Consider the following premises. For all z, if z writes a letter, then z is not playing tennis. For all z, if z writes a letter, then z is running. For all z, if z writes a letter, then z is running. For all z, z will play tennis. For all z, if z goes running, then z is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z will go running.
 From the fact that for all z, if z writes a letter, then z is not playing tennis, and that for all z, z will play tennis we can infer that for all z, z will not write a letter via universal modus tollens. From the fact that for all z, if z writes a letter, then z is running, and that for all z, if z goes running, then z is writing a letter we can infer that for all z, z will write a letter if and only if z will go running via universal biconditional introduction. From the fact that for all z, z will write a letter if and only if z will go running we can infer that for all z, if z goes running, then z is writing a letter via universal biconditional elimination. From the fact that for all z, if z goes running, then z is writing a letter, and that for all z, if z writes a letter, then z is running we can infer that for all z, z will go running if and only if z will write a letter via universal biconditional introduction. Finally, from the fact that for all z, z will go running if and only if z will write a letter, and that for all z, z will not write a letter we can infer that for all z, z will not go running via universal biconditional elimination, which contradicts that There is at least one z for which z will go running. Therefore, the answer is no.