Consider the following premises. If Robert were a bartender, then Mary is an artist. For all x_11, x_11 will not play squash. For all x_11, x_11 is a bartender if and only if x_11 will play squash. If Mary were an artist, then Robert is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Mary is an artist.
 From the fact that for all x_11, x_11 is a bartender if and only if x_11 will play squash, and that for all x_11, x_11 will not play squash we can infer that for all x_11, x_11 is not a bartender via universal biconditional elimination. From the fact that for all x_11, x_11 is not a bartender we can infer that Robert is not a bartender via universal instantiation. From the fact that if Robert were a bartender, then Mary is an artist, and that if Mary were an artist, then Robert is a bartender we can infer that Robert is a bartender if and only if Mary is an artist via biconditional introduction. Finally, from the fact that Robert is a bartender if and only if Mary is an artist, and that Robert is not a bartender we can infer that Mary is not an artist via biconditional elimination, which contradicts that Mary is an artist. Therefore, the answer is no.