Translate the following inference to logic notation: For all x, x_6 is a poet. For all x, x_6 is a writer. For all x, if x_6 goes running, then x_6 is not a writer. For all x, if x_6 were a poet, then x_6 is sleeping. Therefore for all x, x_6 will not go running.
forall x: P(x). forall x: Q(x). forall x: R(x) -> ~Q(x). forall x: P(x) -> S(x). Therefore forall x: ~R(x).