Consider the following premises. If William were an office clerk, then William is writing a letter. William is not an office clerk. For all x_14, x_14 is an office clerk or x_14 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: William is not writing a letter.
 From the fact that for all x_14, x_14 is an office clerk or x_14 will not write a letter we can infer that for all x_14, if x_14 writes a letter, then x_14 is an office clerk via universal rewriting. From the fact that for all x_14, if x_14 writes a letter, then x_14 is an office clerk we can infer that if William writes a letter, then William is an office clerk via universal instantiation. From the fact that if William were an office clerk, then William is writing a letter, and that if William writes a letter, then William is an office clerk we can infer that William is an office clerk if and only if William is writing a letter via biconditional introduction. From the fact that William is an office clerk if and only if William is writing a letter we can infer that if William writes a letter, then William is an office clerk via biconditional elimination. Finally, from the fact that if William writes a letter, then William is an office clerk, and that William is not an office clerk we can infer that William is not writing a letter via modus tollens. Therefore, the answer is yes.