Consider the following premises. David is an electrician or Barbara is not running. If David were an electrician, then it is raining. Barbara is not running. If it rains, then Barbara is running. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that David is an electrician or Barbara is not running we can infer that if Barbara goes running, then David is an electrician via rewriting. From the fact that if Barbara goes running, then David is an electrician, and that if David were an electrician, then it is raining we can infer that if Barbara goes running, then it is raining via transitivity. From the fact that if it rains, then Barbara is running, and that if Barbara goes running, then it is raining we can infer that it is raining if and only if Barbara is running via biconditional introduction. Finally, from the fact that it is raining if and only if Barbara is running, and that Barbara is not running we can infer that it is not raining via biconditional elimination, which contradicts that It is raining. Therefore, the answer is no.