Translate the following inference to logic notation: For all x, x_9 will climb a mountain. There is at least one x for which if x_9 climbs a mountain, then x_9 is listening to a song. For all x, x_9 will not listen to a song. Therefore there is at least one x for which x_9 will play a game.
forall x: P(x). exists x: P(x) -> Q(x). forall x: ~Q(x). Therefore exists x: R(x).