TSTP Solution File: GRP053-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP053-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.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/GRP053-1+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 9 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 9 5)
% (binary-posweight-lex-big-order 30 #f 9 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(3,40,1,6,0,1,29,50,10,32,0,10,88,50,85,91,0,86,12816,4,772)
%
%
% START OF PROOF
% 89 [] equal(X,X).
% 90 [] equal(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(Z)))),inverse(multiply(inverse(X),X)))))),Z).
% 91 [] -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)).
% 92 [para:90.1.1,90.1.1.1.2.1.1.1.2.2] equal(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X)))))),multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(Z)))),inverse(multiply(inverse(U),U)))))).
% 94 [para:92.1.1,90.1.1] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(inverse(Z))))),inverse(multiply(inverse(X),X))))),Z).
% 95 [para:92.1.2,90.1.1.1] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X))))))),Z).
% 98 [para:94.1.1,90.1.1.1.2.1.1.1.2] equal(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X)))))),multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y)))).
% 99 [para:92.1.1,94.1.1.2.1.1.1.2.2.1,demod:90] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X))))),multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,Z))),inverse(multiply(inverse(U),U)))))).
% 102 [para:98.1.1,90.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(Z))))))),inverse(multiply(inverse(Y),Y))),Z).
% 103 [para:98.1.1,92.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y))),multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(Z)))),inverse(multiply(inverse(U),U)))))).
% 104 [para:98.1.2,92.1.2.2.1,demod:90] equal(X,multiply(Y,inverse(inverse(multiply(Z,inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),X)),inverse(multiply(inverse(Z),Z))))))))).
% 106 [para:98.1.1,95.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y)))),Z).
% 110 [para:92.1.1,102.1.1.1.1.2.2.1,demod:90] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(Y),Y))),multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),inverse(multiply(inverse(Y),Y)))).
% 112 [para:90.1.1,104.1.2.2.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,Z)))),multiply(X,inverse(U)))),inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(multiply(Y,Z)))))),multiply(Y,inverse(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(Z),Z))))))))).
% 145 [para:99.1.1,110.1.1.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Z,inverse(multiply(inverse(multiply(inverse(multiply(U,Z)),multiply(U,V))),inverse(multiply(inverse(Z),Z))))))),inverse(multiply(inverse(Y),Y))),multiply(inverse(multiply(inverse(multiply(W,Y)),multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,X)),multiply(X1,V))),inverse(multiply(inverse(X),X))))))),inverse(multiply(inverse(Y),Y)))).
% 147 [para:106.1.1,103.1.1.1.1.1] equal(multiply(inverse(multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(inverse(multiply(Z,X)))))),inverse(inverse(multiply(inverse(multiply(inverse(Z),Z)),U)))))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))),multiply(V,inverse(multiply(inverse(multiply(inverse(multiply(W,V)),multiply(W,inverse(U)))),inverse(multiply(inverse(V),V)))))).
% 150 [para:110.1.1,103.1.1.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(Y),Y)))),multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),V)))))),inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Y),Y))))),multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,W)),multiply(X1,inverse(V)))),inverse(multiply(inverse(W),W)))))).
% 158 [para:112.1.1,94.1.1.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y))))))))),Z).
% 167 [para:92.1.1,158.1.1.2.2.1,demod:90] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 171 [para:90.1.1,167.1.1.1] equal(multiply(X,multiply(Y,Z)),multiply(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,inverse(X)))),inverse(multiply(inverse(Y),Y)))))),multiply(U,Z))).
% 195 [para:167.1.1,102.1.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,inverse(inverse(multiply(multiply(Y,Z),inverse(U))))))),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z)))),U).
% 300 [para:167.1.1,167.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
% 301 [para:167.1.1,167.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))),multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))).
% 450 [para:90.1.1,301.1.2.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(V)))),inverse(multiply(inverse(U),U)))))),multiply(inverse(multiply(W,Y)),multiply(W,X1))),multiply(V,multiply(U,multiply(X,X1)))).
