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 y_3, if y_3 goes running, then y_3 is a carpenter. For all y_3, y_3 is not a carpenter. There is at least one y_3 for which y_3 is a lawyer if and only if y_3 is a writer. For all y_3, y_3 is a writer if and only if y_3 is poor. For all y_3, if y_3 were a carpenter, then y_3 is running. For all y_3, if y_3 were poor, then y_3 is running.
For all y_3, y_3 will not go running can be inferred via the universal modus tollens rule. For all y_3, if y_3 were poor, then y_3 is a carpenter can be inferred via the universal transitivity rule. For all y_3, y_3 will go running if and only if y_3 is a carpenter can be inferred via the universal biconditional introduction rule. For all y_3, y_3 is a carpenter if and only if y_3 will go running can be inferred via the universal biconditional introduction rule. For all y_3, if y_3 were a writer, then y_3 is poor can be inferred via the universal biconditional elimination rule. There is at least one y_3 for which if y_3 were a lawyer, then y_3 is a writer can be inferred via the existential biconditional elimination rule. For all y_3, if y_3 were poor, then y_3 is a writer can be inferred via the universal biconditional elimination rule. There is at least one y_3 for which if y_3 were a writer, then y_3 is a lawyer can be inferred via the existential biconditional elimination rule.