Consider the following premises. For all x_6, x_6 will go running. David is not a writer. For all x_6, x_6 will not go running or x_6 will sleep. Can we infer the following from them? David is not sleeping.
 From the fact that for all x_6, x_6 will go running we can infer that for all x_6, x_6 will go running or x_6 is a writer. From the fact that for all x_6, x_6 will go running or x_6 is a writer, and that for all x_6, x_6 will not go running or x_6 will sleep we can infer that for all x_6, x_6 is a writer or x_6 will sleep. From the fact that for all x_6, x_6 is a writer or x_6 will sleep we can infer that David is a writer or David is sleeping. Finally, from the fact that David is a writer or David is sleeping, and that David is not a writer we can infer that David is sleeping, which contradicts that David is not sleeping. Therefore, the answer is no.