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 Joseph were a musician, then Richard is fast. Patricia is not playing squash. If Richard were fast, then John is a taxi driver. Joseph is a musician if and only if John is a taxi driver. If Joseph were a musician, then Patricia is playing squash.
Joseph is not a musician can be inferred via the modus tollens rule. If Joseph were a musician, then John is a taxi driver can be inferred via the transitivity rule. If Joseph were a musician, then John is a taxi driver can be inferred via the biconditional elimination rule. If John were a taxi driver, then Joseph is a musician can be inferred via the biconditional elimination rule.