% 977 [para:301.1.1,171.1.2.2,demod:450] equal(multiply(X,multiply(Y,multiply(inverse(multiply(Z,U)),multiply(Z,V)))),multiply(X,multiply(Y,multiply(inverse(multiply(W,U)),multiply(W,V))))).
% 985 [para:977.1.1,95.1.1.1.1.2.1.1.1.2,demod:95] equal(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,U)))).
% 1385 [para:158.1.1,195.1.1.1.1] equal(multiply(inverse(X),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),multiply(inverse(X),inverse(multiply(inverse(multiply(U,Z)),multiply(U,Z))))).
% 1427 [para:90.1.1,1385.1.1.1,demod:90] equal(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),multiply(X,inverse(multiply(inverse(multiply(U,Z)),multiply(U,Z))))).
% 1430 [para:1385.1.1,95.1.1.1.1.2.1.1.1.2,demod:90] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y))),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,Y)))).
% 1568 [para:102.1.1,1430.1.1.1.1.1,demod:102] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(multiply(inverse(Z),Z)))))).
% 1764 [para:102.1.1,1568.1.2.1.1.1,demod:102] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 1921 [para:1764.1.1,90.1.1.1.2.1.1] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(X)),inverse(X))))))),X).
% 1923 [para:1764.1.1,90.1.1.1.2.1.1.1.2.2,demod:90] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1942 [para:1764.1.1,95.1.1.1.1.2.1.1] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),X))))))),X).
% 2093 [para:1764.1.1,167.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 2161 [para:1764.1.1,1427.1.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U))))).
% 2167 [para:1764.1.1,1764.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 2171 [para:1923.1.1,167.1.1.2] equal(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X))).
% 2201 [para:1923.1.1,985.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(multiply(Z,U)),multiply(Z,U)))).
% 2618 [para:1764.1.1,2201.1.2.2.1] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U)))).
% 2619 [para:1923.1.1,2201.1.2.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(Z),Z))).
% 2730 [para:1764.1.1,2619.1.1.2.1] equal(multiply(X,multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),multiply(X,multiply(inverse(U),U))).
% 2739 [para:1764.1.1,1942.1.1.1.1.2.1.2] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))))),X).
% 3145 [para:1764.1.1,2161.1.2.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 4232 [para:1764.1.1,1921.1.1.1.2.1.2] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))))),X).
% 4269 [para:1921.1.1,2171.1.2.1,demod:4232] equal(multiply(X,multiply(inverse(Y),Y)),multiply(Z,multiply(inverse(Z),X))).
% 4492 [para:4269.1.1,1923.1.1] equal(multiply(X,multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),multiply(inverse(Z),Z)).
% 5256 [para:4232.1.1,2739.1.1.1.1.2.1.2,demod:4232] equal(inverse(inverse(multiply(X,multiply(inverse(Y),Y)))),X).
% 5323 [para:4232.1.1,4232.1.1.1.2.1.2,demod:4232] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
% 5336 [para:5256.1.1,1923.1.1.1] equal(multiply(X,inverse(multiply(X,multiply(inverse(Y),Y)))),multiply(inverse(Z),Z)).
% 5397 [para:4269.1.1,5256.1.1.1.1] equal(inverse(inverse(multiply(X,multiply(inverse(X),Y)))),Y).
% 5422 [para:167.1.1,5323.1.1.1] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Z),Y)).
% 5451 [para:5323.1.1,1764.1.1] equal(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))).
% 5490 [para:2093.1.2,5323.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))),multiply(inverse(Z),Y)).
% 5495 [para:5323.1.1,3145.1.1.2] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 5536 [para:4269.1.1,5323.1.1.1] equal(inverse(multiply(X,multiply(inverse(X),inverse(Y)))),Y).
% 5592 [para:2093.1.1,5397.1.1.1.1,demod:5422] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
% 5635 [para:4492.1.1,5397.1.1.1.1.2,demod:5256] equal(X,multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y)))).
