TSTP Solution File: GRP083-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP083-1 : TPTP v3.4.2. Bugfixed v2.3.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art10.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 0.0s
% Output : Assurance 0.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP083-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 6 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 6 5)
% (binary-posweight-lex-big-order 30 #f 6 5)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(4,40,0,8,0,0,19556,4,756)
%
%
% START OF PROOF
% 5 [] equal(X,X).
% 6 [] equal(double_divide(double_divide(X,inverse(double_divide(Y,Z))),double_divide(inverse(Y),inverse(double_divide(U,double_divide(X,U))))),Z).
% 7 [] equal(multiply(X,Y),inverse(double_divide(Y,X))).
% 8 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 9 [para:6.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(Y,multiply(U,X))),inverse(U)).
% 10 [para:7.1.2,6.1.1.1.2,demod:7] equal(double_divide(double_divide(X,multiply(Y,Z)),double_divide(inverse(Z),multiply(double_divide(X,U),U))),Y).
% 11 [para:7.1.2,6.1.1.2.1,demod:7] equal(double_divide(double_divide(X,multiply(Y,double_divide(Z,U))),double_divide(multiply(U,Z),multiply(double_divide(X,V),V))),Y).
% 12 [para:6.1.1,6.1.1.1.2.1,demod:7] equal(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),U),multiply(double_divide(X,V),V))),double_divide(inverse(Z),multiply(double_divide(U,W),W))).
% 13 [para:7.1.2,9.1.1.1.1] equal(multiply(double_divide(multiply(X,Y),multiply(double_divide(Z,U),U)),double_divide(Z,multiply(V,double_divide(Y,X)))),inverse(V)).
% 14 [para:9.1.1,9.1.1.2.2,demod:7] equal(multiply(double_divide(multiply(multiply(X,Y),Z),multiply(double_divide(U,V),V)),double_divide(U,inverse(X))),multiply(multiply(double_divide(Z,W),W),inverse(Y))).
% 16 [para:11.1.1,6.1.1.1.2.1,demod:7] equal(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,double_divide(Z,U)),V),multiply(double_divide(X,W),W))),double_divide(multiply(U,Z),multiply(double_divide(V,X1),X1))).
% 18 [para:12.1.2,7.1.2.1,demod:7] equal(multiply(multiply(double_divide(X,Y),Y),inverse(Z)),multiply(double_divide(multiply(multiply(U,Z),X),multiply(double_divide(V,W),W)),double_divide(V,inverse(U)))).
% 19 [para:7.1.2,12.1.1.1.2] equal(double_divide(double_divide(X,multiply(Y,Z)),double_divide(multiply(multiply(double_divide(Z,Y),U),V),multiply(double_divide(X,W),W))),double_divide(inverse(U),multiply(double_divide(V,X1),X1))).
% 21 [para:6.1.1,12.1.2.2.1,demod:7] equal(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),double_divide(U,multiply(V,W))),multiply(double_divide(X,X1),X1))),double_divide(inverse(Z),multiply(V,double_divide(inverse(W),multiply(double_divide(U,X2),X2))))).
% 22 [para:12.1.2,10.1.1.1] equal(double_divide(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),U),multiply(double_divide(X,V),V))),double_divide(inverse(W),multiply(double_divide(inverse(Z),X1),X1))),double_divide(U,W)).
% 26 [para:12.1.2,11.1.1.1] equal(double_divide(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),U),multiply(double_divide(X,V),V))),double_divide(multiply(W,X1),multiply(double_divide(inverse(Z),X2),X2))),double_divide(U,double_divide(X1,W))).
% 27 [para:12.1.2,13.1.1.2,demod:7] equal(multiply(double_divide(multiply(X,Y),multiply(double_divide(inverse(Z),U),U)),double_divide(double_divide(V,inverse(W)),double_divide(multiply(multiply(W,Z),X1),multiply(double_divide(V,X2),X2)))),multiply(double_divide(Y,X),X1)).
