TSTP Solution File: GRP049-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP049-1 : 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 : art02.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/GRP049-1+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 8 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 8 5)
% (binary-posweight-lex-big-order 30 #f 8 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 *********
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,0,6,0,0,7,50,0,10,0,0,5334,4,755)
%
%
% START OF PROOF
% 8 [] equal(X,X).
% 9 [] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(Y),Y)))))),Z).
% 10 [] -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)).
% 11 [para:9.1.1,9.1.1.2.1.1.1] equal(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,multiply(inverse(Z),Z)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),inverse(multiply(U,multiply(inverse(U),U)))))).
% 13 [para:11.1.1,9.1.1] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(X,Y)),U))),inverse(multiply(Z,multiply(inverse(Z),Z))))),U).
% 14 [para:11.1.2,9.1.1.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),inverse(multiply(Y,multiply(inverse(Y),Y))))))),Z).
% 16 [para:9.1.1,13.1.1.1.1.1.1.1.1.1,demod:9] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(X),Z))),inverse(multiply(Y,multiply(inverse(Y),Y))))),Z).
% 23 [para:16.1.1,14.1.1.2.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(inverse(U),Y)),multiply(inverse(U),Z))).
% 25 [para:16.1.1,16.1.1.1.1.1.1.1.1,demod:16] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(Y,multiply(inverse(Y),Y))))),Z).
% 36 [para:23.1.2,23.1.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 41 [para:36.1.1,9.1.1.2.1.2.1.2] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),U)),inverse(multiply(multiply(Y,Z),multiply(inverse(multiply(V,Z)),multiply(V,Z))))))),U).
% 42 [?] ?
% 45 [para:11.1.2,36.1.1.1] equal(multiply(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,multiply(inverse(Z),Z)))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),V)),multiply(inverse(multiply(W,inverse(multiply(U,multiply(inverse(U),U))))),multiply(W,V))).
% 46 [para:36.1.1,36.1.1.1.1] 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))).
% 47 [para:36.1.1,36.1.1.2] 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)))).
% 48 [para:36.1.1,36.1.2.1.1] equal(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,U)),multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,Z))),multiply(inverse(multiply(Y,W)),U))).
% 51 [para:9.1.1,25.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(Y),Y))))),inverse(multiply(inverse(multiply(inverse(multiply(X,U)),Z)),inverse(multiply(U,multiply(inverse(U),U)))))).
% 52 [para:25.1.1,11.1.1.2] equal(multiply(X,Y),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),multiply(inverse(multiply(V,Z)),multiply(V,Y)))),inverse(multiply(U,multiply(inverse(U),U)))))).
% 55 [para:25.1.1,36.1.1.1] equal(multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)),multiply(inverse(multiply(V,inverse(multiply(Z,multiply(inverse(Z),Z))))),multiply(V,U))).
% 60 [para:9.1.1,46.1.1.2,demod:42] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U),multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),U)).
% 289 [para:25.1.1,41.1.1.2.1.1] equal(multiply(inverse(multiply(X,Y)),inverse(multiply(Z,inverse(multiply(multiply(X,Z),multiply(inverse(multiply(U,Z)),multiply(U,Z))))))),inverse(multiply(Y,multiply(inverse(Y),Y)))).
% 298 [para:25.1.1,55.1.2.1] equal(multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)),multiply(V,multiply(inverse(multiply(inverse(multiply(W,Z)),multiply(W,V))),U))).
% 398 [para:289.1.1,14.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),inverse(multiply(Y,multiply(inverse(Y),Y)))),Z).
% 442 [para:398.1.1,298.1.1.2] equal(multiply(inverse(X),X),multiply(Y,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,Y))),inverse(multiply(U,multiply(inverse(U),U)))))).
% 448 [para:442.1.2,9.1.1.2.1.1.1,demod:398] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(Z,multiply(inverse(Z),Z)))))),multiply(X,Z)).
% 451 [para:442.1.2,11.1.2.1.1.1,demod:9,398] equal(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(X,multiply(inverse(X),X)))))).
% 543 [para:398.1.1,442.1.2.2] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 547 [para:543.1.1,9.1.1.2.1.2.1.2] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(U),U)))))),Z).
% 569 [para:543.1.1,60.1.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),Y),multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U))),Y)).
% 622 [para:543.1.1,398.1.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),multiply(inverse(inverse(Y)),inverse(Y))))),Y).
% 642 [para:543.1.1,451.1.2.1.2.1.2] equal(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(X,multiply(inverse(Z),Z)))))).
% 675 [para:543.1.1,622.1.1.2.1.2] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))),Y).
