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