Translate the following inference to logic notation: For all x, if x_6 were a writer, then x_6 is cooking. For all x, x_6 will sleep or x_6 is a writer. For all x, if x_6 cooks, then x_6 is rich. There is at least one x for which x_6 is rich or x_6 will not sleep. Therefore there is at least one x for which x_6 is rich.
forall x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: Q(x) -> S(x). exists x: S(x) or ~R(x). Therefore exists x: S(x).