% 705 [para:543.1.1,675.1.1.2.1] equal(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 800 [para:705.1.1,642.1.2.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 814 [para:800.1.1,543.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 817 [para:800.1.1,642.1.2.1.2.1.2.1] equal(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(X,multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))))))).
% 1486 [para:543.1.1,569.1.2.1.1] equal(multiply(inverse(multiply(inverse(X),X)),Y),multiply(inverse(multiply(inverse(Z),Z)),Y)).
% 1628 [para:705.1.1,547.1.1.2.1.1.1,demod:642] equal(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))).
% 1714 [para:1628.1.1,543.1.1] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
% 1715 [para:1628.1.2,543.1.1.1] equal(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 1725 [para:1628.1.2,675.1.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))),Y).
% 1811 [para:1628.1.2,1486.1.1.1] equal(multiply(multiply(inverse(X),X),Y),multiply(inverse(multiply(inverse(Z),Z)),Y)).
% 1828 [para:1628.1.2,1628.1.2.1.1] equal(multiply(inverse(X),X),inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),Z)))).
% 1842 [para:1628.1.2,1714.1.2.1] equal(inverse(multiply(inverse(X),X)),multiply(multiply(inverse(Y),Y),multiply(inverse(Z),Z))).
% 3009 [para:1811.1.2,448.1.1.2.1.2.1,demod:642] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,inverse(multiply(inverse(Z),Z)))).
% 3011 [para:1628.1.2,1811.1.2.1] equal(multiply(multiply(inverse(X),X),Y),multiply(multiply(inverse(Z),Z),Y)).
% 3077 [para:3011.1.1,448.1.1.2.1.2.1,demod:817] equal(multiply(X,multiply(inverse(Y),Y)),multiply(X,multiply(inverse(Z),Z))).
% 4788 [para:1828.1.1,1725.1.1.2.1.2] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(U),U)))))),Y).
% 4986 [para:1842.1.2,547.1.1.2.1.1.1.1.1,demod:4788] equal(multiply(inverse(inverse(multiply(inverse(X),X))),Y),Y).
% 5029 [para:4986.1.1,36.1.1.1.1,demod:4986] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 5035 [para:4986.1.1,642.1.2.1.1.1,demod:4986] equal(X,inverse(inverse(multiply(X,multiply(inverse(Y),Y))))).
% 5037 [para:800.1.1,4986.1.1.1.1.1.1,demod:5035] equal(multiply(inverse(multiply(inverse(X),X)),Y),Y).
% 5044 [para:1628.1.2,4986.1.1.1.1.1.1,demod:5035] equal(multiply(multiply(inverse(X),X),Y),Y).
% 5055 [para:5044.1.1,1725.1.1] equal(inverse(multiply(inverse(X),multiply(inverse(Y),Y))),X).
% 5057 [para:5037.1.1,298.1.1.2,demod:5029] equal(multiply(X,Y),multiply(Z,multiply(inverse(multiply(inverse(X),Z)),Y))).
% 5062 [para:36.1.1,5035.1.2.1.1,demod:5029] equal(inverse(multiply(inverse(X),Y)),inverse(inverse(multiply(inverse(Y),X)))).
% 5078 [para:5035.1.2,448.1.1.2.1.2.1.2.1,demod:5035,5037,5029] equal(multiply(X,inverse(Y)),multiply(X,inverse(multiply(Y,multiply(inverse(Z),Z))))).
% 5097 [para:5035.1.2,1715.1.1.2.1,demod:5044,5078] equal(multiply(X,inverse(X)),multiply(inverse(Y),Y)).
% 5098 [para:5035.1.2,1715.1.2.1,demod:5078,5044] equal(multiply(inverse(X),X),multiply(Y,inverse(Y))).
% 5101 [para:5035.1.2,1811.1.2.1.1.1,demod:5078,5044] equal(X,multiply(inverse(multiply(Y,inverse(Y))),X)).
% 5125 [para:5097.1.1,46.1.1.1.1.1.1,demod:5029,5037] equal(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,inverse(X))),U)),multiply(inverse(multiply(Z,Y)),U)).
% 5138 [?] ?
% 5139 [para:5097.1.1,547.1.1.2.1.1.1.1.1,demod:5055,5037] equal(multiply(X,inverse(multiply(inverse(Y),X))),Y).
% 5140 [para:5098.1.2,298.1.1.2,demod:5139,5057,5062,5029] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 5141 [para:5098.1.1,642.1.2.1.1.1,demod:5101,5140] equal(X,inverse(inverse(X))).
% 5142 [para:5098.1.1,3077.1.1.2,demod:5140] equal(multiply(X,multiply(Y,inverse(Y))),X).
