Consider the following premises. James is a taxi driver or Robert is not writing a letter. Susan is listening to a song or Robert is writing a letter. If Susan listens to a song, then James is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: James is a taxi driver or Barbara is playing a game.
 From the fact that James is a taxi driver or Robert is not writing a letter we can infer that if Robert writes a letter, then James is a taxi driver via rewriting. From the fact that if Susan listens to a song, then James is a taxi driver, that if Robert writes a letter, then James is a taxi driver, and that Susan is listening to a song or Robert is writing a letter we can infer that James is a taxi driver via disjunction elimination. Finally, from the fact that James is a taxi driver we can infer that James is a taxi driver or Barbara is playing a game via addition. Therefore, the answer is yes.