Translate the following inference to logic notation: For all x, if z_1 makes tea, then z_1 is playing a game. There is at least one x for which if z_1 listens to a song, then z_1 is a police officer. For all x, z_1 will not play a game. For all x, z_1 is a police officer if and only if z_1 will make tea. For all x, if z_1 were a police officer, then z_1 is listening to a song. Therefore there is at least one x for which z_1 will not listen to a song.
forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: ~Q(x). forall x: S(x) <-> P(x). forall x: S(x) -> R(x). Therefore exists x: ~R(x).