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_7, if x_7 were a cashier, then x_7 is sleeping. For all x_7, x_7 is not a mechanic or x_7 is a cashier. For all x_7, if x_7 sleeps, then x_7 is fast. For all x_7, x_7 is a mechanic or x_7 is fast. For all x_7, if x_7 were fast, then x_7 is sleeping.
For all x_7, if x_7 were a cashier, then x_7 is fast can be inferred via the universal transitivity rule. For all x_7, x_7 is fast or x_7 is a cashier can be inferred via the universal resolution rule. For all x_7, x_7 will sleep if and only if x_7 is fast can be inferred via the universal biconditional introduction rule. For all x_7, x_7 is fast if and only if x_7 will sleep can be inferred via the universal biconditional introduction rule.