TSTP Solution File: GRP311-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP311-1 : 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 : art07.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 297.5s
% Output : Assurance 297.5s
% 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/GRP311-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% -equal(multiply(sk_c7,sk_c6),sk_c5).
% -equal(inverse(sk_c7),sk_c5).
% -equal(multiply(sk_c5,sk_c6),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% 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(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574)
%
%
% START OF PROOF
% 292546 [] equal(multiply(identity,X),X).
% 292547 [] equal(multiply(inverse(X),X),identity).
% 292548 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 292549 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 292550 [?] ?
% 292551 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 292555 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 292556 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c6).
% 292560 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 292561 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 292565 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 292566 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 292570 [?] ?
% 292571 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 292582 [hyper:292549,292551,binarycut:292550] equal(inverse(sk_c1),sk_c7).
% 292583 [para:292582.1.1,292547.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 292590 [hyper:292549,292571,binarycut:292570] equal(inverse(sk_c7),sk_c5).
% 292591 [para:292590.1.1,292547.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 292594 [hyper:292549,292556,292555] equal(multiply(sk_c1,sk_c7),sk_c2).
% 292604 [hyper:292549,292560,292561] equal(multiply(sk_c7,sk_c2),sk_c6).
% 292611 [hyper:292549,292565,292566] equal(multiply(sk_c5,sk_c6),sk_c7).
% 292616 [para:292547.1.1,292548.1.1.1,demod:292546] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 292617 [para:292583.1.1,292548.1.1.1,demod:292546] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 292623 [para:292594.1.1,292617.1.2.2,demod:292604] equal(sk_c7,sk_c6).
% 292625 [para:292623.1.1,292590.1.1.1] equal(inverse(sk_c6),sk_c5).
% 292626 [para:292623.1.1,292591.1.1.2,demod:292611] equal(sk_c7,identity).
% 292631 [para:292626.1.1,292583.1.1.1,demod:292546] equal(sk_c1,identity).
% 292632 [para:292626.1.1,292590.1.1.1] equal(inverse(identity),sk_c5).
% 292637 [para:292626.1.1,292617.1.2.1,demod:292546] equal(X,multiply(sk_c1,X)).
% 292640 [para:292631.1.1,292582.1.1.1,demod:292632] equal(sk_c5,sk_c7).
% 292645 [para:292547.1.1,292616.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 292650 [para:292616.1.2,292616.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 292660 [para:292640.1.2,292623.1.1] equal(sk_c5,sk_c6).
% 292669 [para:292650.1.2,292547.1.1] equal(multiply(X,inverse(X)),identity).
% 292671 [para:292650.1.2,292645.1.2] equal(X,multiply(X,identity)).
% 292672 [para:292669.1.1,292548.1.1] equal(identity,multiply(X,multiply(Y,inverse(multiply(X,Y))))).
% 292676 [para:292671.1.2,292645.1.2] equal(X,inverse(inverse(X))).
% 292677 [para:292582.1.1,292676.1.2.1,demod:292590] equal(sk_c1,sk_c5).
% 292679 [para:292637.1.2,292672.1.2.2] equal(identity,multiply(X,inverse(multiply(X,sk_c1)))).
% 292685 [para:292679.1.2,292616.1.2.2,demod:292671] equal(inverse(multiply(X,sk_c1)),inverse(X)).
% 292687 [para:292685.1.1,292645.1.2.1.1,demod:292671,292676] equal(multiply(X,sk_c1),X).
% 292693 [para:292677.1.1,292687.1.1.2] equal(multiply(X,sk_c5),X).
% 292704 [hyper:292549,292693,demod:292625,cut:292660] 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 21
% clause depth limited to 5
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,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 21
% 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 21
% 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 21
% clause depth limited to 5
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580)
%
%
% START OF PROOF
% 292999 [] equal(multiply(identity,X),X).
% 293000 [] equal(multiply(inverse(X),X),identity).
% 293001 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293002 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 293005 [?] ?
% 293006 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 293010 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 293011 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 293015 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 293016 [] equal(multiply(sk_c7,sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 293020 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 293021 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 293025 [?] ?
% 293026 [] equal(inverse(sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 293038 [hyper:293002,293006,binarycut:293005] equal(inverse(sk_c1),sk_c7).
% 293041 [para:293038.1.1,293000.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 293047 [hyper:293002,293026,binarycut:293025] equal(inverse(sk_c7),sk_c5).
% 293048 [para:293047.1.1,293000.1.1.1] equal(multiply(sk_c5,sk_c7),identity).
% 293055 [hyper:293002,293011,293010] equal(multiply(sk_c1,sk_c7),sk_c2).
% 293075 [hyper:293002,293015,293016] equal(multiply(sk_c7,sk_c2),sk_c6).
% 293082 [hyper:293002,293020,293021] equal(multiply(sk_c5,sk_c6),sk_c7).
% 293090 [para:293000.1.1,293001.1.1.1,demod:292999] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293091 [para:293041.1.1,293001.1.1.1,demod:292999] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 293092 [para:293048.1.1,293001.1.1.1,demod:292999] equal(X,multiply(sk_c5,multiply(sk_c7,X))).
% 293097 [para:293055.1.1,293091.1.2.2,demod:293075] equal(sk_c7,sk_c6).
% 293100 [para:293097.1.1,293048.1.1.2,demod:293082] equal(sk_c7,identity).
% 293105 [para:293100.1.1,293041.1.1.1,demod:292999] equal(sk_c1,identity).
% 293106 [para:293100.1.1,293047.1.1.1] equal(inverse(identity),sk_c5).
