Consider the following premises. For all x_9, x_9 will not play tennis. For all x_9, x_9 will play tennis if and only if x_9 is an office clerk. There is at least one x_9 for which if x_9 cooks, then x_9 is an office clerk. For all x_9, if x_9 plays tennis, then x_9 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will not cook.
 From the fact that for all x_9, x_9 will play tennis if and only if x_9 is an office clerk we can infer that for all x_9, if x_9 were an office clerk, then x_9 is playing tennis via universal biconditional elimination. From the fact that for all x_9, if x_9 plays tennis, then x_9 is an office clerk, and that for all x_9, if x_9 were an office clerk, then x_9 is playing tennis we can infer that for all x_9, x_9 will play tennis if and only if x_9 is an office clerk via universal biconditional introduction. From the fact that for all x_9, x_9 will play tennis if and only if x_9 is an office clerk, and that for all x_9, x_9 will not play tennis we can infer that for all x_9, x_9 is not an office clerk via universal biconditional elimination. Finally, from the fact that there is at least one x_9 for which if x_9 cooks, then x_9 is an office clerk, and that for all x_9, x_9 is not an office clerk we can infer that there is at least one x_9 for which x_9 will not cook via existential modus tollens. Therefore, the answer is yes.