Translate the following inference to logic notation: There is at least one x for which x_7 is a soldier. For all x, x_7 is a soldier or x_7 will not play squash. For all x, if x_7 were a soldier, then x_7 is playing squash. Therefore there is at least one x for which x_7 will play squash.
exists x: P(x). forall x: P(x) or ~Q(x). forall x: P(x) -> Q(x). Therefore exists x: Q(x).