Consider the following premises. For all x_6, if x_6 sleeps, then x_6 is not curious. For all x_6, x_6 is curious. For all x_6, x_6 will sleep if and only if x_6 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not an office clerk.
 From the fact that for all x_6, if x_6 sleeps, then x_6 is not curious, and that for all x_6, x_6 is curious we can infer that for all x_6, x_6 will not sleep via universal modus tollens. From the fact that for all x_6, x_6 will sleep if and only if x_6 is an office clerk we can infer that for all x_6, if x_6 were an office clerk, then x_6 is sleeping via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were an office clerk, then x_6 is sleeping, and that for all x_6, x_6 will not sleep we can infer that for all x_6, x_6 is not an office clerk via universal modus tollens. Therefore, the answer is yes.