Consider the following premises. For all x_14, x_14 will go running. For all x_14, if x_14 were an office clerk, then x_14 is running. For all x_14, x_14 will go running if and only if x_14 is an office clerk. There is at least one x_14 for which x_14 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will read a book.
 From the fact that for all x_14, x_14 will go running if and only if x_14 is an office clerk we can infer that for all x_14, if x_14 goes running, then x_14 is an office clerk via universal biconditional elimination. From the fact that for all x_14, if x_14 were an office clerk, then x_14 is running, and that for all x_14, if x_14 goes running, then x_14 is an office clerk we can infer that for all x_14, x_14 is an office clerk if and only if x_14 will go running via universal biconditional introduction. From the fact that for all x_14, x_14 is an office clerk if and only if x_14 will go running, and that there is at least one x_14 for which x_14 is not an office clerk we can infer that there is at least one x_14 for which x_14 will not go running via existential biconditional elimination. From the fact that for all x_14, x_14 will go running we can infer that for all x_14, x_14 will go running or x_14 will read a book via universal addition. Finally, from the fact that for all x_14, x_14 will go running or x_14 will read a book, and that there is at least one x_14 for which x_14 will not go running we can infer that there is at least one x_14 for which x_14 will read a book via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.