Translate the following inference to logic notation: There is at least one x for which if x_11 works, then x_11 is playing tennis. For all x, if x_11 sleeps, then x_11 is playing tennis. For all x, if x_11 plays tennis, then x_11 is sleeping. For all x, x_11 is a police officer. For all x, if x_11 were a police officer, then x_11 is sleeping. Therefore there is at least one x for which x_11 will play tennis.
exists x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x). forall x: S(x) -> R(x). Therefore exists x: Q(x).