Translate the following inference to logic notation: For all x, x_13 is a sailor if and only if x_13 is a cashier. For all x, x_13 is not a sailor. There is at least one x for which if x_13 plays a game, then x_13 is a cashier. For all x, if x_13 were a cashier, then x_13 is a soldier. For all x, x_13 is a soldier if and only if x_13 will play a game. Therefore there is at least one x for which x_13 will not play a game.
forall x: P(x) <-> Q(x). forall x: ~P(x). exists x: R(x) -> Q(x). forall x: Q(x) -> S(x). forall x: S(x) <-> R(x). Therefore exists x: ~R(x).