Consider the following premises. For all x_5, if x_5 were a politician, then x_5 is curious. For all x_5, if x_5 works, then x_5 is a cashier. For all x_5, x_5 is a politician. For all x_5, if x_5 were curious, then x_5 is working. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is not a cashier.
 From the fact that for all x_5, if x_5 were a politician, then x_5 is curious, and that for all x_5, if x_5 were curious, then x_5 is working we can infer that for all x_5, if x_5 were a politician, then x_5 is working via universal transitivity. From the fact that for all x_5, if x_5 were a politician, then x_5 is working, and that for all x_5, x_5 is a politician we can infer that for all x_5, x_5 will work via universal modus ponens. Finally, from the fact that for all x_5, if x_5 works, then x_5 is a cashier, and that for all x_5, x_5 will work we can infer that for all x_5, x_5 is a cashier via universal modus ponens, which contradicts that There is at least one x_5 for which x_5 is not a cashier. Therefore, the answer is no.