Consider the following premises. For all x_6, x_6 is fast. For all x_6, if x_6 were a taxi driver, then x_6 is a nurse. For all x_6, if x_6 were a nurse, then x_6 is working. For all x_6, x_6 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not fast.
 From the fact that for all x_6, if x_6 were a taxi driver, then x_6 is a nurse, and that for all x_6, if x_6 were a nurse, then x_6 is working we can infer that for all x_6, if x_6 were a taxi driver, then x_6 is working via universal transitivity. From the fact that for all x_6, if x_6 were a taxi driver, then x_6 is working, and that for all x_6, x_6 is a taxi driver we can infer that for all x_6, x_6 will work via universal modus ponens. From the fact that for all x_6, x_6 is fast, and that for all x_6, x_6 will work we can infer that for all x_6, x_6 is fast and x_6 will work via universal conjunction. Finally, from the fact that for all x_6, x_6 is fast and x_6 will work we can infer that for all x_6, x_6 is fast via universal simplification, which contradicts that There is at least one x_6 for which x_6 is not fast. Therefore, the answer is no.