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 y, if y writes a letter, then y is a cashier. For all y, if y were fast, then y is writing a letter. For all y, if y cooks, then y is fast. There is at least one y for which if y plays a game, then y is cooking.
For all y, if y were fast, then y is a cashier can be inferred via the universal transitivity rule. For all y, if y cooks, then y is writing a letter can be inferred via the universal transitivity rule. There is at least one y for which if y plays a game, then y is fast can be inferred via the existential transitivity rule.