What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: If Charles were rich, then it is raining. If it rains, then Elisabeth is a writer. If Elisabeth were a writer, then Charles is rich. It is not raining. Michael is a soldier if and only if Elisabeth is a writer.
Charles is not rich can be inferred via the modus tollens rule. If Charles were rich, then Elisabeth is a writer can be inferred via the transitivity rule. If it rains, then Charles is rich can be inferred via the transitivity rule. If Elisabeth were a writer, then it is raining can be inferred via the transitivity rule. If Michael were a soldier, then Elisabeth is a writer can be inferred via the biconditional elimination rule. If Elisabeth were a writer, then Michael is a soldier can be inferred via the biconditional elimination rule.