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_13, x_13 is a soldier if and only if x_13 will listen to a song. For all x_13, x_13 is not a soldier. For all x_13, x_13 will play tennis or x_13 will work. There is at least one x_13 for which if x_13 plays tennis, then x_13 is listening to a song. For all x_13, if x_13 listens to a song, then x_13 is playing tennis.
There is at least one x_13 for which x_13 will play tennis if and only if x_13 will listen to a song can be inferred via the existential biconditional introduction rule. There is at least one x_13 for which x_13 will listen to a song if and only if x_13 will play tennis can be inferred via the existential biconditional introduction rule. For all x_13, if x_13 were a soldier, then x_13 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 listens to a song, then x_13 is a soldier can be inferred via the universal biconditional elimination rule. For all x_13, x_13 will not listen to a song can be inferred via the universal biconditional elimination rule.