Translate the following inference to logic notation: For all x, x_6 is a soldier. For all x, x_6 will play a game or x_6 is a bartender. For all x, x_6 will not play a game. For all x, if x_6 were a soldier, then x_6 is working. Therefore for all x, x_6 will work and x_6 is a bartender.
forall x: P(x). forall x: Q(x) or R(x). forall x: ~Q(x). forall x: P(x) -> S(x). Therefore forall x: S(x) and R(x).