TSTP Solution File: GRP372-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP372-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art01.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 297.9s
% Output : Assurance 297.9s
% 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/GRP372-1+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 3 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(inverse(sk_c8),sk_c7).
% -equal(multiply(sk_c8,sk_c6),sk_c7).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425)
%
%
% START OF PROOF
% 513692 [] equal(X,X).
% 513693 [] equal(multiply(identity,X),X).
% 513694 [] equal(multiply(inverse(X),X),identity).
% 513695 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 513696 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 513715 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 513716 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c8).
% 513717 [?] ?
% 513721 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 513722 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 513723 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 513727 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 513728 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c8),sk_c7).
% 513729 [?] ?
% 513808 [hyper:513696,513716,513715,binarycut:513717] equal(inverse(sk_c1),sk_c8).
% 513818 [para:513808.1.1,513694.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 513851 [hyper:513696,513728,513727,binarycut:513729] equal(inverse(sk_c8),sk_c7).
% 513859 [para:513851.1.1,513694.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 513872 [hyper:513696,513723,513722,513721] equal(multiply(sk_c1,sk_c8),sk_c7).
% 513874 [para:513694.1.1,513695.1.1.1,demod:513693] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 513876 [para:513818.1.1,513695.1.1.1,demod:513693] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 513881 [para:513859.1.1,513695.1.1.1,demod:513693] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 513891 [para:513872.1.1,513876.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 513898 [para:513891.1.2,513881.1.2.2,demod:513859] equal(sk_c7,identity).
% 513905 [para:513898.1.1,513881.1.2.1,demod:513693] equal(X,multiply(sk_c8,X)).
% 513913 [hyper:513696,513874,513872,demod:513905,513874,demod:513808,cut:513692] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425)
%
%
% START OF PROOF
% 513913 [] equal(X,X).
% 513917 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 513939 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 513940 [?] ?
% 513945 [?] ?
% 513946 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 513974 [hyper:513917,513939,binarycut:513945] equal(inverse(sk_c3),sk_c8).
% 513976 [hyper:513917,513939,binarycut:513940] equal(inverse(sk_c1),sk_c8).
% 514001 [hyper:513917,513946,demod:513976,cut:513913] equal(multiply(sk_c3,sk_c8),sk_c7).
% 514003 [hyper:513917,514001,demod:513974,cut:513913] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425,514002,50,29425,514002,30,29425,514002,40,29425,514043,0,29431,514162,50,29432,514203,0,29432)
%
%
% START OF PROOF
% 514164 [] equal(multiply(identity,X),X).
% 514165 [] equal(multiply(inverse(X),X),identity).
% 514166 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 514167 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 514168 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 514169 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 514170 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 514171 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 514172 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 514173 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 514174 [?] ?
% 514175 [?] ?
% 514176 [?] ?
% 514177 [?] ?
% 514178 [?] ?
% 514179 [?] ?
% 514206 [hyper:514167,514168,binarycut:514174] equal(inverse(sk_c4),sk_c8).
% 514207 [para:514206.1.1,514165.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 514211 [hyper:514167,514171,binarycut:514177] equal(inverse(sk_c3),sk_c8).
% 514212 [para:514211.1.1,514165.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 514215 [hyper:514167,514169,binarycut:514175] equal(multiply(sk_c4,sk_c8),sk_c5).
% 514218 [hyper:514167,514170,binarycut:514176] equal(multiply(sk_c8,sk_c5),sk_c7).
% 514221 [hyper:514167,514172,binarycut:514178] equal(multiply(sk_c3,sk_c8),sk_c7).
% 514225 [hyper:514167,514173,binarycut:514179] equal(multiply(sk_c8,sk_c7),sk_c6).
% 514227 [para:514165.1.1,514166.1.1.1,demod:514164] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 514228 [para:514207.1.1,514166.1.1.1,demod:514164] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 514229 [para:514212.1.1,514166.1.1.1,demod:514164] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 514230 [para:514215.1.1,514166.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c4,multiply(sk_c8,X))).
