Consider the following premises. For all x_6, if x_6 were a soldier, then x_6 is excited. For all x_6, x_6 is an artist or x_6 is not excited. For all x_6, x_6 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not an artist.
 From the fact that for all x_6, x_6 is an artist or x_6 is not excited we can infer that for all x_6, if x_6 were excited, then x_6 is an artist via universal rewriting. From the fact that for all x_6, if x_6 were a soldier, then x_6 is excited, and that for all x_6, if x_6 were excited, then x_6 is an artist we can infer that for all x_6, if x_6 were a soldier, then x_6 is an artist via universal transitivity. Finally, from the fact that for all x_6, if x_6 were a soldier, then x_6 is an artist, and that for all x_6, x_6 is a soldier we can infer that for all x_6, x_6 is an artist via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 is not an artist. Therefore, the answer is no.