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 is a politician if and only if x_9 will play tennis. For all x_9, x_9 is not a politician. There is at least one x_9 for which x_9 will work if and only if x_9 will sleep. For all x_9, if x_9 works, then x_9 is playing tennis. For all x_9, if x_9 plays tennis, then x_9 is working.
For all x_9, x_9 will work if and only if x_9 will play tennis can be inferred via the universal biconditional introduction rule. For all x_9, x_9 will play tennis if and only if x_9 will work can be inferred via the universal biconditional introduction rule. For all x_9, if x_9 were a politician, then x_9 is playing tennis can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 works, then x_9 is sleeping can be inferred via the existential biconditional elimination rule. For all x_9, if x_9 plays tennis, then x_9 is a politician can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which if x_9 sleeps, then x_9 is working can be inferred via the existential biconditional elimination rule. For all x_9, x_9 will not play tennis can be inferred via the universal biconditional elimination rule.