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 Barbara were an astronaut, then Joseph is climbing a mountain. If Joseph climbs a mountain, then Barbara is an astronaut. Joseph is climbing a mountain or Barbara is not an astronaut.
If Barbara were an astronaut, then Joseph is climbing a mountain can be inferred via the rewriting rule. Barbara is an astronaut if and only if Joseph is climbing a mountain can be inferred via the biconditional introduction rule. Joseph is climbing a mountain if and only if Barbara is an astronaut can be inferred via the biconditional introduction rule.