Consider the following premises. For all x_9, if x_9 plays squash, then x_9 is working. For all x_9, if x_9 works, then x_9 is playing squash. There is at least one x_9 for which if x_9 plays squash, then x_9 is not fast. For all x_9, x_9 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will work.
 From the fact that for all x_9, if x_9 works, then x_9 is playing squash, and that for all x_9, if x_9 plays squash, then x_9 is working we can infer that for all x_9, x_9 will work if and only if x_9 will play squash via universal biconditional introduction. From the fact that there is at least one x_9 for which if x_9 plays squash, then x_9 is not fast, and that for all x_9, x_9 is fast we can infer that there is at least one x_9 for which x_9 will not play squash via existential modus tollens. Finally, from the fact that for all x_9, x_9 will work if and only if x_9 will play squash, and that there is at least one x_9 for which x_9 will not play squash we can infer that there is at least one x_9 for which x_9 will not work via existential biconditional elimination, which contradicts that For all x_9, x_9 will work. Therefore, the answer is no.