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: There is at least one x_1 for which x_1 is happy if and only if x_1 will play a game. For all x_1, x_1 will go running if and only if x_1 is an office clerk. For all x_1, if x_1 were an office clerk, then x_1 is happy. For all x_1, if x_1 were happy, then x_1 is an office clerk. For all x_1, x_1 will not go running.
For all x_1, x_1 is an office clerk if and only if x_1 is happy can be inferred via the universal biconditional introduction rule. For all x_1, x_1 is happy if and only if x_1 is an office clerk can be inferred via the universal biconditional introduction rule. For all x_1, if x_1 goes running, then x_1 is an office clerk can be inferred via the universal biconditional elimination rule. There is at least one x_1 for which if x_1 were happy, then x_1 is playing a game can be inferred via the existential biconditional elimination rule. For all x_1, if x_1 were an office clerk, then x_1 is running can be inferred via the universal biconditional elimination rule. There is at least one x_1 for which if x_1 plays a game, then x_1 is happy can be inferred via the existential biconditional elimination rule. For all x_1, x_1 is not an office clerk can be inferred via the universal biconditional elimination rule.