Consider the following premises. For all x_1, x_1 is sad if and only if x_1 is a cashier. For all x_1, x_1 is sad if and only if x_1 is a police officer. There is at least one x_1 for which x_1 is not a cashier. For all x_1, if x_1 were sad, then x_1 is a police officer. Can we infer the following from them? There is at least one x_1 for which x_1 is not a police officer.
 From the fact that for all x_1, x_1 is sad if and only if x_1 is a police officer we can infer that for all x_1, if x_1 were a police officer, then x_1 is sad. From the fact that for all x_1, x_1 is sad if and only if x_1 is a cashier, and that there is at least one x_1 for which x_1 is not a cashier we can infer that there is at least one x_1 for which x_1 is not sad. From the fact that for all x_1, if x_1 were sad, then x_1 is a police officer, and that for all x_1, if x_1 were a police officer, then x_1 is sad we can infer that for all x_1, x_1 is sad if and only if x_1 is a police officer. Finally, from the fact that for all x_1, x_1 is sad if and only if x_1 is a police officer, and that there is at least one x_1 for which x_1 is not sad we can infer that there is at least one x_1 for which x_1 is not a police officer. Therefore, the answer is yes.