Consider the following premises. For all x_6, x_6 is fast or x_6 is not an office clerk. For all x_6, x_6 is not fast. For all x_6, x_6 will play squash 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: There is at least one x_6 for which x_6 will play squash.
 From the fact that for all x_6, x_6 is fast or x_6 is not an office clerk we can infer that for all x_6, if x_6 were an office clerk, then x_6 is fast via universal rewriting. From the fact that for all x_6, if x_6 were an office clerk, then x_6 is fast, and that for all x_6, x_6 is not fast we can infer that for all x_6, x_6 is not an office clerk via universal modus tollens. Finally, from the fact that for all x_6, x_6 will play squash if and only if x_6 is an office clerk, and that for all x_6, x_6 is not an office clerk we can infer that for all x_6, x_6 will not play squash via universal biconditional elimination, which contradicts that There is at least one x_6 for which x_6 will play squash. Therefore, the answer is no.