Consider the following premises. For all x_3, if x_3 cooks, then x_3 is writing a letter. For all x_3, x_3 will cook. For all x_24, x_24 is a janitor and x_24 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not writing a letter.
 From the fact that for all x_24, x_24 is a janitor and x_24 will listen to a song we can infer that Richard is a janitor and Richard is listening to a song via universal instantiation. Finally, from the fact that for all x_3, if x_3 cooks, then x_3 is writing a letter, and that for all x_3, x_3 will cook we can infer that for all x_3, x_3 will write a letter via universal modus ponens, which contradicts that Jessica is not writing a letter. Therefore, the answer is no.