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_13, if x_13 sleeps, then x_13 is cooking. For all x_13, x_13 will drink water or x_13 will take a plane. For all x_13, if x_13 takes a plane, then x_13 is sleeping. For all x_13, x_13 will sleep if and only if x_13 will drink water. For all x_13, if x_13 cooks, then x_13 is sleeping.
For all x_13, if x_13 takes a plane, then x_13 is cooking can be inferred via the universal transitivity rule. For all x_13, x_13 will sleep if and only if x_13 will cook can be inferred via the universal biconditional introduction rule. For all x_13, x_13 will cook if and only if x_13 will sleep can be inferred via the universal biconditional introduction rule. For all x_13, if x_13 sleeps, then x_13 is drinking water can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 drinks water, then x_13 is sleeping can be inferred via the universal biconditional elimination rule.