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_9, x_9 will climb a mountain or x_9 is a doctor. For all x_9, if x_9 climbs a mountain, then x_9 is running. For all x_9, if x_9 were a doctor, then x_9 is running. There is at least one x_9 for which x_9 will go running if and only if x_9 will write a letter.
For all x_9, x_9 will go running can be inferred via the universal disjunction elimination rule. There is at least one x_9 for which if x_9 goes running, then x_9 is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 writes a letter, then x_9 is running can be inferred via the existential biconditional elimination rule.