% 514236 [para:514215.1.1,514228.1.2.2,demod:514218] equal(sk_c8,sk_c7).
% 514240 [para:514236.1.1,514218.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 514246 [para:514165.1.1,514227.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 514247 [para:514207.1.1,514227.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 514248 [para:514212.1.1,514227.1.2.2,demod:514247] equal(sk_c3,sk_c4).
% 514249 [para:514218.1.1,514227.1.2.2] equal(sk_c5,multiply(inverse(sk_c8),sk_c7)).
% 514250 [para:514221.1.1,514227.1.2.2,demod:514225,514211] equal(sk_c8,sk_c6).
% 514251 [para:514166.1.1,514227.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 514253 [para:514228.1.2,514227.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c8),X)).
% 514255 [para:514227.1.2,514227.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 514256 [para:514248.1.2,514215.1.1.1,demod:514221] equal(sk_c7,sk_c5).
% 514257 [para:514250.1.1,514207.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 514264 [para:514250.1.1,514236.1.1] equal(sk_c6,sk_c7).
% 514269 [para:514264.1.2,514256.1.1] equal(sk_c6,sk_c5).
% 514271 [para:514229.1.2,514227.1.2.2,demod:514253] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 514276 [para:514240.1.1,514227.1.2.2,demod:514165] equal(sk_c5,identity).
% 514279 [para:514276.1.1,514218.1.1.2] equal(multiply(sk_c8,identity),sk_c7).
% 514280 [para:514276.1.1,514269.1.2] equal(sk_c6,identity).
% 514286 [para:514228.1.2,514230.1.2.2,demod:514271] equal(multiply(sk_c5,multiply(sk_c3,X)),multiply(sk_c3,X)).
% 514297 [para:514280.1.1,514257.1.1.1,demod:514164] equal(sk_c4,identity).
% 514299 [para:514297.1.1,514207.1.1.2,demod:514279] equal(sk_c7,identity).
% 514300 [para:514297.1.1,514215.1.1.1,demod:514164] equal(sk_c8,sk_c5).
% 514305 [para:514300.1.1,514228.1.2.1,demod:514286,514271] equal(X,multiply(sk_c3,X)).
% 514315 [para:514299.1.1,514249.1.2.2,demod:514247] equal(sk_c5,sk_c4).
% 514317 [para:514315.1.2,514248.1.2] equal(sk_c3,sk_c5).
% 514319 [para:514317.1.2,514269.1.2] equal(sk_c6,sk_c3).
% 514339 [para:514319.1.2,514211.1.1.1] equal(inverse(sk_c6),sk_c8).
% 514345 [para:514255.1.2,514165.1.1] equal(multiply(X,inverse(X)),identity).
% 514347 [para:514255.1.2,514246.1.2] equal(X,multiply(X,identity)).
% 514350 [para:514347.1.2,514246.1.2] equal(X,inverse(inverse(X))).
% 514355 [para:514345.1.1,514251.1.2.2.2,demod:514347] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 514359 [para:514228.1.2,514355.1.2.1.1,demod:514305,514271] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 514371 [para:514359.1.2,514255.1.2,demod:514350] equal(multiply(X,sk_c8),X).
% 514372 [para:514236.1.1,514371.1.1.2] equal(multiply(X,sk_c7),X).
% 514377 [hyper:514167,514372,demod:514339,cut:514236] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425,514002,50,29425,514002,30,29425,514002,40,29425,514043,0,29431,514162,50,29432,514203,0,29432,514376,50,29434,514376,30,29434,514376,40,29434,514417,0,29434)
%
%
% START OF PROOF
% 514377 [] equal(X,X).
% 514381 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 514403 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 514404 [?] ?
% 514409 [?] ?
% 514410 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 514438 [hyper:514381,514403,binarycut:514409] equal(inverse(sk_c3),sk_c8).
% 514440 [hyper:514381,514403,binarycut:514404] equal(inverse(sk_c1),sk_c8).
