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_1 for which x_1 will listen to a song if and only if x_1 is an astronaut. For all x_1, x_1 is an astronaut if and only if x_1 will listen to a song. For all x_1, x_1 is not a writer. For all x_1, if x_1 were an astronaut, then x_1 is a writer.
For all x_1, x_1 is not an astronaut can be inferred via the universal modus tollens rule. For all x_1, if x_1 were an astronaut, then x_1 is listening to a song can be inferred via the universal biconditional elimination rule. There is at least one x_1 for which if x_1 listens to a song, then x_1 is an astronaut can be inferred via the existential biconditional elimination rule. For all x_1, if x_1 listens to a song, then x_1 is an astronaut can be inferred via the universal biconditional elimination rule. There is at least one x_1 for which if x_1 were an astronaut, then x_1 is listening to a song can be inferred via the existential biconditional elimination rule.