Consider the following premises. For all x_10, x_10 is an artist. For all x_10, x_10 will listen to a song. For all x_10, x_10 will sleep. For all x_10, if x_10 sleeps, then x_10 is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will write a letter.
 From the fact that for all x_10, x_10 is an artist, and that for all x_10, x_10 will listen to a song we can infer that for all x_10, x_10 is an artist and x_10 will listen to a song via universal conjunction. Finally, from the fact that for all x_10, if x_10 sleeps, then x_10 is writing a letter, and that for all x_10, x_10 will sleep we can infer that for all x_10, x_10 will write a letter via universal modus ponens. Therefore, the answer is yes.