% 28 [para:13.1.1,12.1.1.2.1.1,demod:7] equal(double_divide(double_divide(X,multiply(multiply(double_divide(Y,Z),Z),multiply(U,V))),double_divide(multiply(inverse(W),X1),multiply(double_divide(X,X2),X2))),double_divide(multiply(multiply(W,double_divide(V,U)),Y),multiply(double_divide(X1,X3),X3))).
% 29 [para:12.1.1,12.1.1] equal(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(inverse(X),multiply(double_divide(Y,U),U))).
% 30 [para:12.1.2,12.1.2] equal(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),U),multiply(double_divide(X,V),V))),double_divide(double_divide(W,inverse(X1)),double_divide(multiply(multiply(X1,Z),U),multiply(double_divide(W,X2),X2)))).
% 31 [para:12.1.1,12.1.2.2.1] equal(double_divide(double_divide(X,inverse(Y)),double_divide(multiply(multiply(Y,Z),double_divide(U,inverse(V))),multiply(double_divide(X,W),W))),double_divide(inverse(Z),multiply(double_divide(inverse(X1),multiply(double_divide(X2,X3),X3)),double_divide(multiply(multiply(V,X1),X2),multiply(double_divide(U,X4),X4))))).
% 32 [para:29.1.1,7.1.2.1,demod:7] equal(multiply(multiply(double_divide(X,Y),Y),inverse(Z)),multiply(multiply(double_divide(X,U),U),inverse(Z))).
% 33 [para:7.1.2,29.1.1.1,demod:7] equal(double_divide(multiply(X,Y),multiply(double_divide(Z,U),U)),double_divide(multiply(X,Y),multiply(double_divide(Z,V),V))).
% 34 [para:29.1.1,6.1.1.1.2.1,demod:10,7] equal(multiply(double_divide(X,Y),Y),multiply(double_divide(X,Z),Z)).
% 47 [para:6.1.1,34.1.1.1,demod:7] equal(multiply(X,double_divide(inverse(Y),multiply(double_divide(Z,U),U))),multiply(double_divide(double_divide(Z,multiply(X,Y)),V),V)).
% 49 [para:34.1.1,10.1.1.1.2] equal(double_divide(double_divide(X,multiply(double_divide(Y,Z),Z)),double_divide(inverse(U),multiply(double_divide(X,V),V))),double_divide(Y,U)).
% 50 [para:34.1.1,9.1.1.2.2,demod:7] equal(multiply(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(Y,multiply(double_divide(U,V),V))),multiply(X,U)).
% 51 [para:34.1.1,11.1.1.1.2] equal(double_divide(double_divide(X,multiply(double_divide(Y,Z),Z)),double_divide(multiply(U,V),multiply(double_divide(X,W),W))),double_divide(Y,double_divide(V,U))).
% 53 [para:11.1.1,34.1.1.1] equal(multiply(X,double_divide(multiply(Y,Z),multiply(double_divide(U,V),V))),multiply(double_divide(double_divide(U,multiply(X,double_divide(Z,Y))),W),W)).
% 57 [para:34.1.1,12.1.1.2.1.1,demod:7] equal(double_divide(double_divide(X,multiply(Y,Z)),double_divide(multiply(multiply(double_divide(Z,U),U),V),multiply(double_divide(X,W),W))),double_divide(inverse(Y),multiply(double_divide(V,X1),X1))).
% 58 [para:12.1.1,34.1.1.1] equal(multiply(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(multiply(multiply(U,X),Y),multiply(double_divide(V,W),W))),multiply(double_divide(double_divide(V,inverse(U)),X1),X1)).
% 66 [para:14.1.1,9.1.1.2.2,demod:7] equal(multiply(double_divide(multiply(inverse(X),Y),multiply(double_divide(Z,U),U)),double_divide(Z,multiply(multiply(double_divide(V,W),W),inverse(X1)))),multiply(multiply(double_divide(Y,X2),X2),multiply(multiply(X,X1),V))).
% 67 [para:13.1.1,14.1.1.1.1.1,demod:7] equal(multiply(double_divide(multiply(inverse(X),Y),multiply(double_divide(Z,U),U)),double_divide(Z,multiply(multiply(double_divide(V,W),W),multiply(X1,X2)))),multiply(multiply(double_divide(Y,X3),X3),multiply(multiply(X,double_divide(X2,X1)),V))).
