Consider the following premises. For all x_3, if x_3 were a server, then x_3 is playing a game. For all x_3, x_3 will play a game if and only if x_3 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_3 for which if is not true that x_3 will play a game if and only if x_3 is a server.
 From the fact that for all x_3, x_3 will play a game if and only if x_3 is a server we can infer that for all x_3, if x_3 plays a game, then x_3 is a server via universal biconditional elimination. Finally, from the fact that for all x_3, if x_3 plays a game, then x_3 is a server, and that for all x_3, if x_3 were a server, then x_3 is playing a game we can infer that for all x_3, x_3 will play a game if and only if x_3 is a server via universal biconditional introduction, which contradicts that There is at least one x_3 for which if is not true that x_3 will play a game if and only if x_3 is a server. Therefore, the answer is no.