Consider the following premises. For all x_5, if x_5 works, then x_5 is not driving a car. There is at least one x_5 for which x_5 will work or x_5 will sleep. For all x_5, x_5 is fast. For all x_5, if x_5 were fast, then x_5 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not sleep.
 From the fact that for all x_5, if x_5 were fast, then x_5 is driving a car, and that for all x_5, x_5 is fast we can infer that for all x_5, x_5 will drive a car via universal modus ponens. From the fact that for all x_5, if x_5 works, then x_5 is not driving a car, and that for all x_5, x_5 will drive a car we can infer that for all x_5, x_5 will not work via universal modus tollens. Finally, from the fact that there is at least one x_5 for which x_5 will work or x_5 will sleep, and that for all x_5, x_5 will not work we can infer that there is at least one x_5 for which x_5 will sleep via existential disjunctive syllogism, which contradicts that For all x_5, x_5 will not sleep. Therefore, the answer is no.