Translate the following inference to logic notation: For all x, x_3 is happy and x_3 is a police officer. There is at least one x for which if x_3 were a soldier, then x_3 is not happy. Therefore there is at least one x for which x_3 is not a soldier.
forall x: P(x) and Q(x). exists x: R(x) -> ~P(x). Therefore exists x: ~R(x).