Consider the following premises. If it is cold, then Robert is running. Joseph is not drinking water. If Robert goes running, then Joseph is drinking water. It is cold or Joseph is not drinking water. Can we infer the following from them? If we can, name the inference rule being used: Robert is not running.
 From the fact that it is cold or Joseph is not drinking water we can infer that if Joseph drinks water, then it is cold via rewriting. From the fact that if Joseph drinks water, then it is cold, and that if it is cold, then Robert is running we can infer that if Joseph drinks water, then Robert is running via transitivity. From the fact that if Robert goes running, then Joseph is drinking water, and that if Joseph drinks water, then Robert is running we can infer that Robert is running if and only if Joseph is drinking water via biconditional introduction. Finally, from the fact that Robert is running if and only if Joseph is drinking water, and that Joseph is not drinking water we can infer that Robert is not running via biconditional elimination. Therefore, the answer is yes.