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_9, if x_9 climbs a mountain, then x_9 is cooking. For all x_9, x_9 will play a game if and only if x_9 will listen to a song. There is at least one x_9 for which x_9 will listen to a song if and only if x_9 will climb a mountain. For all x_9, x_9 will not cook.
For all x_9, x_9 will not climb a mountain can be inferred via the universal modus tollens rule. For all x_9, if x_9 plays a game, then x_9 is listening to a song can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 listens to a song, then x_9 is climbing a mountain can be inferred via the existential biconditional elimination rule. For all x_9, if x_9 listens to a song, then x_9 is playing a game can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 climbs a mountain, then x_9 is listening to a song can be inferred via the existential biconditional elimination rule.