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_6, x_6 is not rich. There is at least one x_6 for which x_6 will climb a mountain if and only if x_6 is an astronaut. For all x_6, x_6 is rich or x_6 is a sailor. For all x_6, if x_6 were an astronaut, then x_6 is not a sailor.
For all x_6, x_6 is a sailor can be inferred via the universal disjunctive syllogism rule. There is at least one x_6 for which if x_6 climbs a mountain, then x_6 is an astronaut can be inferred via the existential biconditional elimination rule. There is at least one x_6 for which if x_6 were an astronaut, then x_6 is climbing a mountain can be inferred via the existential biconditional elimination rule.