Consider the following premises. There is at least one z for which z will not cook. For all z, if z were an office clerk, then z is cooking. For all z, z is a sailor if and only if z is an office clerk. For all z, z is an office clerk or z will not cook. Can we infer the following from them? There is at least one z for which z is not a sailor.
 From the fact that for all z, z is an office clerk or z will not cook we can infer that for all z, if z cooks, then z is an office clerk. From the fact that for all z, if z were an office clerk, then z is cooking, and that for all z, if z cooks, then z is an office clerk we can infer that for all z, z is an office clerk if and only if z will cook. From the fact that for all z, z is an office clerk if and only if z will cook, and that there is at least one z for which z will not cook we can infer that there is at least one z for which z is not an office clerk. Finally, from the fact that for all z, z is a sailor if and only if z is an office clerk, 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 a sailor. Therefore, the answer is yes.