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_23, x_23 is rich if and only if x_23 will make tea. For all x_23, x_23 will not sleep. For all x_23, if x_23 were a poet, then x_23 is making tea. There is at least one x_23 for which x_23 is an office clerk if and only if x_23 will sleep. For all x_23, x_23 is rich if and only if x_23 is an office clerk.
For all x_23, if x_23 were rich, then x_23 is making tea can be inferred via the universal biconditional elimination rule. For all x_23, if x_23 were rich, then x_23 is an office clerk can be inferred via the universal biconditional elimination rule. There is at least one x_23 for which if x_23 were an office clerk, then x_23 is sleeping can be inferred via the existential biconditional elimination rule. For all x_23, if x_23 makes tea, then x_23 is rich can be inferred via the universal biconditional elimination rule. For all x_23, if x_23 were an office clerk, then x_23 is rich can be inferred via the universal biconditional elimination rule. There is at least one x_23 for which if x_23 sleeps, then x_23 is an office clerk can be inferred via the existential biconditional elimination rule. There is at least one x_23 for which x_23 is not an office clerk can be inferred via the existential biconditional elimination rule.