Translate the following inference to logic notation: For all x, if x_3 were happy, then x_3 is listening to a song. For all x, if x_3 climbs a mountain, then x_3 is listening to a song. For all x, x_3 will not make tea or x_3 is happy. There is at least one x for which if x_3 plays a game, then x_3 is climbing a mountain. For all x, x_3 will make tea or x_3 will play a game. Therefore there is at least one x for which x_3 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: ~S(x) or P(x). exists x: T(x) -> R(x). forall x: S(x) or T(x). Therefore exists x: Q(x).