Consider the following premises. Thomas is working or it is late. Joseph is an artist or Thomas is not working. It is late if and only if Joseph is an artist. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not an artist.
 From the fact that it is late if and only if Joseph is an artist we can infer that if it is late, then Joseph is an artist via biconditional elimination. From the fact that Joseph is an artist or Thomas is not working we can infer that if Thomas works, then Joseph is an artist via rewriting. Finally, from the fact that if Thomas works, then Joseph is an artist, that if it is late, then Joseph is an artist, and that Thomas is working or it is late we can infer that Joseph is an artist via disjunction elimination, which contradicts that Joseph is not an artist. Therefore, the answer is no.