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 drives a car, then x_15 is cooking. There is at least one x_15 for which if x_15 cooks, then x_15 is a mechanic. For all x_15, x_15 is not an astronaut or x_15 is sad. For all x_15, x_15 will drive a car if and only if x_15 will play a game. For all x_15, x_15 is an astronaut or x_15 will play a game. For all x_15, if x_15 were sad, then x_15 is a mechanic.
There is at least one x_15 for which if x_15 drives a car, then x_15 is a mechanic can be inferred via the existential transitivity rule. For all x_15, x_15 will play a game or x_15 is sad can be inferred via the universal resolution rule. For all x_15, if x_15 drives a car, then x_15 is playing a game can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 plays a game, then x_15 is driving a car can be inferred via the universal biconditional elimination rule.