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_9, x_9 will sleep if and only if x_9 will listen to a song. There is at least one x_9 for which x_9 will not listen to a song. For all x_9, if x_9 cooks, then x_9 is a carpenter. For all x_9, if x_9 were a carpenter, then x_9 is sleeping.
For all x_9, if x_9 cooks, then x_9 is sleeping can be inferred via the universal transitivity rule. For all x_9, if x_9 sleeps, then x_9 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 listens to a song, then x_9 is sleeping can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which x_9 will not sleep can be inferred via the existential biconditional elimination rule.