Consider the following premises. For all x_11, if x_11 drinks water, then x_11 is listening to a song. For all x_11, if x_11 makes tea, then x_11 is drinking water. For all x_11, if x_11 listens to a song, then x_11 is making tea. There is at least one x_11 for which x_11 will make tea if and only if x_11 will drink water. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, if is not true that x_11 will drink water if and only if x_11 will make tea.
 From the fact that for all x_11, if x_11 drinks water, then x_11 is listening to a song, and that for all x_11, if x_11 listens to a song, then x_11 is making tea we can infer that for all x_11, if x_11 drinks water, then x_11 is making tea via universal transitivity. Finally, from the fact that for all x_11, if x_11 makes tea, then x_11 is drinking water, and that for all x_11, if x_11 drinks water, then x_11 is making tea we can infer that for all x_11, x_11 will make tea if and only if x_11 will drink water via universal biconditional introduction, which contradicts that For all x_11, if is not true that x_11 will drink water if and only if x_11 will make tea. Therefore, the answer is no.