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 Elisabeth were a soldier, then Mary is playing a game. Elisabeth is a soldier or Mary is not playing a game. If Mary plays a game, then Elisabeth is a soldier.
If Mary plays a game, then Elisabeth is a soldier can be inferred via the rewriting rule. Elisabeth is a soldier if and only if Mary is playing a game can be inferred via the biconditional introduction rule. Mary is playing a game if and only if Elisabeth is a soldier can be inferred via the biconditional introduction rule.