Consider the following premises. For all x_8, x_8 is happy. For all x_8, x_8 will go running or x_8 is a politician. For all x_8, x_8 is a politician if and only if x_8 is an office clerk. For all x_8, if x_8 were an office clerk, then x_8 is not happy. For all x_8, x_8 will not go running or x_8 will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will sleep.
 From the fact that for all x_8, if x_8 were an office clerk, then x_8 is not happy, and that for all x_8, x_8 is happy we can infer that for all x_8, x_8 is not an office clerk via universal modus tollens. From the fact that for all x_8, x_8 is a politician if and only if x_8 is an office clerk, and that for all x_8, x_8 is not an office clerk we can infer that for all x_8, x_8 is not a politician via universal biconditional elimination. From the fact that for all x_8, x_8 will go running or x_8 is a politician, and that for all x_8, x_8 will not go running or x_8 will sleep we can infer that for all x_8, x_8 is a politician or x_8 will sleep via universal resolution. Finally, from the fact that for all x_8, x_8 is a politician or x_8 will sleep, and that for all x_8, x_8 is not a politician we can infer that for all x_8, x_8 will sleep via universal disjunctive syllogism. Therefore, the answer is yes.