% 71 [para:14.1.2,14.1.2] equal(multiply(double_divide(multiply(multiply(X,Y),Z),multiply(double_divide(U,V),V)),double_divide(U,inverse(X))),multiply(double_divide(multiply(multiply(W,Y),Z),multiply(double_divide(X1,X2),X2)),double_divide(X1,inverse(W)))).
% 75 [para:32.1.1,9.1.1.2.2,demod:9] equal(inverse(multiply(double_divide(X,Y),Y)),inverse(multiply(double_divide(X,Z),Z))).
% 103 [para:14.1.1,33.1.1.1] equal(double_divide(multiply(multiply(double_divide(X,Y),Y),inverse(Z)),multiply(double_divide(U,V),V)),double_divide(multiply(double_divide(multiply(multiply(W,Z),X),multiply(double_divide(X1,X2),X2)),double_divide(X1,inverse(W))),multiply(double_divide(U,X3),X3))).
% 149 [para:75.1.1,49.1.1.2.1,demod:49] equal(double_divide(X,multiply(double_divide(Y,Z),Z)),double_divide(X,multiply(double_divide(Y,U),U))).
% 230 [para:12.1.2,19.1.1.1,demod:26] equal(double_divide(X,double_divide(Y,multiply(double_divide(Z,double_divide(X,Z)),U))),double_divide(inverse(U),multiply(double_divide(Y,V),V))).
% 247 [para:230.1.1,10.1.1,demod:7] equal(double_divide(multiply(X,double_divide(X,multiply(Y,Z))),multiply(double_divide(inverse(Z),U),U)),Y).
% 256 [para:34.1.1,230.1.1.2.2,demod:7] equal(double_divide(X,double_divide(Y,multiply(double_divide(Z,U),U))),double_divide(multiply(Z,X),multiply(double_divide(Y,V),V))).
% 258 [para:230.1.1,49.1.1,demod:7] equal(double_divide(multiply(X,double_divide(X,multiply(double_divide(Y,Z),Z))),multiply(double_divide(inverse(U),V),V)),double_divide(Y,U)).
% 260 [para:230.1.2,149.1.2] equal(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(U,double_divide(Y,multiply(double_divide(V,double_divide(U,V)),X)))).
% 300 [para:256.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,multiply(double_divide(Y,Z),Z)),U),multiply(multiply(double_divide(X,V),V),multiply(Y,U))).
% 307 [para:256.1.2,11.1.1.2] equal(double_divide(double_divide(X,multiply(Y,double_divide(Z,U))),double_divide(Z,double_divide(X,multiply(double_divide(U,V),V)))),Y).
% 338 [para:300.1.1,34.1.1] equal(multiply(multiply(double_divide(X,Y),Y),multiply(Z,multiply(double_divide(Z,U),U))),multiply(double_divide(X,V),V)).
% 399 [para:247.1.1,307.1.1.2.2] equal(double_divide(double_divide(multiply(X,double_divide(X,multiply(Y,Z))),multiply(U,double_divide(V,inverse(Z)))),double_divide(V,Y)),U).
% 432 [para:338.1.1,10.1.1.1.2,demod:49] equal(double_divide(X,multiply(Y,multiply(double_divide(Y,Z),Z))),multiply(double_divide(X,U),U)).
% 515 [para:432.1.2,432.1.2] equal(double_divide(X,multiply(Y,multiply(double_divide(Y,Z),Z))),double_divide(X,multiply(U,multiply(double_divide(U,V),V)))).
% 641 [para:515.1.1,6.1.1.1.2.1,demod:10,7] equal(multiply(X,multiply(double_divide(X,Y),Y)),multiply(Z,multiply(double_divide(Z,U),U))).
% 755 [para:34.1.1,26.1.1.2.1,demod:26] equal(double_divide(X,double_divide(Y,double_divide(Z,Y))),double_divide(X,double_divide(U,double_divide(Z,U)))).
