Consider the following premises. For all y_3, y_3 will listen to a song if and only if y_3 will play a game. For all y_3, if y_3 plays a game, then y_3 is an office clerk. For all y_3, if y_3 were an office clerk, then y_3 is playing a game. There is at least one y_3 for which y_3 is not an office clerk. Can we infer the following from them? There is at least one y_3 for which y_3 will not listen to a song.
 From the fact that for all y_3, if y_3 were an office clerk, then y_3 is playing a game, and that for all y_3, if y_3 plays a game, then y_3 is an office clerk we can infer that for all y_3, y_3 is an office clerk if and only if y_3 will play a game. From the fact that for all y_3, y_3 is an office clerk if and only if y_3 will play a game, and that there is at least one y_3 for which y_3 is not an office clerk we can infer that there is at least one y_3 for which y_3 will not play a game. Finally, from the fact that for all y_3, y_3 will listen to a song if and only if y_3 will play a game, and that there is at least one y_3 for which y_3 will not play a game we can infer that there is at least one y_3 for which y_3 will not listen to a song. Therefore, the answer is yes.