Consider the following premises. There is at least one x_6 for which if x_6 plays tennis, then x_6 is sleeping. For all x_6, if x_6 were a server, then x_6 is playing tennis. For all x_6, x_6 will play a game if and only if x_6 is a server. 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 if x_6 plays a game, then x_6 is sleeping.
 From the fact that for all x_6, if x_6 were a server, then x_6 is playing tennis, and that there is at least one x_6 for which if x_6 plays tennis, then x_6 is sleeping we can infer that there is at least one x_6 for which if x_6 were a server, then x_6 is sleeping via existential transitivity. From the fact that for all x_6, x_6 will play a game if and only if x_6 is a server we can infer that for all x_6, if x_6 plays a game, then x_6 is a server via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 plays a game, then x_6 is a server, and that there is at least one x_6 for which if x_6 were a server, then x_6 is sleeping we can infer that there is at least one x_6 for which if x_6 plays a game, then x_6 is sleeping via existential transitivity. Therefore, the answer is yes.