Translate the following inference to logic notation: For all x, x_8 is a soldier or x_8 is excited. There is at least one x for which x_8 will drive a car. For all x, if x_8 were a soldier, then x_8 is fast. For all x, x_8 is fast if and only if x_8 is excited. Therefore there is at least one x for which x_8 will drive a car and x_8 is fast.
forall x: P(x) or Q(x). exists x: R(x). forall x: P(x) -> S(x). forall x: S(x) <-> Q(x). Therefore exists x: R(x) and S(x).