Translate the following inference to logic notation: For all x, x_5 is a soldier. For all x, if x_5 were a soldier, then x_5 is fast. There is at least one x for which if x_5 drinks water, then x_5 is happy. For all x, if x_5 were fast, then x_5 is drinking water. Therefore there is at least one x for which x_5 is happy.
forall x: P(x). forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: Q(x) -> R(x). Therefore exists x: S(x).