Consider the following premises. For all x_15, x_15 will sleep or x_15 is a cashier. If William writes a letter, then Jessica is not driving a car. For all x_15, x_15 will not sleep or x_15 is poor. For all x_15, if x_15 were poor, then x_15 is driving a car. For all x_15, if x_15 were a cashier, then x_15 is driving a car. Can we infer the following from them? William is not writing a letter.
 From the fact that for all x_15, x_15 will sleep or x_15 is a cashier, and that for all x_15, x_15 will not sleep or x_15 is poor we can infer that for all x_15, x_15 is a cashier or x_15 is poor. From the fact that for all x_15, if x_15 were a cashier, then x_15 is driving a car, that for all x_15, if x_15 were poor, then x_15 is driving a car, and that for all x_15, x_15 is a cashier or x_15 is poor we can infer that for all x_15, x_15 will drive a car. From the fact that for all x_15, x_15 will drive a car we can infer that Jessica is driving a car. Finally, from the fact that if William writes a letter, then Jessica is not driving a car, and that Jessica is driving a car we can infer that William is not writing a letter. Therefore, the answer is yes.