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: Mary is sad if and only if it is cloudy. Thomas is a soldier if and only if Mary is sad. It is late. If Thomas were a soldier, then it is not late.
Thomas is not a soldier can be inferred via the modus tollens rule. If Mary were sad, then it is cloudy can be inferred via the biconditional elimination rule. If Thomas were a soldier, then Mary is sad can be inferred via the biconditional elimination rule. If it is cloudy, then Mary is sad can be inferred via the biconditional elimination rule. If Mary were sad, then Thomas is a soldier can be inferred via the biconditional elimination rule.