;; ----- Otter 3.0.4, August 1995 ----- ;; The job was started by mccune on gyro, Wed Nov 1 21:24:26 1995 ;; ;;;; -> x=x. ;;;; A*B*A*B*A*B=A*A*A*B*B*B, B*B*B*A*A*A=A*A*A*B*B*B -> . ;;;; -> (x*y)*z=x*y*z. ;;;; -> x*y*z*u=y*z*u*x. ;; ;; -----> EMPTY CLAUSE at 4.89 sec ----> 462 [hyper,4,412.1,134.1] -> . ;; ( (1 (input) ((not (= (* (A) (* (B) (* (A) (* (B) (* (A) (B)))))) (* (A) (* (A) (* (A) (* (B) (* (B) (B)))))))) (not (= (* (B) (* (B) (* (B) (* (A) (* (A) (A)))))) (* (A) (* (A) (* (A) (* (B) (* (B) (B)))))))))) (2 (input) ((= (* (* v0 v1) v2) (* v0 (* v1 v2))))) (3 (input) ((= (* v0 (* v1 (* v2 v3))) (* v1 (* v2 (* v3 v0)))))) (4 (flip 3 (1)) ((= (* v1 (* v2 (* v3 v0))) (* v0 (* v1 (* v2 v3)))))) (5 (instantiate 3 ((v0 . v66))) ((= (* v66 (* v1 (* v2 v3))) (* v1 (* v2 (* v3 v66)))))) (6 (instantiate 3 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . (* v1 (* v2 v3))))) ((= (* v64 (* v65 (* v66 (* v1 (* v2 v3))))) (* v65 (* v66 (* (* v1 (* v2 v3)) v64)))))) (7 (paramod 5 (1 1) 6 (1 1 2 2)) ((= (* v64 (* v65 (* v1 (* v2 (* v3 v66))))) (* v65 (* v66 (* (* v1 (* v2 v3)) v64)))))) (8 (instantiate 2 ((v0 . v1)(v1 . (* v2 v3))(v2 . v64))) ((= (* (* v1 (* v2 v3)) v64) (* v1 (* (* v2 v3) v64))))) (9 (paramod 8 (1 1) 7 (1 2 2 2)) ((= (* v64 (* v65 (* v1 (* v2 (* v3 v66))))) (* v65 (* v66 (* v1 (* (* v2 v3) v64))))))) (10 (instantiate 2 ((v0 . v2)(v1 . v3)(v2 . v64))) ((= (* (* v2 v3) v64) (* v2 (* v3 v64))))) (11 (paramod 10 (1 1) 9 (1 2 2 2 2)) ((= (* v64 (* v65 (* v1 (* v2 (* v3 v66))))) (* v65 (* v66 (* v1 (* v2 (* v3 v64)))))))) (12 (instantiate 11 ((v1 . v2)(v2 . v3)(v3 . v4)(v64 . v0)(v65 . v1)(v66 . v5))) ((= (* v0 (* v1 (* v2 (* v3 (* v4 v5))))) (* v1 (* v5 (* v2 (* v3 (* v4 v0)))))))) (13 (instantiate 3 ((v0 . v65)(v1 . v66)(v2 . v67)(v3 . v64))) ((= (* v65 (* v66 (* v67 v64))) (* v66 (* v67 (* v64 v65)))))) (14 (instantiate 4 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . v67))) ((= (* v65 (* v66 (* v67 v64))) (* v64 (* v65 (* v66 v67)))))) (15 (paramod 13 (1 1) 14 (1 1)) ((= (* v66 (* v67 (* v64 v65))) (* v64 (* v65 (* v66 v67)))))) (16 (instantiate 15 ((v64 . v2)(v65 . v3)(v66 . v0)(v67 . v1))) ((= (* v0 (* v1 (* v2 v3))) (* v2 (* v3 (* v0 v1)))))) (17 (instantiate 16 ((v0 . v65)(v1 . v66)(v2 . v67)(v3 . (* v68 v69)))) ((= (* v65 (* v66 (* v67 (* v68 v69)))) (* v67 (* (* v68 v69) (* v65 v66)))))) (18 (instantiate 12 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . v67)(v4 . v68)(v5 . v69))) ((= (* v64 (* v65 (* v66 (* v67 (* v68 v69))))) (* v65 (* v69 (* v66 (* v67 (* v68 v64)))))))) (19 (paramod 17 (1 1) 18 (1 1 2)) ((= (* v64 (* v67 (* (* v68 v69) (* v65 v66)))) (* v65 (* v69 (* v66 (* v67 (* v68 v64)))))))) (20 (instantiate 2 ((v0 . v68)(v1 . v69)(v2 . (* v65 v66)))) ((= (* (* v68 v69) (* v65 v66)) (* v68 (* v69 (* v65 v66)))))) (21 (paramod 20 (1 1) 19 (1 1 2 2)) ((= (* v64 (* v67 (* v68 (* v69 (* v65 v66))))) (* v65 (* v69 (* v66 (* v67 (* v68 v64)))))))) (22 (instantiate 21 ((v64 . v0)(v65 . v4)(v66 . v5)(v67 . v1)(v68 . v2)(v69 . v3))) ((= (* v0 (* v1 (* v2 (* v3 (* v4 v5))))) (* v4 (* v3 (* v5 (* v1 (* v2 v0)))))))) (23 (flip 22 (1)) ((= (* v4 (* v3 (* v5 (* v1 (* v2 v0))))) (* v0 (* v1 (* v2 (* v3 (* v4 v5)))))))) (24 (instantiate 4 ((v0 . (* v66 v64))(v1 . v67)(v2 . v69)(v3 . v65))) ((= (* v67 (* v69 (* v65 (* v66 v64)))) (* (* v66 v64) (* v67 (* v69 v65)))))) (25 (instantiate 23 ((v0 . v64)(v1 . v65)(v2 . v66)(v3 . v67)(v4 . v68)(v5 . v69))) ((= (* v68 (* v67 (* v69 (* v65 (* v66 v64))))) (* v64 (* v65 (* v66 (* v67 (* v68 v69)))))))) (26 (paramod 24 (1 1) 25 (1 1 2)) ((= (* v68 (* (* v66 v64) (* v67 (* v69 v65)))) (* v64 (* v65 (* v66 (* v67 (* v68 v69)))))))) (27 (instantiate 2 ((v0 . v66)(v1 . v64)(v2 . (* v67 (* v69 v65))))) ((= (* (* v66 v64) (* v67 (* v69 v65))) (* v66 (* v64 (* v67 (* v69 v65))))))) (28 (paramod 27 (1 1) 26 (1 1 2)) ((= (* v68 (* v66 (* v64 (* v67 (* v69 v65))))) (* v64 (* v65 (* v66 (* v67 (* v68 v69)))))))) (29 (instantiate 28 ((v64 . v2)(v65 . v5)(v66 . v1)(v67 . v3)(v68 . v0)(v69 . v4))) ((= (* v0 (* v1 (* v2 (* v3 (* v4 v5))))) (* v2 (* v5 (* v1 (* v3 (* v0 v4)))))))) (30 (flip 29 (1)) ((= (* v2 (* v5 (* v1 (* v3 (* v0 v4))))) (* v0 (* v1 (* v2 (* v3 (* v4 v5)))))))) (31 (instantiate 30 ((v0 . (A))(v1 . (A))(v2 . (A))(v3 . (B))(v4 . (B))(v5 . (B)))) ((= (* (A) (* (B) (* (A) (* (B) (* (A) (B)))))) (* (A) (* (A) (* (A) (* (B) (* (B) (B))))))))) (32 (resolve 1 (1) 31 (1)) ((not (= (* (B) (* (B) (* (B) (* (A) (* (A) (A)))))) (* (A) (* (A) (* (A) (* (B) (* (B) (B)))))))))) (33 (instantiate 23 ((v0 . (A))(v1 . (A))(v2 . (A))(v3 . (B))(v4 . (B))(v5 . (B)))) ((= (* (B) (* (B) (* (B) (* (A) (* (A) (A)))))) (* (A) (* (A) (* (A) (* (B) (* (B) (B))))))))) (34 (resolve 32 (1) 33 (1)) ()) )