% 771 [para:641.1.1,26.1.1.2.1,demod:26] equal(double_divide(X,double_divide(multiply(double_divide(Y,Z),Z),Y)),double_divide(X,double_divide(multiply(double_divide(U,V),V),U))).
% 772 [para:755.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,double_divide(Y,X)),Z),multiply(double_divide(U,double_divide(Y,U)),Z)).
% 773 [para:755.1.1,6.1.1.1.2.1,demod:10,7] equal(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(Y,Z))).
% 844 [para:773.1.1,34.1.1.1] equal(multiply(double_divide(X,double_divide(Y,X)),double_divide(Y,Z)),multiply(double_divide(Z,U),U)).
% 848 [para:773.1.1,75.1.1.1.1] equal(inverse(multiply(double_divide(X,double_divide(Y,X)),double_divide(Y,Z))),inverse(multiply(double_divide(Z,U),U))).
% 858 [para:773.1.1,49.1.1.1.2.1] equal(double_divide(double_divide(X,multiply(double_divide(Y,double_divide(Z,Y)),double_divide(Z,U))),double_divide(inverse(V),multiply(double_divide(X,W),W))),double_divide(U,V)).
% 864 [para:149.1.1,773.1.1.2] equal(double_divide(multiply(double_divide(X,Y),Y),double_divide(Z,multiply(double_divide(X,U),U))),double_divide(V,double_divide(Z,V))).
% 900 [para:773.1.1,256.1.1] equal(double_divide(X,double_divide(Y,X)),double_divide(multiply(Z,multiply(double_divide(Z,U),U)),multiply(double_divide(Y,V),V))).
% 957 [para:773.1.1,755.1.1] equal(double_divide(X,double_divide(Y,X)),double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U)))).
% 959 [para:755.1.1,773.1.1.2] equal(double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(U,double_divide(Y,U)))),double_divide(V,double_divide(Z,V))).
% 980 [para:772.1.1,26.1.1.2.1,demod:26] equal(double_divide(X,double_divide(Y,double_divide(Z,double_divide(U,Z)))),double_divide(X,double_divide(Y,double_divide(V,double_divide(U,V))))).
% 1036 [para:773.1.1,844.1.1.2] equal(multiply(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(U,Z))),multiply(double_divide(double_divide(U,Y),V),V)).
% 1408 [para:771.1.1,773.1.1] equal(double_divide(X,double_divide(multiply(double_divide(Y,Z),Z),Y)),double_divide(U,double_divide(multiply(double_divide(X,V),V),U))).
% 1868 [para:864.1.1,49.1.1.1.2.1,demod:858] equal(double_divide(multiply(double_divide(X,Y),Y),Z),double_divide(multiply(double_divide(X,U),U),Z)).
% 2009 [para:432.1.2,1868.1.1.1] equal(double_divide(double_divide(X,multiply(Y,multiply(double_divide(Y,Z),Z))),U),double_divide(multiply(double_divide(X,V),V),U)).
% 6619 [para:399.1.1,432.1.2.1] equal(double_divide(double_divide(multiply(X,double_divide(X,multiply(Y,Z))),multiply(U,double_divide(V,inverse(Z)))),multiply(W,multiply(double_divide(W,X1),X1))),multiply(U,double_divide(V,Y))).
% 6644 [para:258.1.1,399.1.1.1] equal(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,U))),double_divide(inverse(Y),double_divide(Z,inverse(U)))).
% 6652 [para:7.1.2,6644.1.2.2.2] equal(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,double_divide(U,V)))),double_divide(inverse(Y),double_divide(Z,multiply(V,U)))).
% 6657 [para:6.1.1,6644.1.1.2,demod:7] equal(double_divide(double_divide(inverse(X),Y),Z),double_divide(inverse(Y),double_divide(double_divide(U,multiply(Z,X)),inverse(multiply(double_divide(U,V),V))))).
% 6792 [para:773.1.1,6644.1.1.1,demod:7] equal(double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(U,V))),double_divide(multiply(U,Y),double_divide(Z,inverse(V)))).
