Consider the following premises. For all x_9, x_9 will not cook. There is at least one x_9 for which if x_9 plays squash, then x_9 is working. For all x_9, x_9 will go running if and only if x_9 will cook. For all x_9, if x_9 works, then x_9 is running. 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 play squash.
 From the fact that for all x_9, x_9 will go running if and only if x_9 will cook, and that for all x_9, x_9 will not cook we can infer that for all x_9, x_9 will not go running via universal biconditional elimination. From the fact that there is at least one x_9 for which if x_9 plays squash, then x_9 is working, and that for all x_9, if x_9 works, then x_9 is running we can infer that there is at least one x_9 for which if x_9 plays squash, then x_9 is running via existential transitivity. Finally, from the fact that there is at least one x_9 for which if x_9 plays squash, then x_9 is running, and that for all x_9, x_9 will not go running we can infer that there is at least one x_9 for which x_9 will not play squash via existential modus tollens. Therefore, the answer is yes.