Consider the following premises. Charles is not a mechanic. For all x_3, if x_3 sleeps, then x_3 is driving a car. For all x_3, if x_3 drives a car, then x_3 is a mechanic. Charles is a mechanic if and only if Charles is sleeping. Can we infer the following from them? Charles is not sleeping.
 From the fact that for all x_3, if x_3 sleeps, then x_3 is driving a car, and that for all x_3, if x_3 drives a car, then x_3 is a mechanic we can infer that for all x_3, if x_3 sleeps, then x_3 is a mechanic. From the fact that for all x_3, if x_3 sleeps, then x_3 is a mechanic we can infer that if Charles sleeps, then Charles is a mechanic. From the fact that Charles is a mechanic if and only if Charles is sleeping we can infer that if Charles were a mechanic, then Charles is sleeping. From the fact that if Charles sleeps, then Charles is a mechanic, and that if Charles were a mechanic, then Charles is sleeping we can infer that Charles is sleeping if and only if Charles is a mechanic. Finally, from the fact that Charles is sleeping if and only if Charles is a mechanic, and that Charles is not a mechanic we can infer that Charles is not sleeping. Therefore, the answer is yes.