Translate the following inference to logic notation: For all x, if x_12 drinks water, then x_12 is a server. For all x, x_12 is not a server. For all x, if x_12 cooks, then x_12 is playing tennis. There is at least one x for which if x_12 were a server, then x_12 is drinking water. For all x, if x_12 drinks water, then x_12 is cooking. For all x, if x_12 plays tennis, then x_12 is drinking water. Therefore there is at least one x for which x_12 will not play tennis.
forall x: P(x) -> Q(x). forall x: ~Q(x). forall x: R(x) -> S(x). exists x: Q(x) -> P(x). forall x: P(x) -> R(x). forall x: S(x) -> P(x). Therefore exists x: ~S(x).