Translate the following inference to logic notation: For all x, if x_12 were a soldier, then x_12 is a janitor. There is at least one x for which if x_12 were an astronaut, then x_12 is a soldier. For all x, if x_12 were a janitor, then x_12 is a soldier. For all x, if x_12 were a soldier, then x_12 is an astronaut. Therefore there is at least one x for which if x_12 were a janitor, then x_12 is an astronaut.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: Q(x) -> P(x). forall x: P(x) -> R(x). Therefore exists x: Q(x) -> R(x).