Consider the following premises. There is at least one x_16 for which x_16 will write a letter if and only if x_16 is a doctor. For all x_16, x_16 will not sleep. For all x_16, x_16 will drive a car if and only if x_16 will sleep. For all x_16, x_16 is a politician if and only if x_16 is a doctor. For all x_16, x_16 will drive a car if and only if x_16 is a politician. Can we infer the following from them? There is at least one x_16 for which x_16 will not write a letter.
 From the fact that for all x_16, x_16 is a politician if and only if x_16 is a doctor we can infer that for all x_16, if x_16 were a doctor, then x_16 is a politician. From the fact that for all x_16, x_16 will drive a car if and only if x_16 will sleep, and that for all x_16, x_16 will not sleep we can infer that for all x_16, x_16 will not drive a car. From the fact that for all x_16, x_16 will drive a car if and only if x_16 is a politician, and that for all x_16, x_16 will not drive a car we can infer that for all x_16, x_16 is not a politician. From the fact that for all x_16, if x_16 were a doctor, then x_16 is a politician, and that for all x_16, x_16 is not a politician we can infer that for all x_16, x_16 is not a doctor. Finally, from the fact that there is at least one x_16 for which x_16 will write a letter if and only if x_16 is a doctor, and that for all x_16, x_16 is not a doctor we can infer that there is at least one x_16 for which x_16 will not write a letter. Therefore, the answer is yes.