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_5, if x_5 sleeps, then x_5 is listening to a song. There is at least one x_5 for which x_5 will sleep if and only if x_5 is a lawyer. For all x_5, if x_5 listens to a song, then x_5 is sleeping. For all x_5, x_5 will not listen to a song.
For all x_5, x_5 will not sleep can be inferred via the universal modus tollens rule. For all x_5, x_5 will sleep if and only if x_5 will listen to a song can be inferred via the universal biconditional introduction rule. For all x_5, x_5 will listen to a song if and only if x_5 will sleep can be inferred via the universal biconditional introduction rule. There is at least one x_5 for which if x_5 sleeps, then x_5 is a lawyer can be inferred via the existential biconditional elimination rule. There is at least one x_5 for which if x_5 were a lawyer, then x_5 is sleeping can be inferred via the existential biconditional elimination rule.