Translate the following inference to logic notation: For all x, if x_6 goes running, then x_6 is a politician. For all x, x_6 will go running. For all x, if x_6 were a politician, then y_4 is an astronaut. Therefore there is at least one x for which y_4 is an astronaut.
forall x: P(x) -> Q(x). forall x: P(x). forall x: Q(x) -> R(x). Therefore exists x: R(x).