Consider the following premises. For all x_3, x_3 will drive a car if and only if x_3 will work. There is at least one x_3 for which x_3 will not sleep. For all x_3, x_3 will drive a car if and only if x_3 will sleep. For all x_3, if x_3 drives a car, then x_3 is working. Can we infer the following from them? For all x_3, x_3 will work.
 From the fact that for all x_3, x_3 will drive a car if and only if x_3 will work we can infer that for all x_3, if x_3 works, then x_3 is driving a car. From the fact that for all x_3, x_3 will drive a car if and only if x_3 will sleep, and that there is at least one x_3 for which x_3 will not sleep we can infer that there is at least one x_3 for which x_3 will not drive a car. From the fact that for all x_3, if x_3 drives a car, then x_3 is working, and that for all x_3, if x_3 works, then x_3 is driving a car we can infer that for all x_3, x_3 will drive a car if and only if x_3 will work. Finally, from the fact that for all x_3, x_3 will drive a car if and only if x_3 will work, and that there is at least one x_3 for which x_3 will not drive a car we can infer that there is at least one x_3 for which x_3 will not work, which contradicts that For all x_3, x_3 will work. Therefore, the answer is no.