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: John is making tea if and only if it is late. William is a politician. Mary is reading a book if and only if Thomas is a bartender. Thomas is a bartender or it is not late. If Mary reads a book, then William is not a politician.
Mary is not reading a book can be inferred via the modus tollens rule. If it is late, then Thomas is a bartender can be inferred via the rewriting rule. If John makes tea, then it is late can be inferred via the biconditional elimination rule. If Mary reads a book, then Thomas is a bartender can be inferred via the biconditional elimination rule. If it is late, then John is making tea can be inferred via the biconditional elimination rule. If Thomas were a bartender, then Mary is reading a book can be inferred via the biconditional elimination rule.