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, x will cook if and only if x will sleep. For all x, if x cooks, then x is sleeping. For all x, x will not cook. For all x, x will sleep if and only if x is a scientist.
For all x, if x cooks, then x is sleeping can be inferred via the universal biconditional elimination rule. For all x, if x sleeps, then x is a scientist can be inferred via the universal biconditional elimination rule. For all x, if x sleeps, then x is cooking can be inferred via the universal biconditional elimination rule. For all x, if x were a scientist, then x is sleeping can be inferred via the universal biconditional elimination rule. For all x, x will not sleep can be inferred via the universal biconditional elimination rule.