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_10, if x_10 makes tea, then x_10 is happy. For all x_10, if x_10 were happy, then x_10 is cooking. For all x_10, x_10 is an office clerk. There is at least one x_10 for which x_10 will cook or x_10 is not an office clerk.
For all x_10, if x_10 makes tea, then x_10 is cooking can be inferred via the universal transitivity rule. There is at least one x_10 for which if x_10 were an office clerk, then x_10 is cooking can be inferred via the existential rewriting rule.