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: There is at least one x for which if x writes a letter, then x is happy. For all x, if x were happy, then x is cooking. For all x, if x cooks, then x is writing a letter. For all x, x is not happy.
There is at least one x for which x will not write a letter can be inferred via the existential modus tollens rule. For all x, if x were happy, then x is writing a letter can be inferred via the universal transitivity rule. There is at least one x for which if x writes a letter, then x is cooking can be inferred via the existential transitivity rule. There is at least one x for which if x cooks, then x is happy can be inferred via the existential transitivity rule.