Consider the following premises. For all x_9, if x_9 plays a game, then x_9 is sad. For all x_9, x_9 will not go running. For all x_9, x_9 will listen to a song if and only if x_9 is sad. For all x_9, if x_9 listens to a song, then x_9 is running. Can we infer the following from them? For all x_9, x_9 will not play a game.
 From the fact that for all x_9, if x_9 listens to a song, then x_9 is running, and that for all x_9, x_9 will not go running we can infer that for all x_9, x_9 will not listen to a song. From the fact that for all x_9, x_9 will listen to a song if and only if x_9 is sad we can infer that for all x_9, if x_9 were sad, then x_9 is listening to a song. From the fact that for all x_9, if x_9 plays a game, then x_9 is sad, and that for all x_9, if x_9 were sad, then x_9 is listening to a song we can infer that for all x_9, if x_9 plays a game, then x_9 is listening to a song. Finally, from the fact that for all x_9, if x_9 plays a game, then x_9 is listening to a song, and that for all x_9, x_9 will not listen to a song we can infer that for all x_9, x_9 will not play a game. Therefore, the answer is yes.