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_1, x_1 will not cook. There is at least one x_1 for which x_1 is an electrician if and only if x_1 is an artist. For all x_1, if x_1 were an electrician, then x_1 is cooking.
For all x_1, x_1 is not an electrician can be inferred via the universal modus tollens rule. There is at least one x_1 for which if x_1 were an electrician, then x_1 is an artist can be inferred via the existential biconditional elimination rule. There is at least one x_1 for which if x_1 were an artist, then x_1 is an electrician can be inferred via the existential biconditional elimination rule.