Consider the following premises. For all x_7, if x_7 were an artist, then x_7 is running. For all x_7, x_7 is a writer. For all x_7, x_7 will go running if and only if x_7 is an artist. For all x_7, if x_7 were an artist, then x_7 is not a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not go running.
 From the fact that for all x_7, if x_7 were an artist, then x_7 is not a writer, and that for all x_7, x_7 is a writer we can infer that for all x_7, x_7 is not an artist via universal modus tollens. From the fact that for all x_7, x_7 will go running if and only if x_7 is an artist we can infer that for all x_7, if x_7 goes running, then x_7 is an artist via universal biconditional elimination. From the fact that for all x_7, if x_7 were an artist, then x_7 is running, and that for all x_7, if x_7 goes running, then x_7 is an artist we can infer that for all x_7, x_7 is an artist if and only if x_7 will go running via universal biconditional introduction. Finally, from the fact that for all x_7, x_7 is an artist if and only if x_7 will go running, and that for all x_7, x_7 is not an artist we can infer that for all x_7, x_7 will not go running via universal biconditional elimination. Therefore, the answer is yes.