Consider the following premises. For all x, x is a taxi driver if and only if x will go running. There is at least one x for which if x were a taxi driver, then x is a politician. For all x, if x were a politician, then x is a taxi driver. For all x, if x goes running, then x is an astronaut. For all x, x is not an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is a politician.
 From the fact that for all x, if x were a politician, then x is a taxi driver, and that there is at least one x for which if x were a taxi driver, then x is a politician we can infer that there is at least one x for which x is a politician if and only if x is a taxi driver via existential biconditional introduction. From the fact that for all x, if x goes running, then x is an astronaut, and that for all x, x is not an astronaut we can infer that for all x, x will not go running via universal modus tollens. From the fact that for all x, x is a taxi driver if and only if x will go running, and that for all x, x will not go running we can infer that for all x, x is not a taxi driver via universal biconditional elimination. Finally, from the fact that there is at least one x for which x is a politician if and only if x is a taxi driver, and that for all x, x is not a taxi driver we can infer that there is at least one x for which x is not a politician via existential biconditional elimination, which contradicts that For all x, x is a politician. Therefore, the answer is no.