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: For all x_10, if x_10 sleeps, then x_10 is a sailor. For all x_10, if x_10 were a sailor, then x_10 is sleeping. For all x_10, if x_10 were a writer, then x_10 is playing a game. For all x_10, x_10 is a sailor if and only if x_10 will play a game. For all x_10, if x_10 plays a game, then x_10 is a writer. For all x_10, x_10 is not a writer.
For all x_10, x_10 will not play a game can be inferred via the universal modus tollens rule. For all x_10, x_10 will sleep if and only if x_10 is a sailor can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is a sailor if and only if x_10 will sleep can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is a writer if and only if x_10 will play a game can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will play a game if and only if x_10 is a writer can be inferred via the universal biconditional introduction rule. For all x_10, if x_10 were a sailor, then x_10 is playing a game can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 plays a game, then x_10 is a sailor can be inferred via the universal biconditional elimination rule.