Translate the following inference to logic notation: For all x, if x_17 were an office clerk, then x_17 is not a server. For all x, x_17 is a soldier or x_17 is happy. For all x, x_17 is not a soldier. There is at least one x for which x_17 is happy if and only if x_17 is a server. Therefore there is at least one x for which x_17 is not an office clerk.
forall x: P(x) -> ~Q(x). forall x: R(x) or S(x). forall x: ~R(x). exists x: S(x) <-> Q(x). Therefore exists x: ~P(x).