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_6, x_6 will go running. For all x_6, if x_6 were excited, then x_6 is not running. For all x_6, x_6 is happy. For all x_6, if x_6 were happy, then x_6 is writing a letter.
For all x_6, x_6 will write a letter can be inferred via the universal modus ponens rule. For all x_6, x_6 is not excited can be inferred via the universal modus tollens rule. For all x_6, x_6 will go running and x_6 is happy can be inferred via the universal conjunction rule. For all x_6, x_6 is happy and x_6 will go running can be inferred via the universal conjunction rule.