Consider the following premises. For all x_6, x_6 is not a poet. For all x_6, if x_6 were an astronaut, then x_6 is a poet. There is at least one x_6 for which if x_6 were an astronaut, then x_6 is an artist. For all x_6, if x_6 were an artist, then x_6 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is an artist.
 From the fact that for all x_6, if x_6 were an artist, then x_6 is an astronaut, and that there is at least one x_6 for which if x_6 were an astronaut, then x_6 is an artist we can infer that there is at least one x_6 for which x_6 is an artist if and only if x_6 is an astronaut via existential biconditional introduction. From the fact that for all x_6, if x_6 were an astronaut, then x_6 is a poet, and that for all x_6, x_6 is not a poet we can infer that for all x_6, x_6 is not an astronaut via universal modus tollens. Finally, from the fact that there is at least one x_6 for which x_6 is an artist if and only if x_6 is an astronaut, and that for all x_6, x_6 is not an astronaut we can infer that there is at least one x_6 for which x_6 is not an artist via existential biconditional elimination, which contradicts that For all x_6, x_6 is an artist. Therefore, the answer is no.