% 6811 [para:6644.1.1,957.1.2] equal(double_divide(X,double_divide(Y,X)),double_divide(inverse(Y),double_divide(Z,inverse(Z)))).
% 6814 [para:6644.1.2,957.1.2.2,demod:6652] equal(double_divide(X,double_divide(Y,X)),double_divide(inverse(Y),double_divide(double_divide(Z,U),multiply(U,Z)))).
% 7227 [para:6811.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,Y),Y),multiply(double_divide(Z,inverse(Z)),inverse(X))).
% 7230 [para:6811.1.2,6.1.1.1.2.1,demod:49,7] equal(double_divide(X,inverse(X)),double_divide(Y,inverse(Y))).
% 7711 [para:2009.1.2,6811.1.2.2,demod:6657] equal(double_divide(X,double_divide(Y,X)),double_divide(double_divide(inverse(multiply(double_divide(Z,U),U)),Y),Z)).
% 7845 [para:7230.1.1,7.1.2.1,demod:7] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 7846 [para:7.1.2,7230.1.1.2] equal(double_divide(double_divide(X,Y),multiply(Y,X)),double_divide(Z,inverse(Z))).
% 8097 [para:7.1.2,7845.1.1.1] equal(multiply(multiply(X,Y),double_divide(Y,X)),multiply(inverse(Z),Z)).
% 8102 [para:7845.1.1,13.1.1.2.2,demod:7] equal(multiply(double_divide(multiply(X,Y),multiply(double_divide(Z,U),U)),double_divide(Z,multiply(inverse(V),V))),inverse(multiply(X,Y))).
% 8135 [para:7845.1.1,27.1.1.1.1,demod:27] equal(multiply(double_divide(X,inverse(X)),Y),multiply(double_divide(Z,inverse(Z)),Y)).
% 8292 [para:7846.1.1,50.1.1.2.2.1] equal(multiply(double_divide(inverse(X),multiply(double_divide(Y,Z),Z)),double_divide(Y,multiply(double_divide(U,inverse(U)),multiply(V,W)))),multiply(X,double_divide(W,V))).
% 8962 [para:7230.1.1,7846.1.1.1] equal(double_divide(double_divide(X,inverse(X)),multiply(inverse(Y),Y)),double_divide(Z,inverse(Z))).
% 9170 [para:7230.1.1,8097.1.1.2] equal(multiply(multiply(inverse(X),X),double_divide(Y,inverse(Y))),multiply(inverse(Z),Z)).
% 9815 [para:8962.1.1,50.1.1.2.2.1,demod:8292] equal(multiply(X,double_divide(Y,inverse(Y))),multiply(X,double_divide(Z,inverse(Z)))).
% 10545 [para:9170.1.1,9.1.1.2.2,demod:8102,7] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 10675 [para:10545.1.1,49.1.1.2.1,demod:49] equal(double_divide(X,multiply(inverse(Y),Y)),double_divide(X,multiply(inverse(Z),Z))).
% 13627 [para:7711.1.2,6.1.1.1.2.1,demod:51,7] equal(double_divide(X,double_divide(inverse(multiply(double_divide(Y,Z),Z)),X)),Y).
% 13739 [para:13627.1.1,7.1.2.1] equal(multiply(double_divide(inverse(multiply(double_divide(X,Y),Y)),Z),Z),inverse(X)).
% 13747 [para:13627.1.1,256.1.1,demod:13739] equal(X,double_divide(multiply(Y,multiply(double_divide(Y,Z),Z)),inverse(X))).
% 13800 [para:7.1.2,13747.1.2.2] equal(double_divide(X,Y),double_divide(multiply(Z,multiply(double_divide(Z,U),U)),multiply(Y,X))).
% 13842 [para:13747.1.2,432.1.2.1,demod:13800] equal(double_divide(multiply(double_divide(X,Y),Y),X),multiply(Z,inverse(Z))).
% 13911 [para:13747.1.2,959.1.2.2,demod:13800,7,6792] equal(double_divide(multiply(X,Y),double_divide(Y,X)),double_divide(inverse(Z),Z)).
