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_15, if x_15 works, then x_15 is sleeping. For all x_15, x_15 will work if and only if x_15 is sad. There is at least one x_15 for which if x_15 sleeps, then x_15 is playing a game. For all x_15, if x_15 plays a game, then x_15 is sad.
There is at least one x_15 for which if x_15 sleeps, then x_15 is sad can be inferred via the existential transitivity rule. There is at least one x_15 for which if x_15 works, then x_15 is playing a game can be inferred via the existential transitivity rule. For all x_15, if x_15 works, then x_15 is sad can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were sad, then x_15 is working can be inferred via the universal biconditional elimination rule.