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 cooks, then y is running. For all y, if y cooks, then y is running. For all y, y will not cook. There is at least one y for which if y goes running, then y is cooking.
There is at least one y for which y will not go running can be inferred via the existential modus tollens rule. There is at least one y for which y will go running if and only if y will cook can be inferred via the existential biconditional introduction rule. There is at least one y for which y will go running if and only if y will cook can be inferred via the existential biconditional introduction rule. There is at least one y for which y will cook if and only if y will go running can be inferred via the existential biconditional introduction rule. There is at least one y for which y will cook if and only if y will go running can be inferred via the existential biconditional introduction rule.