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 is not a carpenter. There is at least one x for which x will sleep if and only if x is a carpenter. For all x, x will sleep if and only if x will work.
For all x, if x sleeps, then x is working can be inferred via the universal biconditional elimination rule. There is at least one x for which if x sleeps, then x is a carpenter can be inferred via the existential biconditional elimination rule. For all x, if x works, then x is sleeping can be inferred via the universal biconditional elimination rule. There is at least one x for which if x were a carpenter, then x is sleeping can be inferred via the existential biconditional elimination rule. There is at least one x for which x will not sleep can be inferred via the existential biconditional elimination rule.