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: There is at least one x_15 for which if x_15 listens to a song, then x_15 is a cashier. For all x_15, x_15 will play a game if and only if x_15 is curious. For all x_15, x_15 will not take a plane or x_15 will climb a mountain. For all x_15, if x_15 plays a game, then x_15 is listening to a song. For all x_15, if x_15 climbs a mountain, then x_15 is a cashier. For all x_15, x_15 will take a plane or x_15 is curious.
There is at least one x_15 for which if x_15 plays a game, then x_15 is a cashier can be inferred via the existential transitivity rule. For all x_15, x_15 is curious or x_15 will climb a mountain can be inferred via the universal resolution rule. For all x_15, if x_15 plays a game, then x_15 is curious can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were curious, then x_15 is playing a game can be inferred via the universal biconditional elimination rule.