therefore for all x, x_13 is not a soldier.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: P(x) -> S(x). forall x: S(x) -> P(x). Therefore forall x: ~Q(x).