Consider the following premises. For all x_7, x_7 is not excited or x_7 will write a letter. For all x_7, x_7 will sleep or x_7 is excited. Michael is not poor. For all x_7, x_7 will not sleep or x_7 is poor. Can we infer the following from them? If we can, name the inference rule being used: Michael is not writing a letter.
 From the fact that for all x_7, x_7 will sleep or x_7 is excited, and that for all x_7, x_7 will not sleep or x_7 is poor we can infer that for all x_7, x_7 is excited or x_7 is poor via universal resolution. From the fact that for all x_7, x_7 is excited or x_7 is poor, and that for all x_7, x_7 is not excited or x_7 will write a letter we can infer that for all x_7, x_7 is poor or x_7 will write a letter via universal resolution. From the fact that for all x_7, x_7 is poor or x_7 will write a letter we can infer that Michael is poor or Michael is writing a letter via universal instantiation. Finally, from the fact that Michael is poor or Michael is writing a letter, and that Michael is not poor we can infer that Michael is writing a letter via disjunctive syllogism, which contradicts that Michael is not writing a letter. Therefore, the answer is no.