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 James were a poet, then Sarah is excited. If Sarah were excited, then James is a poet. If Patricia were a janitor, then Sarah is excited. If Richard were a server, then Patricia is a janitor.
If Patricia were a janitor, then James is a poet can be inferred via the transitivity rule. If Richard were a server, then Sarah is excited can be inferred via the transitivity rule. James is a poet if and only if Sarah is excited can be inferred via the biconditional introduction rule. Sarah is excited if and only if James is a poet can be inferred via the biconditional introduction rule.