Consider the following premises. For all x_12, x_12 is not poor. For all x_12, x_12 is an artist if and only if x_12 is poor. Barbara is an artist. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a cashier.
 From the fact that for all x_12, x_12 is an artist if and only if x_12 is poor, and that for all x_12, x_12 is not poor we can infer that for all x_12, x_12 is not an artist via universal biconditional elimination. From the fact that for all x_12, x_12 is not an artist we can infer that Barbara is not an artist via universal instantiation. From the fact that Barbara is an artist we can infer that Barbara is an artist or Sarah is a cashier via addition. Finally, from the fact that Barbara is an artist or Sarah is a cashier, and that Barbara is not an artist we can infer that Sarah is a cashier via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.