Consider the following premises. For all x_11, x_11 will play tennis if and only if x_11 is a janitor. For all x_11, if x_11 drinks water, then x_11 is a janitor. For all x_11, x_11 will play tennis 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: There is at least one x_11 for which if is not true that x_11 will play tennis if and only if x_11 is a janitor.
 From the fact that for all x_11, x_11 will play tennis if and only if x_11 will drink water we can infer that for all x_11, if x_11 plays tennis, then x_11 is drinking water via universal biconditional elimination. From the fact that for all x_11, x_11 will play tennis if and only if x_11 is a janitor we can infer that for all x_11, if x_11 were a janitor, then x_11 is playing tennis via universal biconditional elimination. From the fact that for all x_11, if x_11 plays tennis, then x_11 is drinking water, and that for all x_11, if x_11 drinks water, then x_11 is a janitor we can infer that for all x_11, if x_11 plays tennis, then x_11 is a janitor via universal transitivity. Finally, from the fact that for all x_11, if x_11 plays tennis, then x_11 is a janitor, and that for all x_11, if x_11 were a janitor, then x_11 is playing tennis we can infer that for all x_11, x_11 will play tennis if and only if x_11 is a janitor via universal biconditional introduction, which contradicts that There is at least one x_11 for which if is not true that x_11 will play tennis if and only if x_11 is a janitor. Therefore, the answer is no.