Consider the following premises. There is at least one z for which z will work if and only if z is an office clerk. For all z, z will not work. For all z, if z were an office clerk, then z is bored. For all z, if z were bored, then z is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is bored.
 From the fact that there is at least one z for which z will work if and only if z is an office clerk, and that for all z, z will not work we can infer that there is at least one z for which z is not an office clerk via existential biconditional elimination. From the fact that for all z, if z were an office clerk, then z is bored, and that for all z, if z were bored, then z is an office clerk we can infer that for all z, z is an office clerk if and only if z is bored via universal biconditional introduction. Finally, from the fact that for all z, z is an office clerk if and only if z is bored, and that there is at least one z for which z is not an office clerk we can infer that there is at least one z for which z is not bored via existential biconditional elimination, which contradicts that For all z, z is bored. Therefore, the answer is no.