% 13961 [para:13747.1.2,7230.1.1] equal(multiply(X,multiply(double_divide(X,Y),Y)),double_divide(Z,inverse(Z))).
% 14458 [para:13842.1.1,13842.1.1] equal(multiply(X,inverse(X)),multiply(Y,inverse(Y))).
% 14613 [para:14458.1.1,57.1.1.2.1,demod:13739] equal(double_divide(double_divide(X,multiply(Y,Z)),double_divide(multiply(U,inverse(U)),multiply(double_divide(X,V),V))),double_divide(inverse(Y),inverse(Z))).
% 14793 [para:6.1.1,13911.1.1.2,demod:9,7] equal(double_divide(inverse(X),X),double_divide(inverse(Y),Y)).
% 14798 [para:13911.1.2,11.1.1.1.2.2,demod:7,14613] equal(double_divide(inverse(X),multiply(double_divide(Y,Z),multiply(Z,Y))),X).
% 16504 [para:13961.1.2,399.1.1.2,demod:6619] equal(multiply(X,double_divide(Y,inverse(Y))),X).
% 16536 [para:13961.1.2,9815.1.1.2,demod:16504] equal(multiply(X,multiply(Y,multiply(double_divide(Y,Z),Z))),X).
% 16574 [para:13961.1.1,13747.1.2.1] equal(X,double_divide(double_divide(Y,inverse(Y)),inverse(X))).
% 16590 [para:7.1.2,16504.1.1.2.2] equal(multiply(X,double_divide(double_divide(Y,Z),multiply(Z,Y))),X).
% 16923 [para:7.1.2,16574.1.2.2] equal(double_divide(X,Y),double_divide(double_divide(Z,inverse(Z)),multiply(Y,X))).
% 17905 [para:6.1.1,14798.1.1.2.1,demod:9,7] equal(double_divide(inverse(X),multiply(Y,inverse(Y))),X).
% 17991 [para:641.1.1,14798.1.1.2.2,demod:16536] equal(double_divide(inverse(X),double_divide(multiply(double_divide(Y,Z),Z),Y)),X).
% 18286 [para:7.1.2,17905.1.1.1] equal(double_divide(multiply(X,Y),multiply(Z,inverse(Z))),double_divide(Y,X)).
% 18632 [para:17905.1.1,14793.1.1] equal(multiply(X,inverse(X)),double_divide(inverse(Y),Y)).
% 18899 [para:18632.1.2,864.1.1.2,demod:13627,18286] equal(double_divide(X,double_divide(Y,X)),Y).
% 18918 [para:18632.1.2,900.1.1.2,demod:18899,13800] equal(double_divide(X,multiply(Y,inverse(Y))),inverse(X)).
% 18938 [para:18632.1.2,980.1.1.2,demod:18899,18918] equal(inverse(X),double_divide(X,double_divide(inverse(Y),Y))).
% 18949 [para:18632.1.2,1036.1.1.1.2,demod:18899,18918] equal(multiply(inverse(X),Y),multiply(double_divide(double_divide(Y,inverse(X)),Z),Z)).
% 18979 [para:18632.1.2,1408.1.2.2.1.1,demod:18899,17991] equal(X,multiply(multiply(Y,inverse(Y)),X)).
% 19043 [para:18632.1.2,260.1.1.2.1,demod:18899,18979] equal(double_divide(inverse(X),Y),double_divide(Z,double_divide(inverse(Y),multiply(Z,X)))).
% 19164 [para:18632.1.2,6814.1.2.2.1,demod:18938,18286,18899] equal(X,inverse(inverse(X))).
% 19185 [para:18632.1.2,16536.1.1.2.2.1,demod:18979] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 19186 [para:18632.1.2,16590.1.1.2.1,demod:18286] equal(multiply(X,double_divide(inverse(Y),Y)),X).
% 19189 [para:7.1.2,19164.1.2.1] equal(double_divide(X,Y),inverse(multiply(Y,X))).
% 19195 [para:75.1.1,19164.1.2.1,demod:18899,19189] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 19198 [para:19164.1.2,49.1.1.2.1,demod:19195] equal(double_divide(double_divide(X,inverse(Y)),double_divide(Z,inverse(X))),double_divide(Y,inverse(Z))).
