Consider the following premises. There is at least one x_8 for which x_8 is an office clerk if and only if x_8 is a cashier. For all x_8, if x_8 were a cashier, then x_8 is an office clerk. For all x_8, x_8 is not rich. For all x_8, if x_8 were an office clerk, then x_8 is rich. Can we infer the following from them? For all x_8, x_8 is a cashier.
 From the fact that for all x_8, if x_8 were an office clerk, then x_8 is rich, and that for all x_8, x_8 is not rich we can infer that for all x_8, x_8 is not an office clerk. From the fact that there is at least one x_8 for which x_8 is an office clerk if and only if x_8 is a cashier we can infer that there is at least one x_8 for which if x_8 were an office clerk, then x_8 is a cashier. From the fact that there is at least one x_8 for which if x_8 were an office clerk, then x_8 is a cashier, and that for all x_8, if x_8 were a cashier, then x_8 is an office clerk we can infer that there is at least one x_8 for which x_8 is an office clerk if and only if x_8 is a cashier. Finally, from the fact that there is at least one x_8 for which x_8 is an office clerk if and only if x_8 is a cashier, and that for all x_8, x_8 is not an office clerk we can infer that there is at least one x_8 for which x_8 is not a cashier, which contradicts that For all x_8, x_8 is a cashier. Therefore, the answer is no.