Translate the following inference to logic notation: For all x, if x_10 were an astronaut, then x_10 is cooking. For all x, if x_10 cooks, then x_10 is a server. For all x, if x_10 were a server, then x_10 is rich. There is at least one x for which x_10 will not cook. For all x, if x_10 were rich, then x_10 is an astronaut. Therefore there is at least one x for which x_10 is not a server.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). exists x: ~Q(x). forall x: S(x) -> P(x). Therefore exists x: ~R(x).