Translate the following inference to logic notation: There is at least one x for which x_12 is not a soldier or x_12 is a bartender. For all x, if x_12 were an astronaut, then x_12 is a bartender. For all x, x_12 is an astronaut or x_12 is not a server. For all x, if x_12 were a bartender, then x_12 is an astronaut. For all x, x_12 is a soldier or x_12 is a server. Therefore there is at least one x for which x_12 is an astronaut.
exists x: ~P(x) or Q(x). forall x: R(x) -> Q(x). forall x: R(x) or ~S(x). forall x: Q(x) -> R(x). forall x: P(x) or S(x). Therefore exists x: R(x).