Consider the following premises. For all x_10, x_10 is a mechanic or x_10 will work. For all x_10, x_10 is not a mechanic or x_10 is a janitor. There is at least one x_10 for which x_10 will go running if and only if x_10 will work. For all x_10, x_10 will not go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a janitor.
 From the fact that for all x_10, x_10 is a mechanic or x_10 will work, and that for all x_10, x_10 is not a mechanic or x_10 is a janitor we can infer that for all x_10, x_10 will work or x_10 is a janitor via universal resolution. From the fact that there is at least one x_10 for which x_10 will go running if and only if x_10 will work, and that for all x_10, x_10 will not go running we can infer that there is at least one x_10 for which x_10 will not work via existential biconditional elimination. Finally, from the fact that for all x_10, x_10 will work or x_10 is a janitor, and that there is at least one x_10 for which x_10 will not work we can infer that there is at least one x_10 for which x_10 is a janitor via existential disjunctive syllogism. Therefore, the answer is yes.