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_17, if x_17 were happy, then x_17 is running. For all x_17, if x_17 writes a letter, then x_17 is rich. For all x_17, if x_17 goes running, then x_17 is rich. There is at least one x_17 for which x_17 will not write a letter. For all x_17, if x_17 were rich, then x_17 is writing a letter.
There is at least one x_17 for which x_17 is not rich can be inferred via the existential modus tollens rule. For all x_17, if x_17 were happy, then x_17 is rich can be inferred via the universal transitivity rule. For all x_17, if x_17 goes running, then x_17 is writing a letter can be inferred via the universal transitivity rule. For all x_17, x_17 will write a letter if and only if x_17 is rich can be inferred via the universal biconditional introduction rule. For all x_17, x_17 is rich if and only if x_17 will write a letter can be inferred via the universal biconditional introduction rule.