Consider the following premises. For all x_7, if x_7 plays a game, then x_7 is playing tennis. For all x_7, x_7 will play a game or x_7 is an office clerk. There is at least one x_7 for which if x_7 were an office clerk, then x_7 is working. For all x_7, x_7 will play tennis if and only if x_7 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not work.
 From the fact that for all x_7, x_7 will play tennis if and only if x_7 will work we can infer that for all x_7, if x_7 plays tennis, then x_7 is working via universal biconditional elimination. From the fact that for all x_7, if x_7 plays a game, then x_7 is playing tennis, and that for all x_7, if x_7 plays tennis, then x_7 is working we can infer that for all x_7, if x_7 plays a game, then x_7 is working via universal transitivity. Finally, from the fact that for all x_7, if x_7 plays a game, then x_7 is working, that there is at least one x_7 for which if x_7 were an office clerk, then x_7 is working, and that for all x_7, x_7 will play a game or x_7 is an office clerk we can infer that there is at least one x_7 for which x_7 will work via existential disjunction elimination, which contradicts that For all x_7, x_7 will not work. Therefore, the answer is no.