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: p -> s. s -> r_1. r_1 -> u. u -> p. ~r_1.
~s can be inferred via the modus tollens rule. p -> r_1 can be inferred via the transitivity rule. s -> u can be inferred via the transitivity rule. r_1 -> p can be inferred via the transitivity rule. u -> s can be inferred via the transitivity rule.