Consider the following premises. There is at least one z_3 for which z_3 will not go running or z_3 is a cashier. For all z_3, if z_3 were a cashier, then z_3 is reading a book. For all z_3, z_3 will read a book or z_3 is not an artist. For all z_3, if z_3 reads a book, then z_3 is a cashier. For all z_3, z_3 will go running or z_3 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, z_3 will not read a book.
 From the fact that for all z_3, if z_3 were a cashier, then z_3 is reading a book, and that for all z_3, if z_3 reads a book, then z_3 is a cashier we can infer that for all z_3, z_3 is a cashier if and only if z_3 will read a book via universal biconditional introduction. From the fact that for all z_3, z_3 will read a book or z_3 is not an artist we can infer that for all z_3, if z_3 were an artist, then z_3 is reading a book via universal rewriting. From the fact that for all z_3, z_3 will go running or z_3 is an artist, and that there is at least one z_3 for which z_3 will not go running or z_3 is a cashier we can infer that there is at least one z_3 for which z_3 is an artist or z_3 is a cashier via existential resolution. From the fact that for all z_3, z_3 is a cashier if and only if z_3 will read a book we can infer that for all z_3, if z_3 were a cashier, then z_3 is reading a book via universal biconditional elimination. Finally, from the fact that for all z_3, if z_3 were an artist, then z_3 is reading a book, that for all z_3, if z_3 were a cashier, then z_3 is reading a book, and that there is at least one z_3 for which z_3 is an artist or z_3 is a cashier we can infer that there is at least one z_3 for which z_3 will read a book via existential disjunction elimination, which contradicts that For all z_3, z_3 will not read a book. Therefore, the answer is no.