Consider the following premises. For all x_9, x_9 will cook or x_9 will sleep. For all x_9, if x_9 were an electrician, then x_9 is a janitor. There is at least one x_9 for which if x_9 cooks, then x_9 is driving a car. For all x_9, if x_9 were a janitor, then x_9 is working. For all x_9, if x_9 sleeps, then x_9 is an electrician. For all x_9, if x_9 works, then x_9 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will not drive a car.
 From the fact that for all x_9, if x_9 were a janitor, then x_9 is working, and that for all x_9, if x_9 works, then x_9 is driving a car we can infer that for all x_9, if x_9 were a janitor, then x_9 is driving a car via universal transitivity. From the fact that for all x_9, if x_9 sleeps, then x_9 is an electrician, and that for all x_9, if x_9 were an electrician, then x_9 is a janitor we can infer that for all x_9, if x_9 sleeps, then x_9 is a janitor via universal transitivity. From the fact that for all x_9, if x_9 sleeps, then x_9 is a janitor, and that for all x_9, if x_9 were a janitor, then x_9 is driving a car we can infer that for all x_9, if x_9 sleeps, then x_9 is driving a car via universal transitivity. Finally, from the fact that there is at least one x_9 for which if x_9 cooks, then x_9 is driving a car, that for all x_9, if x_9 sleeps, then x_9 is driving a car, and that for all x_9, x_9 will cook or x_9 will sleep we can infer that there is at least one x_9 for which x_9 will drive a car via existential disjunction elimination, which contradicts that For all x_9, x_9 will not drive a car. Therefore, the answer is no.