Translate the following inference to logic notation: For all x, if x_6 goes running, then x_6 is fast. For all x, if x_6 were fast, then x_6 is happy. There is at least one x for which x_6 is a politician if and only if x_6 is happy. Therefore there is at least one x for which if x_6 goes running, then x_6 is a politician.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: S(x) <-> R(x). Therefore exists x: P(x) -> S(x).