% 19200 [para:19164.1.2,50.1.1.1.1,demod:19195] equal(multiply(double_divide(X,inverse(Y)),double_divide(Y,inverse(Z))),multiply(inverse(X),Z)).
% 19201 [para:19164.1.2,18.1.2.2.2,demod:19195] equal(multiply(inverse(X),inverse(Y)),multiply(double_divide(multiply(multiply(inverse(Z),Y),X),inverse(U)),double_divide(U,Z))).
% 19214 [para:848.1.1,19164.1.2.1,demod:19164,19195,18899] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 19222 [para:19164.1.2,6644.1.2.1] equal(double_divide(double_divide(X,inverse(Y)),double_divide(Z,double_divide(X,U))),double_divide(Y,double_divide(Z,inverse(U)))).
% 19228 [para:19164.1.2,7227.1.2.2,demod:19164,19195] equal(X,multiply(double_divide(Y,inverse(Y)),X)).
% 19229 [para:19164.1.2,8135.1.1.1.2,demod:19228] equal(multiply(double_divide(inverse(X),X),Y),Y).
% 19235 [para:19164.1.2,10675.1.1.2.1,demod:18918] equal(inverse(X),double_divide(X,multiply(inverse(Y),Y))).
% 19247 [para:19164.1.2,71.1.1.2.2,demod:19189,19200,19201,19195] equal(multiply(inverse(X),inverse(Y)),multiply(double_divide(X,multiply(Z,Y)),Z)).
% 19255 [para:6.1.1,18899.1.1.2,demod:7,18899] equal(double_divide(double_divide(inverse(X),inverse(Y)),Z),double_divide(Y,multiply(Z,X))).
% 19262 [para:18899.1.1,16.1.1.2.2.1,demod:19195,19189,19198,19214] equal(double_divide(X,double_divide(Y,multiply(X,double_divide(Z,U)))),double_divide(multiply(U,Z),inverse(Y))).
% 19265 [para:18899.1.1,247.1.1.2.1,demod:19164,19189,19214] equal(double_divide(double_divide(X,Y),X),Y).
% 19268 [para:18899.1.1,256.1.1.2.2.1,demod:19195,19214] equal(double_divide(X,double_divide(Y,inverse(Z))),double_divide(multiply(Z,X),inverse(Y))).
% 19269 [para:256.1.2,18899.1.1.2,demod:19195] equal(double_divide(inverse(X),double_divide(Y,double_divide(X,inverse(Z)))),multiply(Z,Y)).
% 19270 [para:18899.1.1,300.1.1.1.2.1,demod:19195,19214] equal(multiply(double_divide(X,inverse(Y)),Z),multiply(inverse(X),multiply(Y,Z))).
% 19272 [para:307.1.1,18899.1.1.2,demod:19195] equal(double_divide(double_divide(X,double_divide(Y,inverse(Z))),U),double_divide(Y,multiply(U,double_divide(X,Z)))).
% 19288 [para:18899.1.1,53.1.1.2.2.1,demod:7,19195,19268,19214] equal(multiply(X,double_divide(Y,double_divide(Z,inverse(U)))),multiply(multiply(X,double_divide(Y,U)),Z)).
% 19295 [para:18899.1.1,6644.1.1.1,demod:7] equal(double_divide(X,double_divide(Y,double_divide(Z,U))),double_divide(multiply(Z,X),double_divide(Y,inverse(U)))).
% 19299 [para:18899.1.1,58.1.1.1.2.1,demod:18949,7,19164,19270,19189,19268,19195,19214] equal(multiply(X,multiply(double_divide(X,Y),Z)),multiply(inverse(Y),Z)).
% 19319 [para:16.1.2,19265.1.1.1,demod:19272,19262,7,19222,19189,19268,19195] equal(double_divide(X,multiply(multiply(Y,Z),double_divide(Z,Y))),inverse(X)).
% 19364 [para:57.1.1,19265.1.1.1,demod:19164,19268,19247,19255,19195] equal(double_divide(X,multiply(inverse(Y),inverse(Z))),double_divide(X,double_divide(Y,Z))).
