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: It is cloudy and Susan is playing tennis. If William were poor, then Elisabeth is drinking water. If Elisabeth drinks water, then William is poor. If William were poor, then William is a bartender. If William were a bartender, then it is not cloudy.
If Elisabeth drinks water, then William is a bartender can be inferred via the transitivity rule. If William were poor, then it is not cloudy can be inferred via the transitivity rule. It is cloudy can be inferred via the simplification rule. Susan is playing tennis can be inferred via the simplification rule. William is poor if and only if Elisabeth is drinking water can be inferred via the biconditional introduction rule. Elisabeth is drinking water if and only if William is poor can be inferred via the biconditional introduction rule.