% 514465 [hyper:514381,514410,demod:514440,cut:514377] equal(multiply(sk_c3,sk_c8),sk_c7).
% 514467 [hyper:514381,514465,demod:514438,cut:514377] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425,514002,50,29425,514002,30,29425,514002,40,29425,514043,0,29431,514162,50,29432,514203,0,29432,514376,50,29434,514376,30,29434,514376,40,29434,514417,0,29434,514466,50,29434,514466,30,29434,514466,40,29434,514507,0,29438,514647,50,29439,514688,0,29439,514878,50,29443,514919,0,29448,515117,50,29453,515158,0,29453,515364,50,29460,515405,0,29460,515617,50,29471,515658,0,29475,515878,50,29494,515919,0,29494,516147,50,29528,516188,0,29533,516426,50,29599,516467,0,29599,516715,50,29732,516715,40,29732,516756,0,29732)
%
%
% START OF PROOF
% 516717 [] equal(multiply(identity,X),X).
% 516718 [] equal(multiply(inverse(X),X),identity).
% 516719 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 516720 [] -equal(inverse(sk_c8),sk_c7).
% 516751 [?] ?
% 516752 [?] ?
% 516753 [?] ?
% 516754 [?] ?
% 516755 [?] ?
% 516756 [?] ?
% 516771 [input:516751,cut:516720] equal(inverse(sk_c4),sk_c8).
% 516772 [para:516771.1.1,516718.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 516775 [input:516754,cut:516720] equal(inverse(sk_c3),sk_c8).
% 516776 [para:516775.1.1,516718.1.1.1] equal(multiply(sk_c8,sk_c3),identity).
% 516797 [input:516752,cut:516720] equal(multiply(sk_c4,sk_c8),sk_c5).
% 516799 [input:516753,cut:516720] equal(multiply(sk_c8,sk_c5),sk_c7).
% 516800 [input:516755,cut:516720] equal(multiply(sk_c3,sk_c8),sk_c7).
% 516801 [input:516756,cut:516720] equal(multiply(sk_c8,sk_c7),sk_c6).
% 516818 [para:516718.1.1,516719.1.1.1,demod:516717] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 516820 [para:516772.1.1,516719.1.1.1,demod:516717] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 516822 [para:516776.1.1,516719.1.1.1,demod:516717] equal(X,multiply(sk_c8,multiply(sk_c3,X))).
% 516842 [para:516799.1.1,516719.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 516864 [para:516797.1.1,516820.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 516868 [para:516864.1.2,516799.1.1] equal(sk_c8,sk_c7).
% 516869 [para:516864.1.2,516719.1.1.1,demod:516842] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 516870 [para:516868.1.1,516720.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 516887 [para:516868.1.1,516797.1.1.2] equal(multiply(sk_c4,sk_c7),sk_c5).
% 516889 [para:516868.1.1,516799.1.1.1] equal(multiply(sk_c7,sk_c5),sk_c7).
% 516890 [para:516868.1.1,516800.1.1.2] equal(multiply(sk_c3,sk_c7),sk_c7).
% 516891 [para:516868.1.1,516801.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c6).
% 516912 [para:516800.1.1,516822.1.2.2,demod:516891,516869] equal(sk_c8,sk_c6).
% 516913 [para:516890.1.1,516822.1.2.2,demod:516891,516869] equal(sk_c7,sk_c6).
% 516916 [para:516912.1.1,516772.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 516974 [para:516772.1.1,516818.1.2.2] equal(sk_c4,multiply(inverse(sk_c8),identity)).
% 516976 [para:516776.1.1,516818.1.2.2,demod:516974] equal(sk_c3,sk_c4).
% 517012 [para:516889.1.1,516818.1.2.2,demod:516718] equal(sk_c5,identity).
% 517024 [para:516976.1.2,516887.1.1.1,demod:516890] equal(sk_c7,sk_c5).
% 517028 [para:517012.1.1,516799.1.1.2,demod:516869] equal(multiply(sk_c7,identity),sk_c7).
