Consider the following premises. For all x_5, x_5 is a scientist. For all x_5, if x_5 were a scientist, then x_5 is writing a letter. For all x_5, if x_5 writes a letter, then x_5 is a bartender. For all x_5, if x_5 were a bartender, then x_5 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is not an artist.
 From the fact that for all x_5, if x_5 were a scientist, then x_5 is writing a letter, and that for all x_5, x_5 is a scientist we can infer that for all x_5, x_5 will write a letter via universal modus ponens. From the fact that for all x_5, if x_5 writes a letter, then x_5 is a bartender, and that for all x_5, if x_5 were a bartender, then x_5 is an artist we can infer that for all x_5, if x_5 writes a letter, then x_5 is an artist via universal transitivity. Finally, from the fact that for all x_5, if x_5 writes a letter, then x_5 is an artist, and that for all x_5, x_5 will write a letter we can infer that for all x_5, x_5 is an artist via universal modus ponens, which contradicts that There is at least one x_5 for which x_5 is not an artist. Therefore, the answer is no.