% 19379 [para:19265.1.1,67.1.2.2.1.2,demod:19364,19214,19164,19268,19195] equal(multiply(double_divide(X,double_divide(Y,Z)),double_divide(Y,double_divide(U,V))),multiply(inverse(X),multiply(multiply(Z,V),U))).
% 19388 [para:18979.1.2,12.1.1.2.1.1,demod:19269,19268,19195,18938,19189] equal(multiply(X,Y),double_divide(inverse(X),inverse(Y))).
% 19395 [para:18979.1.2,21.1.1.2.1,demod:19388,19164,7,19198,19195] equal(double_divide(X,multiply(multiply(Y,Z),U)),double_divide(X,multiply(Y,multiply(Z,U)))).
% 19396 [para:18979.1.2,21.1.1.2.1.1,demod:19388,19269,19268,19195,18938,19189] equal(multiply(X,double_divide(Y,multiply(Z,U))),double_divide(inverse(X),multiply(Z,multiply(U,Y)))).
% 19398 [para:18979.1.2,22.1.1.1.2.1,demod:19388,19164,19198,19195] equal(double_divide(double_divide(X,inverse(Y)),multiply(Z,X)),double_divide(Y,Z)).
% 19407 [para:18979.1.2,30.1.1.2.1.1,demod:7,19222,19269,19268,19195,18938,19189] equal(multiply(X,Y),double_divide(Z,double_divide(Y,multiply(Z,X)))).
% 19409 [para:18979.1.2,31.1.2.2.2.1.1,demod:19319,19396,19395,19288,19388,19043,7,19222,19268,19195,18938,19189] equal(double_divide(inverse(X),Y),multiply(X,inverse(Y))).
% 19411 [para:18979.1.2,53.1.1,demod:7,19229,19409,19268,19195] equal(double_divide(X,double_divide(Y,inverse(Z))),multiply(double_divide(X,Z),Y)).
% 19423 [para:19185.1.1,47.1.1.2.2,demod:7,19195,19388,19235] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 19426 [para:19185.1.1,21.1.1.2.1.1,demod:16923,19388,19189,18899,19398,19411,19268,19195] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 19428 [para:19185.1.1,300.1.1,demod:19185,19195] equal(double_divide(X,inverse(Y)),multiply(inverse(X),Y)).
% 19443 [para:19186.1.1,66.1.1,demod:19189,19423,19247,19426,7,19164,19195,19428] equal(double_divide(double_divide(X,inverse(Y)),double_divide(Z,U)),double_divide(Y,double_divide(Z,multiply(X,U)))).
% 19453 [para:19189.1.2,12.1.2.1,demod:19407,7,19299,19443,19426,19295,19268,19195,19423] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(Y,X),inverse(Z))).
% 19462 [para:28.1.1,19195.1.1.1,demod:19426,7,19379,19189,19453,19428,19295,19268,19195,19423] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(double_divide(X,double_divide(U,Z)),Y)).
% 19484 [para:19229.1.1,31.1.2.2.2.2,demod:19189,19214,19407,7,19222,19462,19426,19295,19268,19195,19423,19388] equal(multiply(X,multiply(Y,Z)),double_divide(inverse(X),double_divide(Z,Y))).
% 19556 [para:103.1.1,6644.1.1.2.2,demod:19484,19453,18899,19398,19462,19295,19268,19423,19164,19428,19195] equal(double_divide(double_divide(double_divide(X,Y),Z),double_divide(U,multiply(Y,multiply(X,V)))),multiply(Z,multiply(V,U))).
% 19557 [input:8,cut:7845] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 19558 [para:19556.1.2,19557.2.2,demod:19228,19428,19556,19423,cut:5,cut:5] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 361
% derived clauses: 339920
% kept clauses: 19545
% kept size sum: 515703
% kept mid-nuclei: 2
% kept new demods: 1633
% forw unit-subs: 214194
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 42
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.94
% process. runtime: 7.90
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP083-1+eq_r.in")
%
%------------------------------------------------------------------------------