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_1, if x_1 drives a car, then x_1 is a politician. For all x_1, if x_1 were a soldier, then x_1 is a politician. There is at least one x_1 for which if x_1 were a politician, then x_1 is a soldier. For all x_1, x_1 is a soldier or x_1 will drive a car.
There is at least one x_1 for which if x_1 drives a car, then x_1 is a soldier can be inferred via the existential transitivity rule. For all x_1, x_1 is a politician can be inferred via the universal disjunction elimination rule. There is at least one x_1 for which x_1 is a politician if and only if x_1 is a soldier can be inferred via the existential biconditional introduction rule. There is at least one x_1 for which x_1 is a soldier if and only if x_1 is a politician can be inferred via the existential biconditional introduction rule.