Consider the following premises. For all x_12, if x_12 were excited, then x_12 is writing a letter. For all x_12, if x_12 writes a letter, then x_12 is excited. Elisabeth is not excited. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not writing a letter or Joseph is a taxi driver.
 From the fact that for all x_12, if x_12 writes a letter, then x_12 is excited, and that for all x_12, if x_12 were excited, then x_12 is writing a letter we can infer that for all x_12, x_12 will write a letter if and only if x_12 is excited via universal biconditional introduction. From the fact that for all x_12, x_12 will write a letter if and only if x_12 is excited we can infer that Elisabeth is writing a letter if and only if Elisabeth is excited via universal instantiation. From the fact that Elisabeth is writing a letter if and only if Elisabeth is excited, and that Elisabeth is not excited we can infer that Elisabeth is not writing a letter via biconditional elimination. Finally, from the fact that Elisabeth is not writing a letter we can infer that Elisabeth is not writing a letter or Joseph is a taxi driver via addition. Therefore, the answer is yes.