Consider the following premises. For all x_12, x_12 is a server if and only if x_12 will go running. There is at least one x_12 for which x_12 will go running if and only if x_12 is excited. For all x_12, x_12 is not excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 is a server.
 From the fact that there is at least one x_12 for which x_12 will go running if and only if x_12 is excited we can infer that there is at least one x_12 for which if x_12 goes running, then x_12 is excited via existential biconditional elimination. From the fact that there is at least one x_12 for which if x_12 goes running, then x_12 is excited, and that for all x_12, x_12 is not excited we can infer that there is at least one x_12 for which x_12 will not go running via existential modus tollens. Finally, from the fact that for all x_12, x_12 is a server if and only if x_12 will go running, and that there is at least one x_12 for which x_12 will not go running we can infer that there is at least one x_12 for which x_12 is not a server via existential biconditional elimination, which contradicts that For all x_12, x_12 is a server. Therefore, the answer is no.