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 Karen cooks, then Elisabeth is making tea. If John were not an astronaut, then it is cold. It is not snowing. If it is cold, then Karen is cooking. It is snowing if and only if John is an astronaut.
If John were not an astronaut, then Karen is cooking can be inferred via the transitivity rule. If it is cold, then Elisabeth is making tea can be inferred via the transitivity rule. If it snows, then John is an astronaut can be inferred via the biconditional elimination rule. If John were an astronaut, then it is snowing can be inferred via the biconditional elimination rule. John is not an astronaut can be inferred via the biconditional elimination rule.