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 an astronaut. For all x_10, x_10 will listen to a song or x_10 will take a plane. For all x_10, x_10 will play a game if and only if x_10 will listen to a song. For all x_10, x_10 will not play a game.
For all x_10, if x_10 plays a game, then x_10 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_10, if x_10 listens to a song, then x_10 is playing a game can be inferred via the universal biconditional elimination rule. For all x_10, x_10 will not listen to a song can be inferred via the universal biconditional elimination rule.