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 is windy, then William is a doctor. If William were a doctor, then Sarah is sleeping. If Joseph were excited, then it is windy. If Sarah sleeps, then Joseph is excited. It is not windy.
Joseph is not excited can be inferred via the modus tollens rule. If it is windy, then Sarah is sleeping can be inferred via the transitivity rule. If William were a doctor, then Joseph is excited can be inferred via the transitivity rule. If Joseph were excited, then William is a doctor can be inferred via the transitivity rule. If Sarah sleeps, then it is windy can be inferred via the transitivity rule.