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 it rains, then Barbara is climbing a mountain. If Barbara climbs a mountain, then Robert is a mechanic. If Robert were a mechanic, then it is cloudy. If it is cloudy, then it is raining.
If it rains, then Robert is a mechanic can be inferred via the transitivity rule. If Barbara climbs a mountain, then it is cloudy can be inferred via the transitivity rule. If Robert were a mechanic, then it is raining can be inferred via the transitivity rule. If it is cloudy, then Barbara is climbing a mountain can be inferred via the transitivity rule.