Consider the following premises. There is at least one x_11 for which x_11 will not write a letter or x_11 is poor. For all x_11, x_11 is a writer and x_11 will go running. For all x_11, if x_11 were bored, then x_11 is not a writer. For all x_11, x_11 will write a letter or x_11 is bored. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is poor.
 From the fact that for all x_11, x_11 will write a letter or x_11 is bored, and that there is at least one x_11 for which x_11 will not write a letter or x_11 is poor we can infer that there is at least one x_11 for which x_11 is bored or x_11 is poor via existential resolution. From the fact that for all x_11, x_11 is a writer and x_11 will go running we can infer that for all x_11, x_11 is a writer via universal simplification. From the fact that for all x_11, if x_11 were bored, then x_11 is not a writer, and that for all x_11, x_11 is a writer we can infer that for all x_11, x_11 is not bored via universal modus tollens. Finally, from the fact that there is at least one x_11 for which x_11 is bored or x_11 is poor, and that for all x_11, x_11 is not bored we can infer that there is at least one x_11 for which x_11 is poor via existential disjunctive syllogism. Therefore, the answer is yes.