Consider the following premises. It is sunny if and only if it is late. David is fast or Robert is curious. If David were fast, then it is late. It is not sunny. If Robert were curious, then it is late. Can we infer the following from them? If we can, name the inference rule being used: Joseph is rich.
 From the fact that it is sunny if and only if it is late, and that it is not sunny we can infer that it is not late via biconditional elimination. From the fact that if David were fast, then it is late, that if Robert were curious, then it is late, and that David is fast or Robert is curious we can infer that it is late via disjunction elimination. From the fact that it is late we can infer that it is late or Joseph is rich via addition. Finally, from the fact that it is late or Joseph is rich, and that it is not late we can infer that Joseph is rich via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.