Consider the following premises. If it snows, then Barbara is an artist. For all x_8, x_8 is a cashier if and only if x_8 is an artist. Barbara is a cashier or it is snowing. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not an artist.
 From the fact that for all x_8, x_8 is a cashier if and only if x_8 is an artist we can infer that for all x_8, if x_8 were a cashier, then x_8 is an artist via universal biconditional elimination. From the fact that for all x_8, if x_8 were a cashier, then x_8 is an artist we can infer that if Barbara were a cashier, then Barbara is an artist via universal instantiation. Finally, from the fact that if Barbara were a cashier, then Barbara is an artist, that if it snows, then Barbara is an artist, and that Barbara is a cashier or it is snowing we can infer that Barbara is an artist via disjunction elimination, which contradicts that Barbara is not an artist. Therefore, the answer is no.