Consider the following premises. For all x_9, if x_9 were an artist, then x_9 is a mechanic. There is at least one x_9 for which if x_9 were a mechanic, then x_9 is happy. For all x_9, if x_9 were happy, then x_9 is a mechanic. For all x_9, x_9 is not happy. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is an artist.
 From the fact that there is at least one x_9 for which if x_9 were a mechanic, then x_9 is happy, and that for all x_9, if x_9 were happy, then x_9 is a mechanic we can infer that there is at least one x_9 for which x_9 is a mechanic if and only if x_9 is happy via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 is a mechanic if and only if x_9 is happy, and that for all x_9, x_9 is not happy we can infer that there is at least one x_9 for which x_9 is not a mechanic via existential biconditional elimination. Finally, from the fact that for all x_9, if x_9 were an artist, then x_9 is a mechanic, and that there is at least one x_9 for which x_9 is not a mechanic we can infer that there is at least one x_9 for which x_9 is not an artist via existential modus tollens, which contradicts that For all x_9, x_9 is an artist. Therefore, the answer is no.