Translate the following inference to logic notation: There is at least one x for which if x_3 were a soldier, then x_3 is a writer. For all x, if x_3 were a writer, then x_3 is fast. For all x, if x_3 were fast, then x_3 is a writer. For all x, x_3 is an astronaut. For all x, if x_3 were an astronaut, then x_3 is fast. Therefore there is at least one x for which x_3 is a writer.
exists x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> Q(x). forall x: S(x). forall x: S(x) -> R(x). Therefore exists x: Q(x).