an isSubClassOf term is tested, that term is asserted as a success or failure. Then, the next time the term needs to be tested, the answer is found in the new assertion, so it is not necessary to run the full test again. 

| Table 19. The Code Minimization Algorithm  IF   |                                                                                                                                                    |                                                                                                                                                                                                                                   |
|-------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Base Case 1:                                    | and                                                                                                                                                |                                                                                                                                                                                                                                   |
| THEN                                            | P is a built-in predicate (reserved keyword) in Prolog,  P is not findall,  P is a satisfiable predicate.                                          |                                                                                                                                                                                                                                   |
| Base Case 2:                                    | IF                                                                                                                                                 | P is a predicate in a fact,                                                                                                                                                                                                       |
| THEN                                            | P is a satisfiable predicate.                                                                                                                      |                                                                                                                                                                                                                                   |
| IF                                              |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| and                                             |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| THEN  and                                       | P is the predicate in the head of a rule, R,  each predicate in R's body is P,  P is a satisfiable predicate,  R is a satisfiable rule.            |                                                                                                                                                                                                                                   |
| Base Case 3:                                    | IF                                                                                                                                                 |                                                                                                                                                                                                                                   |
| and                                             |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| THEN  and                                       | P is the predicate in the head of a rule, R,  every predicate in R's body is satisfiable,  P is a satisfiable predicate,  R is a satisfiable rule. |                                                                                                                                                                                                                                   |
| Inductive Case 1:                               |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| a.                                              | IF                                                                                                                                                 | a rule, R, has a term, T, in its body, where T is  assert(F), asserta(F), or assertz(F),  P is the predicate of F,  all of the predicates preceding T in the body of R are satisfiable predicates,  P is a satisfiable predicate. |
| and and                                         |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| Inductive Case 2:                               | THEN IF  and THEN                                                                                                                                  | A is the second argument of a findall,  all of the predicates in A are satisfiable predicates,  the findall is treated as if it was a satisfiable  predicate                                                                      |
| Inductive Case 3:                               | IF                                                                                                                                                 |                                                                                                                                                                                                                                   |
| Base Case:                                      | P is a predicate that can be called from outside the  rules, 4 P is a testable predicate.                                                          |                                                                                                                                                                                                                                   |
| THEN                                            |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| Inductive Case 1:                               | IF                                                                                                                                                 | findall is determined to be a testable predicate,                                                                                                                                                                                 |
| THEN                                            | each predicate in P's second argument is also testable.                                                                                            |                                                                                                                                                                                                                                   |
| b.                                              | IF                                                                                                                                                 | P is a predicate such that P or not(P) is found in the  body of a rule, R,  R's head can be determined to have a testable  predicate,  P is a testable predicate,  R is a testable rule.                                          |
| and                                             |                                                                                                                                                    |                                                                                                                                                                                                                                   |
| Inductive Case 2:                               | THEN  and                                                                                                                                          |                                                                                                                                                                                                                                   |
