Consider the following premises. For all x_6, x_6 is a musician. For all x_6, x_6 will go running. For all x_6, x_6 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not read a book.
 From the fact that for all x_6, x_6 will read a book, and that for all x_6, x_6 will go running we can infer that for all x_6, x_6 will read a book and x_6 will go running via universal conjunction. From the fact that for all x_6, x_6 will read a book and x_6 will go running we can infer that for all x_6, x_6 will read a book via universal simplification. From the fact that for all x_6, x_6 is a musician, and that for all x_6, x_6 will read a book we can infer that for all x_6, x_6 is a musician and x_6 will read a book via universal conjunction. Finally, from the fact that for all x_6, x_6 is a musician and x_6 will read a book we can infer that for all x_6, x_6 is a musician via universal simplification, which contradicts that There is at least one x_6 for which x_6 will not read a book. Therefore, the answer is no.