Consider the following premises. For all x_4, x_4 will drive a car or x_4 is not a scientist. There is at least one x_4 for which if x_4 drives a car, then x_4 is a scientist. Can we infer the following from them? For all x_4, if is not true that x_4 will drive a car if and only if x_4 is a scientist.
 From the fact that for all x_4, x_4 will drive a car or x_4 is not a scientist we can infer that for all x_4, if x_4 were a scientist, then x_4 is driving a car. Finally, from the fact that there is at least one x_4 for which if x_4 drives a car, then x_4 is a scientist, and that for all x_4, if x_4 were a scientist, then x_4 is driving a car we can infer that there is at least one x_4 for which x_4 will drive a car if and only if x_4 is a scientist, which contradicts that For all x_4, if is not true that x_4 will drive a car if and only if x_4 is a scientist. Therefore, the answer is no.