The Efficacy of RUE Resolution Experimental Results and Heuristic Theory

We p r e s e n t and a n a l y s e e x p e r i m e n t a l r e s u l t s i n t h e f i r s t e x t e n s i v e use o f a theo rem p r o v e r based o n R e s o l u t i o n b y U n i f i c a t i o n and E q u a l i t y . I m p l i c i t use i s made o f e q u a l i t y ax ioms b y t h e I n f e r e n c e r u l e s RUE and NRF to a c h i e v e i n c i s i v e r e f u t a t i o n s f o r E u n s a t l s f l a b i l i t y . S i n c e a p r i m a r y i s s u e i n au tomated d e d u c t i o n i s t h e e f f i c a c y o f conve rgence t o p r o o f , w e d e s c r i b e i n d e t a i l t he h e u r i s t i c s w h i c h were used t o o b t a i n p r o o f s . A c o m p a r a t i v e t a b u l a t i o n w i t h t h e r e s u l t s o f McCharen, Overbeek and Wos, who used u n i f i c a t i o n r e s o l u t i o n , shows s h a r p l y reduced c u m u l a t i v e u n i f i c a t i o n c o u n t s . 1 . I n t r o d u c t i o n A p r i m a r y r e a s o n f o r t h e f a i l u r e o f b i n a r y r e s o l u t i o n r e l a t e s t o t h e h a n d l i n g o f e q u a l i t y , a p r e d i c a t e w h i c h p l a y s a c e n t r a l r o l e i n most a x i o m a t i c s y s t e m s . The use o f t h e e q u a l i t y ax ioms I n t h e i n p u t c l a u s e s e t l e a d s t o v e r y l o n g p r o o f s w h i c h a re u n n e c e s s a r i l y cumbersome and p a r a m o d u l a t i o n w h i c h l e a d s t o much s h o r t e r p r o o f s p r e s e n t s p rob lems o f h e u r i s t i c s e a r c h f o r t h e p r o p e r p a r a m o d u l a n t s w h i c h e x p e r i m e n t o r s have n o t been a b l e t o s u r m o u n t . I n [ 8 , 9 ] t h e a u t h o r p r e s e n t e d t h e t h e o r y o f r e s o l u t i o n b y u n i f i c a t i o n and e q u a l i t y i n w h i c h t h e ax ioms o f e q u a l i t y a r e i n c o r p o r a t e d i n t o t h e d e f i n i t i o n o f r e s o l u t i o n . I n c o n t r a s t t o p a r a m o d u l a t l o n , RUE r e s o l u t i o n does l e n d i t s e l f t o h e u r i s t i c s w h i c h conve rge t o r e f u t a t i o n s and i t i s t h e purpose o f t h i s paper t o c a r e f u l l y s t u d y t h i s i s s u e . W e w i l l f i r s t g i v e a s y n o p s i s o f t h e b a s i c theorems and d e f i n i t i o n s o f RUE r e s o l u t i o n as p r e s e n t e d i n [ 9 ] and t h e n p roceed t o t h e d i s c u s s i o n o f e x p e r i m e n t s and h e u r i s t i c s e a r c h p r o c e d u r e s . (1.1) A disagreement set of a pair of terms (t1,t2) is defined in the following manner: (1) If t 1 , t 2 sre ident ical the empty set is the sole disagreement set. (2) If t1,t2 are not ident ica l , the set of one element the pair ( t 1 , t 2 ) is the or ig in disagreement set. (3) If t 1 , t 2 have the form