Consider the following premises. There is at least one x_7 for which x_7 will not work or x_7 will go running. For all x_7, x_7 will work or x_7 will play squash. For all x_7, if x_7 plays squash, then x_7 is a janitor. For all x_7, x_7 is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will go running.
 From the fact that for all x_7, x_7 will work or x_7 will play squash, and that there is at least one x_7 for which x_7 will not work or x_7 will go running we can infer that there is at least one x_7 for which x_7 will play squash or x_7 will go running via existential resolution. From the fact that for all x_7, if x_7 plays squash, then x_7 is a janitor, and that for all x_7, x_7 is not a janitor we can infer that for all x_7, x_7 will not play squash via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 will play squash or x_7 will go running, and that for all x_7, x_7 will not play squash we can infer that there is at least one x_7 for which x_7 will go running via existential disjunctive syllogism. Therefore, the answer is yes.