Consider the following premises. For all x_12, x_12 will play tennis if and only if x_12 is an office clerk. For all x_12, x_12 will read a book if and only if x_12 is an office clerk. For all x_12, if x_12 reads a book, then x_12 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_12 for which the fact that x_12 plays tennis does not imply that x_12 is reading a book.
 From the fact that for all x_12, x_12 will play tennis if and only if x_12 is an office clerk we can infer that for all x_12, if x_12 plays tennis, then x_12 is an office clerk via universal biconditional elimination. From the fact that for all x_12, x_12 will read a book if and only if x_12 is an office clerk we can infer that for all x_12, if x_12 were an office clerk, then x_12 is reading a book via universal biconditional elimination. From the fact that for all x_12, if x_12 plays tennis, then x_12 is an office clerk, and that for all x_12, if x_12 were an office clerk, then x_12 is reading a book we can infer that for all x_12, if x_12 plays tennis, then x_12 is reading a book via universal transitivity. From the fact that for all x_12, if x_12 plays tennis, then x_12 is reading a book, and that for all x_12, if x_12 reads a book, then x_12 is playing tennis we can infer that for all x_12, x_12 will play tennis if and only if x_12 will read a book via universal biconditional introduction. Finally, from the fact that for all x_12, x_12 will play tennis if and only if x_12 will read a book we can infer that for all x_12, if x_12 plays tennis, then x_12 is reading a book via universal biconditional elimination, which contradicts that There is at least one x_12 for which the fact that x_12 plays tennis does not imply that x_12 is reading a book. Therefore, the answer is no.