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 is happy or x_9 is an artist. There is at least one x_9 for which if x_9 were rich, then x_9 is a cashier. For all x_9, x_9 is not happy. For all x_9, if x_9 were a cashier, then x_9 is a politician. For all x_9, if x_9 were an artist, then x_9 is rich.
There is at least one x_9 for which if x_9 were rich, then x_9 is a politician can be inferred via the existential transitivity rule. There is at least one x_9 for which if x_9 were an artist, then x_9 is a cashier can be inferred via the existential transitivity rule. For all x_9, x_9 is an artist can be inferred via the universal disjunctive syllogism rule.