Consider the following premises. There is at least one x_7 for which x_7 will listen to a song. For all x_7, x_7 is a soldier. For all x_7, x_7 is a soldier if and only if x_7 will go running. Can we infer the following from them? There is at least one x_7 for which x_7 will go running and x_7 will listen to a song.
 From the fact that for all x_7, x_7 is a soldier if and only if x_7 will go running we can infer that for all x_7, if x_7 were a soldier, then x_7 is running. From the fact that for all x_7, if x_7 were a soldier, then x_7 is running, and that for all x_7, x_7 is a soldier we can infer that for all x_7, x_7 will go running. Finally, from the fact that for all x_7, x_7 will go running, and that there is at least one x_7 for which x_7 will listen to a song we can infer that there is at least one x_7 for which x_7 will go running and x_7 will listen to a song. Therefore, the answer is yes.