Consider the following premises. For all x_9, x_9 is a bartender if and only if x_9 will work. Mary is working. Can we infer the following from them? If we can, name the inference rule being used: Mary is not a bartender.
 From the fact that for all x_9, x_9 is a bartender if and only if x_9 will work we can infer that for all x_9, if x_9 works, then x_9 is a bartender via universal biconditional elimination. From the fact that for all x_9, if x_9 works, then x_9 is a bartender we can infer that if Mary works, then Mary is a bartender via universal instantiation. Finally, from the fact that if Mary works, then Mary is a bartender, and that Mary is working we can infer that Mary is a bartender via modus ponens, which contradicts that Mary is not a bartender. Therefore, the answer is no.