Translate the following inference to logic notation: For all x, if x_17 were a politician, then x_17 is sleeping. For all x, x_17 will not go running. There is at least one x for which if x_17 sleeps, then x_17 is running. For all x, if x_17 sleeps, then x_17 is a politician. For all x, x_17 is excited if and only if x_17 is a politician. Therefore there is at least one x for which x_17 is not excited.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: Q(x) -> R(x). forall x: Q(x) -> P(x). forall x: S(x) <-> P(x). Therefore exists x: ~S(x).