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: There is at least one x_3 for which if x_3 cooks, then x_3 is running. For all x_3, x_3 will not cook. For all x_3, if x_3 goes running, then x_3 is happy. For all x_3, if x_3 were happy, then x_3 is cooking.
For all x_3, x_3 is not happy can be inferred via the universal modus tollens rule. For all x_3, if x_3 goes running, then x_3 is cooking can be inferred via the universal transitivity rule. There is at least one x_3 for which if x_3 cooks, then x_3 is happy can be inferred via the existential transitivity rule. There is at least one x_3 for which if x_3 were happy, then x_3 is running can be inferred via the existential transitivity rule.