Consider the following premises. For all x_8, x_8 is not happy or x_8 will work. There is at least one x_8 for which x_8 will not climb a mountain. For all x_8, x_8 will climb a mountain or x_8 is happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will read a book or x_8 will work.
 From the fact that for all x_8, x_8 will climb a mountain or x_8 is happy, and that there is at least one x_8 for which x_8 will not climb a mountain we can infer that there is at least one x_8 for which x_8 is happy via existential disjunctive syllogism. From the fact that there is at least one x_8 for which x_8 is happy we can infer that there is at least one x_8 for which x_8 is happy or x_8 will read a book via existential addition. Finally, from the fact that there is at least one x_8 for which x_8 is happy or x_8 will read a book, and that for all x_8, x_8 is not happy or x_8 will work we can infer that there is at least one x_8 for which x_8 will read a book or x_8 will work via existential resolution. Therefore, the answer is yes.