And-Or Graphs Applied to RUE Resolution

I n equa l i t y -based b ina ry r e s o l u t i o n , the v i a b i l i t y t e s t is used as a d e c i s i o n mechanism to s e l e c t disagreement sets and a lso to de f i ne the RUE u n i f i e r . In t h i s paper we solve the problem of n o n t e r m i n a t i o n o f the v i a b i l i t y t e s t by a p p l y i n g the theory of And-Or graphs. RUE r e f u t a t i o n s are succ inc t and t y p i c a l l y l e ss than h a l f as l ong as corresponding r e f u t a t i o n s w i t h the e q u a l i t y axioms. Fur thermore, RUE r e s o l u t i o n i s complete w i t h o u t us ing paramodulat ion or the e q u a l i t y axioms. Experiments w i t h a theorem prover based on t h i s method have produced super io r r e s u l t s which are descr ibed i n [ D i g r i c o l i and H a r r i s o n , 1 9 8 6 ] .