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, x_7 is not happy. For all x_7, x_7 is happy or x_7 will play squash. For all x_7, if x_7 plays squash, then x_7 is reading a book. There is at least one x_7 for which if x_7 reads a book, then x_7 is writing a letter.
There is at least one x_7 for which if x_7 plays squash, then x_7 is writing a letter can be inferred via the existential transitivity rule. For all x_7, x_7 will play squash can be inferred via the universal disjunctive syllogism rule.