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 y, if y works, then y is writing a letter. For all y, if y were a writer, then y is a cashier. For all y, if y were a cashier, then y is working. There is at least one y for which y is not a cashier. For all y, if y writes a letter, then y is a writer.
There is at least one y for which y is not a writer can be inferred via the existential modus tollens rule. For all y, if y works, then y is a writer can be inferred via the universal transitivity rule. For all y, if y were a writer, then y is working can be inferred via the universal transitivity rule. For all y, if y were a cashier, then y is writing a letter can be inferred via the universal transitivity rule. For all y, if y writes a letter, then y is a cashier can be inferred via the universal transitivity rule.