Consider the following premises. For all x_8, x_8 will not work. There is at least one x_8 for which x_8 will listen to a song if and only if x_8 will go running. For all x_8, x_8 will work if and only if x_8 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will not go running.
 From the fact that for all x_8, x_8 will work if and only if x_8 will listen to a song, and that for all x_8, x_8 will not work we can infer that for all x_8, x_8 will not listen to a song via universal biconditional elimination. From the fact that there is at least one x_8 for which x_8 will listen to a song if and only if x_8 will go running we can infer that there is at least one x_8 for which if x_8 goes running, then x_8 is listening to a song via existential biconditional elimination. Finally, from the fact that there is at least one x_8 for which if x_8 goes running, then x_8 is listening to a song, and that for all x_8, x_8 will not listen to a song we can infer that there is at least one x_8 for which x_8 will not go running via existential modus tollens. Therefore, the answer is yes.