% 5143 [para:5098.1.1,3009.1.1.2,demod:5142] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
% 5145 [para:45.1.2,36.1.1,demod:5141,5029,5140] equal(multiply(multiply(X,inverse(multiply(inverse(Y),inverse(Z)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),V)),multiply(U,V)).
% 5147 [para:36.1.1,45.1.1.2,demod:5057,5141,5029,5140] equal(multiply(multiply(X,inverse(multiply(inverse(Y),inverse(Z)))),multiply(inverse(Y),U)),multiply(multiply(X,Z),U)).
% 5154 [para:46.1.1,45.1.2.1.1.2.1.2,demod:5062,5145,5029,5140] equal(multiply(multiply(inverse(X),Y),Z),multiply(inverse(multiply(inverse(Y),X)),Z)).
% 5165 [para:60.1.1,45.1.2.1.1,demod:5141,5029,5154,5140] equal(multiply(multiply(X,inverse(multiply(inverse(Y),inverse(Z)))),multiply(inverse(multiply(multiply(inverse(U),multiply(X,Z)),Y)),V)),multiply(U,V)).
% 5186 [para:45.1.2,48.1.1.1.1,demod:5029,5125,5165,5154,5140] equal(multiply(inverse(multiply(X,Y)),Z),multiply(multiply(inverse(Y),U),multiply(inverse(multiply(X,U)),Z))).
% 5191 [para:48.1.1,45.1.1.2,demod:5141,5147,5186,5154,5029,5140] equal(multiply(multiply(X,Y),Z),multiply(U,multiply(multiply(inverse(U),multiply(X,Y)),Z))).
% 5207 [para:543.1.1,45.1.1.2,demod:5191,5141,5029,5154,5140] equal(multiply(X,inverse(multiply(inverse(Y),inverse(Z)))),multiply(multiply(X,Z),Y)).
% 5212 [para:543.1.1,45.1.2.1.1,demod:5044,5141,5154,5207,5140] equal(multiply(multiply(multiply(X,Y),Z),multiply(inverse(multiply(multiply(inverse(U),multiply(X,Y)),Z)),V)),multiply(U,V)).
% 5213 [para:45.1.2,642.1.2.1.2.1,demod:5138,5044,5212,5154,5207,5140] equal(inverse(multiply(inverse(X),inverse(Y))),multiply(Y,X)).
% 5220 [para:642.1.2,45.1.2.1,demod:5044,5154,5213,5140] equal(multiply(multiply(X,multiply(Y,Z)),multiply(inverse(multiply(multiply(inverse(U),multiply(X,Y)),Z)),V)),multiply(U,V)).
% 5222 [para:45.1.2,675.1.1.2.1,demod:5044,5220,5154,5213,5140] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 5224 [para:675.1.1,45.1.1.2.1.1,demod:5029,5138,5222,5141,5140] equal(multiply(multiply(X,multiply(Y,Z)),multiply(inverse(Z),U)),multiply(multiply(X,Y),U)).
% 5231 [para:705.1.2,45.1.1.2,demod:5191,5141,5029,5143,5044,5154,5138,5222,5140] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 5232 [para:705.1.1,45.1.1.2.1.1.1.1,demod:5143,5062,5224,5044,5154,5138,5222,5140] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 5243 [para:814.1.1,45.1.1.2.1.1.1.1,demod:5143,5044,5154,5232,5138,5222,5140] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 5274 [?] ?
% 5280 [para:51.1.1,675.1.1.2.1.1,demod:5044,5140,5142,5231,5154,5243] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),X)).
% 5293 [para:47.1.2,52.1.2.1.1.1.1.1,demod:5243,5274,5231,5224,5029,5280] equal(multiply(X,Y),multiply(inverse(multiply(Z,multiply(U,inverse(multiply(X,multiply(Z,U)))))),Y)).
% 5305 [para:642.1.2,5139.1.1.2.1.1,demod:5044,5140,5280] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 5306 [para:52.1.2,5139.1.1.2.1.1,demod:5142,5243,5274,5224,5029,5280,5231] equal(multiply(X,inverse(multiply(Y,multiply(Z,X)))),inverse(multiply(Y,Z))).
% 5335 [input:10,cut:5044,cut:543] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 5336 [para:5293.1.1,5335.1.2,demod:5141,5305,5306,5231,cut:8] 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 9
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 229
% derived clauses: 203978
% kept clauses: 5319
% kept size sum: 148597
% kept mid-nuclei: 4
% kept new demods: 466
% forw unit-subs: 192988
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 54
% fast unit cutoff: 5
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.63
% process. runtime: 7.61
% 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/GRP049-1+eq_r.in")
%
%------------------------------------------------------------------------------