% 5758 [para:5451.1.1,2167.1.2.1,demod:5490] equal(multiply(inverse(X),X),inverse(inverse(multiply(inverse(Y),Y)))).
% 5764 [para:5451.1.1,2739.1.1.1.1.2.1.1.1,demod:5635] equal(inverse(inverse(multiply(X,inverse(multiply(inverse(Y),Y))))),X).
% 5813 [para:5451.1.1,4269.1.1.2] equal(multiply(X,inverse(multiply(inverse(Y),Y))),multiply(Z,multiply(inverse(Z),X))).
% 5874 [para:2739.1.1,5536.1.1.1.2.1,demod:5422,5592] equal(multiply(inverse(inverse(X)),multiply(inverse(Y),Y)),X).
% 5975 [para:5874.1.1,4269.1.1] equal(X,multiply(Y,multiply(inverse(Y),inverse(inverse(X))))).
% 5986 [para:5975.1.2,301.1.2.2] equal(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(V))))),multiply(inverse(multiply(X,Z)),V)).
% 6013 [para:5975.1.2,5397.1.1.1.1.2] equal(inverse(inverse(multiply(X,Y))),multiply(inverse(inverse(X)),inverse(inverse(Y)))).
% 6195 [para:5758.1.1,2739.1.1.1.1.2.1.1.1,demod:5635] equal(inverse(inverse(multiply(X,inverse(inverse(multiply(inverse(Y),Y)))))),X).
% 6346 [para:5758.1.1,5764.1.1.1.1.2.1] equal(inverse(inverse(multiply(X,inverse(inverse(inverse(multiply(inverse(Y),Y))))))),X).
% 7360 [para:6013.1.2,301.1.2.2.2,demod:5986] equal(multiply(inverse(multiply(inverse(X),Y)),Z),multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(multiply(X,Z)))))).
% 7398 [para:6013.1.2,4269.1.2.2,demod:5874] equal(X,multiply(inverse(Y),inverse(inverse(multiply(Y,X))))).
% 7410 [para:5764.1.1,6013.1.2.2.1] equal(inverse(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(inverse(Z),Z))))))),multiply(inverse(inverse(X)),inverse(Y))).
% 7458 [para:2093.1.1,7398.1.2.2.1.1,demod:5422] equal(multiply(inverse(X),Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Y),X)))).
% 8599 [para:5422.1.1,6013.1.2.2.1] equal(inverse(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U))))),multiply(inverse(inverse(X)),inverse(multiply(inverse(U),Z)))).
% 8602 [para:7398.1.2,5422.1.1.1.1.1] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Z))),multiply(inverse(Z),inverse(inverse(multiply(Y,X))))).
% 8603 [para:7398.1.2,5422.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(inverse(inverse(multiply(X,Z)))),Y)).
% 12398 [para:147.1.2,2739.1.1.1.1,demod:5592,7458,8602,7360] equal(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),multiply(inverse(multiply(inverse(Z),Z)),X)))))),inverse(Y)).
% 12486 [para:147.1.1,5764.1.1.1.1,demod:12398,8602,7360,7410,5422] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(inverse(Y)),X))),inverse(Y)).
% 12661 [para:2167.1.2,12486.1.1.1.1,demod:5874,5490] equal(multiply(inverse(multiply(inverse(X),X)),inverse(Y)),inverse(Y)).
% 12666 [para:2739.1.1,12486.1.1.2.1.1.1,demod:6195,12661] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))),Y).
% 12685 [para:12486.1.1,5536.1.1.1.2] equal(inverse(multiply(inverse(X),inverse(Y))),multiply(inverse(inverse(Y)),X)).
% 12686 [para:5536.1.1,12486.1.1.2,demod:8603,6013,12685] equal(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),inverse(Y)).
% 12690 [para:5758.1.2,12486.1.1.1,demod:5874] equal(multiply(multiply(inverse(X),X),inverse(Y)),inverse(Y)).
% 12699 [para:6013.1.2,12486.1.1.2.1,demod:12685,6013] equal(multiply(inverse(inverse(X)),inverse(multiply(Y,X))),inverse(Y)).
