Consider the following premises. For all x_10, x_10 will not cook. For all x_10, x_10 will work if and only if x_10 is an artist. There is at least one x_10 for which if x_10 works, then x_10 is not a musician. For all x_10, x_10 will cook or x_10 is a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is not an artist.
 From the fact that for all x_10, x_10 will cook or x_10 is a musician, and that for all x_10, x_10 will not cook we can infer that for all x_10, x_10 is a musician via universal disjunctive syllogism. From the fact that there is at least one x_10 for which if x_10 works, then x_10 is not a musician, and that for all x_10, x_10 is a musician we can infer that there is at least one x_10 for which x_10 will not work via existential modus tollens. Finally, from the fact that for all x_10, x_10 will work if and only if x_10 is an artist, and that there is at least one x_10 for which x_10 will not work we can infer that there is at least one x_10 for which x_10 is not an artist via existential biconditional elimination. Therefore, the answer is yes.