Consider the following premises. There is at least one x_5 for which if x_5 makes tea, then x_5 is playing a game. For all x_5, x_5 will listen to a song. For all x_5, if x_5 plays a game, then x_5 is making tea. For all x_5, if x_5 plays a game, then x_5 is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will not make tea.
 From the fact that there is at least one x_5 for which if x_5 makes tea, then x_5 is playing a game, and that for all x_5, if x_5 plays a game, then x_5 is making tea we can infer that there is at least one x_5 for which x_5 will make tea if and only if x_5 will play a game via existential biconditional introduction. From the fact that for all x_5, if x_5 plays a game, then x_5 is not listening to a song, and that for all x_5, x_5 will listen to a song we can infer that for all x_5, x_5 will not play a game via universal modus tollens. Finally, from the fact that there is at least one x_5 for which x_5 will make tea if and only if x_5 will play a game, and that for all x_5, x_5 will not play a game we can infer that there is at least one x_5 for which x_5 will not make tea via existential biconditional elimination. Therefore, the answer is yes.