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_7, x_7 is a cashier or x_7 will cook. For all x_7, x_7 is not a cashier or x_7 is a mechanic. For all x_7, if x_7 cooks, then x_7 is writing a letter. For all x_7, if x_7 were a mechanic, then x_7 is curious. There is at least one x_7 for which if x_7 writes a letter, then x_7 is curious.
There is at least one x_7 for which if x_7 cooks, then x_7 is curious can be inferred via the existential transitivity rule. For all x_7, x_7 will cook or x_7 is a mechanic can be inferred via the universal resolution rule.