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, x_10 is not a soldier. For all x_10, x_10 will climb a mountain if and only if x_10 is a musician. For all x_10, if x_10 sleeps, then x_10 is a soldier. For all x_10, x_10 will climb a mountain if and only if x_10 will sleep. For all x_10, if x_10 plays a game, then x_10 is sleeping. For all x_10, if x_10 were a soldier, then x_10 is playing a game.
For all x_10, x_10 will not sleep can be inferred via the universal modus tollens rule. For all x_10, if x_10 sleeps, then x_10 is playing a game can be inferred via the universal transitivity rule. For all x_10, if x_10 plays a game, then x_10 is a soldier can be inferred via the universal transitivity rule. For all x_10, if x_10 were a soldier, then x_10 is sleeping can be inferred via the universal transitivity rule. For all x_10, if x_10 climbs a mountain, then x_10 is a musician can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 climbs a mountain, then x_10 is sleeping can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 were a musician, then x_10 is climbing a mountain can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 sleeps, then x_10 is climbing a mountain can be inferred via the universal biconditional elimination rule.