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, if x_9 cooks, then x_9 is playing tennis. For all x_9, x_9 will sleep. There is at least one x_9 for which if x_9 cooks, then x_9 is not sleeping. For all x_9, if x_9 plays tennis, then x_9 is cooking.
There is at least one x_9 for which x_9 will not cook can be inferred via the existential modus tollens rule. For all x_9, x_9 will cook 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 cook can be inferred via the universal biconditional introduction rule.