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, x_12 will listen to a song if and only if x_12 is an astronaut. For all x_12, x_12 will not listen to a song. There is at least one x_12 for which x_12 will make tea if and only if x_12 is an electrician. For all x_12, x_12 is an astronaut if and only if x_12 will make tea.
For all x_12, if x_12 listens to a song, then x_12 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were an astronaut, then x_12 is making tea can be inferred via the universal biconditional elimination rule. There is at least one x_12 for which if x_12 makes tea, then x_12 is an electrician can be inferred via the existential biconditional elimination rule. For all x_12, if x_12 were an astronaut, then x_12 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 makes tea, then x_12 is an astronaut can be inferred via the universal biconditional elimination rule. There is at least one x_12 for which if x_12 were an electrician, then x_12 is making tea can be inferred via the existential biconditional elimination rule. For all x_12, x_12 is not an astronaut can be inferred via the universal biconditional elimination rule.