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_10, if x_10 sleeps, then x_10 is writing a letter. For all x_10, if x_10 were bored, then x_10 is writing a letter. For all x_10, x_10 will not cook. For all x_10, if x_10 cooks, then x_10 is bored. For all x_10, if x_10 were bored, then x_10 is cooking. For all x_10, if x_10 writes a letter, then x_10 is bored.
For all x_10, x_10 is not bored can be inferred via the universal modus tollens rule. For all x_10, if x_10 sleeps, then x_10 is bored can be inferred via the universal transitivity rule. For all x_10, if x_10 cooks, then x_10 is writing a letter can be inferred via the universal transitivity rule. For all x_10, if x_10 writes a letter, then x_10 is cooking can be inferred via the universal transitivity rule. For all x_10, x_10 is bored if and only if x_10 will write a letter can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will cook if and only if x_10 is bored can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is bored if and only if x_10 will cook can be inferred via the universal biconditional introduction rule. For all x_10, x_10 will write a letter if and only if x_10 is bored can be inferred via the universal biconditional introduction rule.