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_4, x_4 is an office clerk if and only if x_4 is a musician. For all x_4, x_4 is bored if and only if x_4 is a musician. For all x_4, x_4 is bored if and only if x_4 will cook. There is at least one x_4 for which x_4 will not cook.
For all x_4, if x_4 were an office clerk, then x_4 is a musician can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 were bored, then x_4 is a musician can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 were bored, then x_4 is cooking can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 were a musician, then x_4 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 were a musician, then x_4 is bored can be inferred via the universal biconditional elimination rule. For all x_4, if x_4 cooks, then x_4 is bored can be inferred via the universal biconditional elimination rule. There is at least one x_4 for which x_4 is not bored can be inferred via the existential biconditional elimination rule.