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 plays tennis, then Joseph is cooking. If Jennifer climbs a mountain, then it is sunny. It is sunny if and only if Barbara is playing tennis. It is cloudy or Joseph is not cooking.
If Joseph cooks, then it is cloudy can be inferred via the rewriting rule. If it is sunny, then Barbara is playing tennis can be inferred via the biconditional elimination rule. If Barbara plays tennis, then it is sunny can be inferred via the biconditional elimination rule.