Translate the following inference to logic notation: For all x, if x_11 were a police officer, then x_11 is listening to a song. For all x, x_11 will play tennis if and only if x_11 is a police officer. There is at least one x for which if x_11 plays a game, then x_11 is playing tennis. For all x, if x_11 listens to a song, then x_11 is an office clerk. Therefore there is at least one x for which if x_11 plays a game, then x_11 is an office clerk.
forall x: P(x) -> Q(x). forall x: R(x) <-> P(x). exists x: S(x) -> R(x). forall x: Q(x) -> T(x). Therefore exists x: S(x) -> T(x).