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_8, x_8 is not happy or x_8 is bored. For all x_8, if x_8 were bored, then x_8 is cooking. For all x_8, x_8 is happy or x_8 will climb a mountain. For all x_8, if x_8 climbs a mountain, then x_8 is cooking. There is at least one x_8 for which if x_8 cooks, then x_8 is bored.
There is at least one x_8 for which if x_8 climbs a mountain, then x_8 is bored can be inferred via the existential transitivity rule. For all x_8, x_8 will climb a mountain or x_8 is bored can be inferred via the universal resolution rule. There is at least one x_8 for which x_8 will cook if and only if x_8 is bored can be inferred via the existential biconditional introduction rule. There is at least one x_8 for which x_8 is bored if and only if x_8 will cook can be inferred via the existential biconditional introduction rule.