Consider the following premises. For all x_17, x_17 is happy or x_17 will sleep. For all x_17, if x_17 writes a letter, then x_17 is not driving a car. There is at least one x_17 for which x_17 will sleep if and only if x_17 will drive a car. For all x_17, x_17 is not happy. Can we infer the following from them? There is at least one x_17 for which x_17 will not write a letter.
 From the fact that there is at least one x_17 for which x_17 will sleep if and only if x_17 will drive a car we can infer that there is at least one x_17 for which if x_17 sleeps, then x_17 is driving a car. From the fact that for all x_17, x_17 is happy or x_17 will sleep, and that for all x_17, x_17 is not happy we can infer that for all x_17, x_17 will sleep. From the fact that there is at least one x_17 for which if x_17 sleeps, then x_17 is driving a car, and that for all x_17, x_17 will sleep we can infer that there is at least one x_17 for which x_17 will drive a car. Finally, from the fact that for all x_17, if x_17 writes a letter, then x_17 is not driving a car, and that there is at least one x_17 for which x_17 will drive a car we can infer that there is at least one x_17 for which x_17 will not write a letter. Therefore, the answer is yes.