Consider the following premises. For all x_4, x_4 will not go running. For all x_4, x_4 will go running or x_4 will not listen to a song. There is at least one x_4 for which if x_4 goes running, then x_4 is listening to a song. Can we infer the following from them? There is at least one x_4 for which x_4 will not listen to a song.
 From the fact that for all x_4, x_4 will go running or x_4 will not listen to a song we can infer that for all x_4, if x_4 listens to a song, then x_4 is running. From the fact that there is at least one x_4 for which if x_4 goes running, then x_4 is listening to a song, and that for all x_4, if x_4 listens to a song, then x_4 is running we can infer that there is at least one x_4 for which x_4 will go running if and only if x_4 will listen to a song. Finally, from the fact that there is at least one x_4 for which x_4 will go running if and only if x_4 will listen to a song, and that for all x_4, x_4 will not go running we can infer that there is at least one x_4 for which x_4 will not listen to a song. Therefore, the answer is yes.