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_6, x_6 is a carpenter if and only if x_6 will cook. There is at least one x_6 for which x_6 will sleep if and only if x_6 will cook. For all x_6, x_6 will work. For all x_6, if x_6 were a carpenter, then x_6 is not working.
For all x_6, x_6 is not a carpenter can be inferred via the universal modus tollens rule. For all x_6, if x_6 were a carpenter, then x_6 is cooking can be inferred via the universal biconditional elimination rule. There is at least one x_6 for which if x_6 sleeps, then x_6 is cooking can be inferred via the existential biconditional elimination rule. For all x_6, if x_6 cooks, then x_6 is a carpenter can be inferred via the universal biconditional elimination rule. There is at least one x_6 for which if x_6 cooks, then x_6 is sleeping can be inferred via the existential biconditional elimination rule.