Consider the following premises. For all x_11, x_11 will make tea or x_11 will drink water. For all x_11, x_11 will make tea if and only if x_11 will work. For all x_11, x_11 will drink water if and only if x_11 will work. 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 neither x_11 will work nor x_11 is excited.
 From the fact that for all x_11, x_11 will make tea if and only if x_11 will work we can infer that for all x_11, if x_11 makes tea, then x_11 is working via universal biconditional elimination. From the fact that for all x_11, x_11 will drink water if and only if x_11 will work we can infer that for all x_11, if x_11 drinks water, then x_11 is working via universal biconditional elimination. From the fact that for all x_11, if x_11 makes tea, then x_11 is working, that for all x_11, if x_11 drinks water, then x_11 is working, and that for all x_11, x_11 will make tea or x_11 will drink water we can infer that for all x_11, x_11 will work via universal disjunction elimination. Finally, from the fact that for all x_11, x_11 will work we can infer that for all x_11, x_11 will work or x_11 is excited via universal addition, which contradicts that There is at least one x_11 for which neither x_11 will work nor x_11 is excited. Therefore, the answer is no.