Consider the following premises. For all x_3, x_3 will cook if and only if x_3 will listen to a song. For all x_3, x_3 is a cashier. There is at least one x_3 for which if x_3 cooks, then x_3 is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will listen to a song.
 From the fact that there is at least one x_3 for which if x_3 cooks, then x_3 is not a cashier, and that for all x_3, x_3 is a cashier we can infer that there is at least one x_3 for which x_3 will not cook via existential modus tollens. Finally, from the fact that for all x_3, x_3 will cook if and only if x_3 will listen to a song, and that there is at least one x_3 for which x_3 will not cook we can infer that there is at least one x_3 for which x_3 will not listen to a song via existential biconditional elimination, which contradicts that For all x_3, x_3 will listen to a song. Therefore, the answer is no.