Consider the following premises. There is at least one x_12 for which x_12 will sleep or x_12 will drink water. For all x_12, x_12 is a politician. For all x_12, x_12 will drink water if and only if x_12 will cook. For all x_12, if x_12 sleeps, then x_12 is cooking. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which x_12 will cook and x_12 is a politician.
 From the fact that for all x_12, x_12 will drink water if and only if x_12 will cook we can infer that for all x_12, if x_12 drinks water, then x_12 is cooking via universal biconditional elimination. From the fact that for all x_12, if x_12 sleeps, then x_12 is cooking, that for all x_12, if x_12 drinks water, then x_12 is cooking, and that there is at least one x_12 for which x_12 will sleep or x_12 will drink water we can infer that there is at least one x_12 for which x_12 will cook via existential disjunction elimination. Finally, from the fact that there is at least one x_12 for which x_12 will cook, and that for all x_12, x_12 is a politician we can infer that there is at least one x_12 for which x_12 will cook and x_12 is a politician via existential conjunction. Therefore, the answer is yes.