Consider the following premises. There is at least one x_5 for which x_5 is a musician or x_5 will climb a mountain. For all x_5, x_5 is not a musician or x_5 will read a book. For all x_5, x_5 will not read a book or x_5 will play a game. For all x_5, x_5 will not climb a mountain or x_5 will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will work or x_5 will play a game.
 From the fact that there is at least one x_5 for which x_5 is a musician or x_5 will climb a mountain, and that for all x_5, x_5 is not a musician or x_5 will read a book we can infer that there is at least one x_5 for which x_5 will climb a mountain or x_5 will read a book via existential resolution. From the fact that there is at least one x_5 for which x_5 will climb a mountain or x_5 will read a book, and that for all x_5, x_5 will not climb a mountain or x_5 will work we can infer that there is at least one x_5 for which x_5 will read a book or x_5 will work via existential resolution. Finally, from the fact that there is at least one x_5 for which x_5 will read a book or x_5 will work, and that for all x_5, x_5 will not read a book or x_5 will play a game we can infer that there is at least one x_5 for which x_5 will work or x_5 will play a game via existential resolution. Therefore, the answer is yes.