Consider the following premises. For all x_6, if x_6 sleeps, then x_6 is a politician. For all x_6, x_6 is a taxi driver or x_6 is fast. For all x_6, x_6 is not a taxi driver or x_6 will sleep. For all x_6, x_6 is a politician if and only if x_6 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is a politician.
 From the fact that for all x_6, x_6 is a taxi driver or x_6 is fast, and that for all x_6, x_6 is not a taxi driver or x_6 will sleep we can infer that for all x_6, x_6 is fast or x_6 will sleep via universal resolution. From the fact that for all x_6, x_6 is a politician if and only if x_6 is fast we can infer that for all x_6, if x_6 were fast, then x_6 is a politician via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were fast, then x_6 is a politician, that for all x_6, if x_6 sleeps, then x_6 is a politician, and that for all x_6, x_6 is fast or x_6 will sleep we can infer that for all x_6, x_6 is a politician via universal disjunction elimination. Therefore, the answer is yes.