Consider the following premises. It is not cloudy or it is sunny. It is cloudy or Elisabeth is an artist. Richard is a scientist or it is not sunny. Richard is a scientist if and only if Elisabeth is an artist. Can we infer the following from them? If we can, name the inference rule being used: Richard is a scientist.
 From the fact that it is cloudy or Elisabeth is an artist, and that it is not cloudy or it is sunny we can infer that Elisabeth is an artist or it is sunny via resolution. From the fact that Richard is a scientist or it is not sunny we can infer that if it is sunny, then Richard is a scientist via rewriting. From the fact that Richard is a scientist if and only if Elisabeth is an artist we can infer that if Elisabeth were an artist, then Richard is a scientist via biconditional elimination. Finally, from the fact that if Elisabeth were an artist, then Richard is a scientist, that if it is sunny, then Richard is a scientist, and that Elisabeth is an artist or it is sunny we can infer that Richard is a scientist via disjunction elimination. Therefore, the answer is yes.