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_5, if x_5 cooks, then x_5 is playing squash. For all x_5, if x_5 writes a letter, then x_5 is playing squash. There is at least one x_5 for which if x_5 were fast, then x_5 is writing a letter. For all x_5, x_5 will sleep or x_5 is fast. For all x_5, if x_5 sleeps, then x_5 is cooking.
For all x_5, if x_5 sleeps, then x_5 is playing squash can be inferred via the universal transitivity rule. There is at least one x_5 for which if x_5 were fast, then x_5 is playing squash can be inferred via the existential transitivity rule.