Consider the following premises. There is at least one x_9 for which if x_9 were a writer, then x_9 is an office clerk. For all x_9, x_9 is not an office clerk. For all x_9, x_9 is a writer if and only if x_9 will sleep. For all x_9, x_9 will sleep or x_9 will go 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 go running.
 From the fact that there is at least one x_9 for which if x_9 were a writer, 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 is not a writer via existential modus tollens. From the fact that for all x_9, x_9 is a writer if and only if x_9 will sleep, and that there is at least one x_9 for which x_9 is not a writer we can infer that there is at least one x_9 for which x_9 will not sleep via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will sleep or x_9 will go running, and that there is at least one x_9 for which x_9 will not sleep we can infer that there is at least one x_9 for which x_9 will go running via existential disjunctive syllogism. Therefore, the answer is yes.