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: There is at least one x_4 for which if x_4 cooks, then x_4 is not working. For all x_4, if x_4 cooks, then x_4 is sleeping. For all x_4, if x_4 sleeps, then x_4 is cooking. For all x_4, x_4 will work.
There is at least one x_4 for which x_4 will not cook can be inferred via the existential modus tollens rule. For all x_4, x_4 will cook if and only if x_4 will sleep can be inferred via the universal biconditional introduction rule. For all x_4, x_4 will sleep if and only if x_4 will cook can be inferred via the universal biconditional introduction rule.