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: John is working if and only if it is cloudy. If Mary takes a plane, then it is cold. If John works, then Mary is taking a plane. It is not cold.
Mary is not taking a plane can be inferred via the modus tollens rule. If John works, then it is cold can be inferred via the transitivity rule. If John works, then it is cloudy can be inferred via the biconditional elimination rule. If it is cloudy, then John is working can be inferred via the biconditional elimination rule.