Consider the following premises. If Barbara were curious, then Joseph is a bartender. Barbara is curious or Barbara is not a doctor. If Joseph were a bartender, then Barbara is a doctor. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Barbara is a doctor if and only if Barbara is curious.
 From the fact that Barbara is curious or Barbara is not a doctor we can infer that if Barbara were a doctor, then Barbara is curious via rewriting. From the fact that if Barbara were curious, then Joseph is a bartender, and that if Joseph were a bartender, then Barbara is a doctor we can infer that if Barbara were curious, then Barbara is a doctor via transitivity. Finally, from the fact that if Barbara were a doctor, then Barbara is curious, and that if Barbara were curious, then Barbara is a doctor we can infer that Barbara is a doctor if and only if Barbara is curious via biconditional introduction, which contradicts that If is not true that Barbara is a doctor if and only if Barbara is curious. Therefore, the answer is no.