Consider the following premises. For all x_5, x_5 will drink water if and only if x_5 will listen to a song. For all x_5, if x_5 listens to a song, then x_5 is reading a book. There is at least one x_5 for which x_5 will drink water if and only if x_5 will make tea. For all x_5, x_5 will not read a book. 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 for all x_5, if x_5 listens to a song, then x_5 is reading a book, and that for all x_5, x_5 will not read a book we can infer that for all x_5, x_5 will not listen to a song via universal modus tollens. From the fact that for all x_5, x_5 will drink water if and only if x_5 will listen to a song, and that for all x_5, x_5 will not listen to a song we can infer that for all x_5, x_5 will not drink water via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which x_5 will drink water if and only if x_5 will make tea, and that for all x_5, x_5 will not drink water 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.