% 517043 [para:517024.1.1,516913.1.1] equal(sk_c5,sk_c6).
% 517048 [para:517043.1.1,517012.1.1] equal(sk_c6,identity).
% 517055 [para:517048.1.1,516916.1.1.1,demod:516717] equal(sk_c4,identity).
% 517061 [para:517055.1.1,516771.1.1.1] equal(inverse(identity),sk_c8).
% 517062 [para:517055.1.1,516772.1.1.2,demod:517028,516869] equal(sk_c7,identity).
% 517069 [para:517062.1.1,516870.1.1.1,demod:517061,cut:516868] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425,514002,50,29425,514002,30,29425,514002,40,29425,514043,0,29431,514162,50,29432,514203,0,29432,514376,50,29434,514376,30,29434,514376,40,29434,514417,0,29434,514466,50,29434,514466,30,29434,514466,40,29434,514507,0,29438,514647,50,29439,514688,0,29439,514878,50,29443,514919,0,29448,515117,50,29453,515158,0,29453,515364,50,29460,515405,0,29460,515617,50,29471,515658,0,29475,515878,50,29494,515919,0,29494,516147,50,29528,516188,0,29533,516426,50,29599,516467,0,29599,516715,50,29732,516715,40,29732,516756,0,29732,517068,50,29733,517068,30,29733,517068,40,29733,517109,0,29734,517249,50,29735,517290,0,29739,517480,50,29743,517521,0,29743,517719,50,29748,517760,0,29748,517966,50,29755,518007,0,29760,518219,50,29771,518260,0,29771,518480,50,29790,518521,0,29795,518749,50,29829,518790,0,29829,519028,50,29898,519069,0,29899,519317,50,30027,519317,40,30027,519358,0,30028)
%
%
% START OF PROOF
% 519260 [?] ?
% 519319 [] equal(multiply(identity,X),X).
% 519320 [] equal(multiply(inverse(X),X),identity).
% 519321 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 519322 [] -equal(multiply(sk_c8,sk_c6),sk_c7).
% 519335 [?] ?
% 519336 [?] ?
% 519337 [?] ?
% 519389 [input:519335,cut:519322] equal(inverse(sk_c4),sk_c8).
% 519390 [para:519389.1.1,519320.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 519418 [input:519336,cut:519322] equal(multiply(sk_c4,sk_c8),sk_c5).
% 519419 [input:519337,cut:519322] equal(multiply(sk_c8,sk_c5),sk_c7).
% 519442 [para:519390.1.1,519321.1.1.1,demod:519319] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 519482 [para:519418.1.1,519442.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 519487 [para:519482.1.2,519419.1.1] equal(sk_c8,sk_c7).
% 519489 [para:519487.1.1,519322.1.1.1,cut:519260] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,sk_c6),sk_c7) | -equal(multiply(Y,sk_c7),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1234,50,11,1280,0,11,3176,50,34,3222,0,34,5633,50,64,5679,0,65,8981,50,99,9027,0,99,12564,50,142,12610,0,142,16407,50,198,16453,0,198,20595,50,279,20641,0,279,25129,50,407,25175,0,407,30094,50,611,30140,0,611,35491,50,901,35491,40,901,35537,0,901,47496,3,1205,48136,4,1352,48748,1,1502,48748,50,1502,48748,40,1502,48794,0,1502,49016,3,1812,49024,4,1954,49032,5,2103,49032,1,2103,49032,50,2103,49032,40,2103,49078,0,2103,90925,3,3604,91501,4,4354,91937,5,5104,91938,1,5104,91938,50,5106,91938,40,5106,91984,0,5106,118354,3,5858,118811,4,6232,119188,5,6607,119189,1,6607,119189,50,6608,119189,40,6608,119235,0,6608,145416,3,7359,145693,4,7734,145840,1,8109,145840,50,8109,145840,40,8109,145886,0,8110,306923,3,12028,307845,4,13961,308486,1,15911,308486,50,15913,308486,40,15913,308532,0,15913,389427,3,18472,390115,4,19739,390565,5,21014,390566,1,21014,390566,50,21017,390566,40,21017,390612,0,21017,426012,3,22