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_10, if x_10 were a cashier, then x_10 is a soldier. For all x_10, if x_10 were a cashier, then x_10 is a soldier. There is at least one x_10 for which if x_10 were a soldier, then x_10 is a carpenter. For all x_10, if x_10 were a carpenter, then x_10 is a cashier. For all x_10, x_10 is not a soldier.
For all x_10, x_10 is not a cashier can be inferred via the universal modus tollens rule. For all x_10, x_10 is not a cashier can be inferred via the universal modus tollens rule. For all x_10, if x_10 were a carpenter, then x_10 is a soldier can be inferred via the universal transitivity rule. For all x_10, if x_10 were a carpenter, then x_10 is a soldier can be inferred via the universal transitivity rule. There is at least one x_10 for which if x_10 were a soldier, then x_10 is a cashier can be inferred via the existential transitivity rule. There is at least one x_10 for which if x_10 were a cashier, then x_10 is a carpenter can be inferred via the existential transitivity rule. There is at least one x_10 for which if x_10 were a cashier, then x_10 is a carpenter can be inferred via the existential transitivity rule.