% 12706 [para:6346.1.1,12486.1.1.2.1.1,demod:12699] equal(inverse(X),inverse(multiply(X,inverse(inverse(inverse(multiply(inverse(Y),Y))))))).
% 12707 [para:6346.1.1,12486.1.1.2.1.1.1,demod:12706,12666] equal(X,inverse(inverse(X))).
% 12708 [para:5336.1.1,12486.1.1.2.1,demod:5256,12707] equal(multiply(inverse(X),inverse(multiply(inverse(Y),Y))),inverse(X)).
% 12720 [para:12486.1.1,5422.1.1.1.1.1,demod:12707] equal(inverse(multiply(X,multiply(Y,Z))),multiply(inverse(Z),inverse(multiply(X,Y)))).
% 12721 [para:12486.1.1,5422.1.1.1.2,demod:12685,12707] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 12730 [?] ?
% 12731 [para:5495.1.1,12486.1.1.2.1,demod:12690,12707] equal(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),inverse(X)).
% 12735 [para:12486.1.1,5813.1.2.2,demod:12708,12707] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 12736 [para:5813.1.1,12486.1.1,demod:12735,12707] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 12738 [para:5813.1.2,12486.1.1.2.1,demod:12721,12731,12707] equal(multiply(inverse(X),multiply(Y,inverse(Y))),inverse(X)).
% 12759 [para:147.1.2,12486.1.1.2.1,demod:8599,12730,12690,12686,12736,12721,5422,12707] equal(multiply(inverse(multiply(X,Y)),X),inverse(Y)).
% 12767 [para:12707.1.2,2739.1.1,demod:12707,12661] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 12774 [para:12707.1.2,2171.1.1.1.1.1,demod:12730] equal(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(X)))).
% 12775 [para:12707.1.2,2171.1.1.2.1,demod:12738] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(Z,Y)),multiply(Z,X))).
% 12780 [para:12707.1.2,2618.1.2.2.2.1,demod:12738,12767] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
% 12781 [para:12707.1.2,2730.1.2.2.1,demod:12780,12730] equal(X,multiply(X,multiply(Y,inverse(Y)))).
% 12782 [para:12707.1.2,4269.1.1.2.1,demod:12781] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 12783 [para:12707.1.2,4269.1.2.2.1,demod:12767] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 12787 [para:12707.1.2,145.1.1.1.1.2.2.1.2.1.1,demod:12774,12780,12721,12708,12783,12720,12707,12735,12775] equal(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Z),multiply(X,Y))).
% 12788 [para:12707.1.2,145.1.2.1.1.2.2.1.2.1.1,demod:12708,12783,12720,12735,12787,12736,12780,12721,12707,12775] equal(multiply(inverse(X),multiply(inverse(Y),Z)),inverse(multiply(inverse(Z),multiply(Y,X)))).
% 12793 [para:12767.1.1,300.1.1.1.1.2,demod:12775,12767,12707,12759] equal(multiply(X,multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(Z),Y))).
% 12795 [para:12767.1.1,301.1.1.2.2,demod:12775,12767,12781,12721,12759,12787] equal(multiply(inverse(X),Y),inverse(multiply(inverse(Y),X))).
% 12812 [para:300.1.2,150.1.2.2.1.1.1.1.1,demod:12735,12787,12793,12788,12707,12783,12782,12721,12795,12775] equal(inverse(X),multiply(Y,multiply(Z,multiply(U,inverse(multiply(X,multiply(Y,multiply(Z,U)))))))).
% 12817 [input:91,cut:1923] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 12818 [para:12812.1.1,12817.1.1.1.1,demod:12783,12721,12812,cut:89,cut:89] 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 11
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 255
% derived clauses: 153109
% kept clauses: 12799
% kept size sum: 457241
% kept mid-nuclei: 2
% kept new demods: 1189
% forw unit-subs: 99948
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 83
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.90
% process. runtime: 7.86
% 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/GRP053-1+eq_r.in")
%
%------------------------------------------------------------------------------