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_9 for which x_9 is a carpenter if and only if x_9 is curious. For all x_9, if x_9 plays tennis, then x_9 is a carpenter. For all x_9, if x_9 were curious, then x_9 is cooking.
There is at least one x_9 for which if x_9 were a carpenter, then x_9 is curious can be inferred via the existential biconditional elimination rule. There is at least one x_9 for which if x_9 were curious, then x_9 is a carpenter can be inferred via the existential biconditional elimination rule.