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_12, if x_12 plays tennis, then x_12 is listening to a song. There is at least one x_12 for which if x_12 plays tennis, then x_12 is taking a plane. For all x_12, if x_12 takes a plane, then x_12 is playing tennis. For all x_12, if x_12 listens to a song, then x_12 is playing tennis.
For all x_12, if x_12 takes a plane, then x_12 is listening to a song can be inferred via the universal transitivity rule. There is at least one x_12 for which if x_12 listens to a song, then x_12 is taking a plane can be inferred via the existential transitivity rule. For all x_12, x_12 will play tennis if and only if x_12 will listen to a song can be inferred via the universal biconditional introduction rule. For all x_12, x_12 will listen to a song if and only if x_12 will play tennis can be inferred via the universal biconditional introduction rule. There is at least one x_12 for which x_12 will play tennis if and only if x_12 will take a plane can be inferred via the existential biconditional introduction rule. There is at least one x_12 for which x_12 will take a plane if and only if x_12 will play tennis can be inferred via the existential biconditional introduction rule.