Translate the following inference to logic notation: For all x, if x_8 were an astronaut, then x_8 is a taxi driver. There is at least one x for which if x_8 were a taxi driver, then x_8 is playing tennis. For all x, x_8 is a police officer if and only if x_8 will play tennis. For all x, x_8 is not a police officer. For all x, if x_8 plays tennis, then x_8 is an astronaut. Therefore there is at least one x for which x_8 is not an astronaut.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: ~S(x). forall x: R(x) -> P(x). Therefore exists x: ~P(x).