Consider the following premises. For all x_9, x_9 will not listen to a song. There is at least one x_9 for which x_9 will go running if and only if x_9 is a police officer. For all x_9, x_9 will go running if and only if x_9 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is a police officer.
 From the fact that for all x_9, x_9 will go running if and only if x_9 will listen to a song, and that for all x_9, x_9 will not listen to a song we can infer that for all x_9, x_9 will not go running via universal biconditional elimination. From the fact that there is at least one x_9 for which x_9 will go running if and only if x_9 is a police officer we can infer that there is at least one x_9 for which if x_9 were a police officer, then x_9 is running via existential biconditional elimination. Finally, from the fact that there is at least one x_9 for which if x_9 were a police officer, then x_9 is running, and that for all x_9, x_9 will not go running we can infer that there is at least one x_9 for which x_9 is not a police officer via existential modus tollens, which contradicts that For all x_9, x_9 is a police officer. Therefore, the answer is no.