519,427020,4,23268,427713,5,24018,427714,1,24018,427714,50,24020,427714,40,24020,427760,0,24020,444641,3,24771,445135,4,25146,445533,5,25521,445534,1,25521,445534,50,25521,445534,40,25521,445580,0,25521,483047,3,26722,483728,4,27322,484283,1,27922,484283,50,27923,484283,40,27923,484329,0,27923,512811,3,28675,513351,4,29049,513690,5,29424,513691,1,29424,513691,50,29425,513691,40,29425,513691,40,29425,513732,0,29425,513912,50,29425,513912,30,29425,513912,40,29425,513953,0,29425,514002,50,29425,514002,30,29425,514002,40,29425,514043,0,29431,514162,50,29432,514203,0,29432,514376,50,29434,514376,30,29434,514376,40,29434,514417,0,29434,514466,50,29434,514466,30,29434,514466,40,29434,514507,0,29438,514647,50,29439,514688,0,29439,514878,50,29443,514919,0,29448,515117,50,29453,515158,0,29453,515364,50,29460,515405,0,29460,515617,50,29471,515658,0,29475,515878,50,29494,515919,0,29494,516147,50,29528,516188,0,29533,516426,50,29599,516467,0,29599,516715,50,29732,516715,40,29732,516756,0,29732,517068,50,29733,517068,30,29733,517068,40,29733,517109,0,29734,517249,50,29735,517290,0,29739,517480,50,29743,517521,0,29743,517719,50,29748,517760,0,29748,517966,50,29755,518007,0,29760,518219,50,29771,518260,0,29771,518480,50,29790,518521,0,29795,518749,50,29829,518790,0,29829,519028,50,29898,519069,0,29899,519317,50,30027,519317,40,30027,519358,0,30028,519488,50,30028,519488,30,30028,519488,40,30028,519529,0,30028,519645,50,30029,519686,0,30033,519843,50,30036,519884,0,30036,520049,50,30039,520090,0,30039,520267,50,30046,520308,0,30050,520492,50,30060,520533,0,30060,520725,50,30076,520766,0,30081,520967,50,30113,521008,0,30113,521219,50,30180,521260,0,30180,521482,50,30305,521482,40,30305,521523,0,30305)
%
%
% START OF PROOF
% 521330 [?] ?
% 521484 [] equal(multiply(identity,X),X).
% 521485 [] equal(multiply(inverse(X),X),identity).
% 521486 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 521487 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 521511 [?] ?
% 521517 [?] ?
% 521566 [input:521511,cut:521487] equal(inverse(sk_c1),sk_c8).
% 521567 [para:521566.1.1,521485.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 521595 [input:521517,cut:521487] equal(multiply(sk_c1,sk_c8),sk_c7).
% 521613 [para:521567.1.1,521486.1.1.1,demod:521484] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 521656 [para:521595.1.1,521613.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 521657 [para:521656.1.2,521487.1.1,cut:521330] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 32247
% derived clauses: 5941200
% kept clauses: 368892
% kept size sum: 456091
% kept mid-nuclei: 23486
% kept new demods: 5912
% forw unit-subs: 1980053
% forw double-subs: 3211503
% forw overdouble-subs: 232031
% backward subs: 11983
% fast unit cutoff: 24286
% full unit cutoff: 0
% dbl unit cutoff: 16627
% real runtime : 305.47
% process. runtime: 303.5
% specific non-discr-tree subsumption statistics:
% tried: 31076174
% length fails: 4022968
% strength fails: 5790962
% predlist fails: 575952
% aux str. fails: 4886818
% by-lit fails: 5964422
% full subs tried: 1126351
% full subs fail: 1029784
%
% ; 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/GRP372-1+eq_r.in")
%
%------------------------------------------------------------------------------