% 293114 [para:293105.1.1,293038.1.1.1,demod:293106] equal(sk_c5,sk_c7).
% 293118 [para:292999.1.1,293090.1.2.2,demod:293106] equal(X,multiply(sk_c5,X)).
% 293119 [para:293000.1.1,293090.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 293124 [para:293090.1.2,293090.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 293143 [para:293124.1.2,293000.1.1] equal(multiply(X,inverse(X)),identity).
% 293145 [para:293124.1.2,293119.1.2] equal(X,multiply(X,identity)).
% 293146 [para:293143.1.1,293001.1.1] equal(identity,multiply(X,multiply(Y,inverse(multiply(X,Y))))).
% 293150 [para:293145.1.2,293119.1.2] equal(X,inverse(inverse(X))).
% 293152 [para:293146.1.2,293090.1.2.2,demod:293145] equal(multiply(X,inverse(multiply(Y,X))),inverse(Y)).
% 293171 [para:293152.1.1,293092.1.2.2,demod:293118] equal(inverse(multiply(X,sk_c7)),inverse(X)).
% 293179 [para:293171.1.1,293119.1.2.1.1,demod:293145,293150] equal(multiply(X,sk_c7),X).
% 293180 [para:293097.1.1,293179.1.1.2] equal(multiply(X,sk_c6),X).
% 293182 [hyper:293002,293180,demod:293047,cut:293114] 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 21
% clause depth limited to 5
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580,293181,50,29581,293181,30,29581,293181,40,29581,293216,0,29581)
%
%
% START OF PROOF
% 293182 [] equal(X,X).
% 293183 [] equal(multiply(identity,X),X).
% 293184 [] equal(multiply(inverse(X),X),identity).
% 293185 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 293186 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 293187 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 293188 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 293189 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 293190 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 293191 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 293192 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 293193 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c4),sk_c6).
% 293194 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 293195 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(inverse(sk_c3),sk_c7).
% 293196 [] equal(multiply(sk_c1,sk_c7),sk_c2) | equal(multiply(sk_c6,sk_c7),sk_c5).
% 293197 [?] ?
% 293198 [?] ?
% 293199 [?] ?
% 293200 [?] ?
% 293201 [?] ?
% 293257 [hyper:293186,293192,293187,binarycut:293197] equal(multiply(sk_c4,sk_c5),sk_c6).
% 293260 [hyper:293186,293193,binarycut:293198,binarycut:293188] equal(inverse(sk_c4),sk_c6).
% 293261 [para:293260.1.1,293184.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 293264 [hyper:293186,293195,binarycut:293200,binarycut:293190] equal(inverse(sk_c3),sk_c7).
% 293272 [hyper:293186,293194,293189,binarycut:293199] equal(multiply(sk_c3,sk_c6),sk_c7).
% 293275 [para:293264.1.1,293184.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 293284 [hyper:293186,293196,293191,binarycut:293201] equal(multiply(sk_c6,sk_c7),sk_c5).
% 293287 [para:293184.1.1,293185.1.1.1,demod:293183] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 293288 [para:293257.1.1,293185.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 293289 [para:293261.1.1,293185.1.1.1,demod:293183] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 293290 [para:293272.1.1,293185.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 293291 [para:293275.1.1,293185.1.1.1,demod:293183] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 293297 [para:293257.1.1,293289.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 293301 [para:293272.1.1,293291.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 293306 [para:293261.1.1,293287.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 293308 [para:293284.1.1,293287.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 293309 [para:293289.1.2,293287.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c6),X)).
% 293310 [para:293297.1.2,293287.1.2.2,demod:293308] equal(sk_c6,sk_c7).
% 293312 [para:293310.1.2,293275.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 293314 [para:293310.1.2,293301.1.2.1,demod:293284] equal(sk_c6,sk_c5).
% 293317 [para:293314.1.1,293272.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 293322 [para:293312.1.1,293287.1.2.2,demod:293306] equal(sk_c3,sk_c4).
% 293327 [para:293322.1.2,293288.1.2.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c5,X))).
% 293332 [para:293317.1.1,293185.1.1.1,demod:293327] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 293337 [para:293289.1.2,293290.1.2.2,demod:293289,293332] equal(X,multiply(sk_c3,X)).
% 293340 [para:293337.1.2,293291.1.2.2,demod:293332] equal(X,multiply(sk_c6,X)).
% 293347 [para:293340.1.2,293289.1.2] equal(X,multiply(sk_c4,X)).
% 293373 [hyper:293186,293309,demod:293260,293301,293347,293309,cut:293182,cut:293310] 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c6),sk_c5).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580,293181,50,29581,293181,30,29581,293181,40,29581,293216,0,29581,293372,50,29581,293372,30,29581,293372,40,29581,293407,0,29586,293518,50,29587,293553,0,29587,293729,50,29589,293764,0,29589,293957,50,29592,293992,0,29597,294198,50,29601,294233,0,29601,294445,50,29608,294480,0,29612,294700,50,29626,294735,0,29626,294963,50,29653,294998,0,29653,295236,50,29711,295271,0,29711,295519,50,29821,295519,40,29821,295554,0,29822)
%
%
% START OF PROOF
% 295520 [] equal(X,X).
% 295521 [] equal(multiply(identity,X),X).
% 295522 [] equal(multiply(inverse(X),X),identity).
% 295523 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 295524 [] -equal(multiply(sk_c7,sk_c6),sk_c5).
% 295550 [?] ?
% 295551 [?] ?
% 295554 [?] ?
% 295593 [input:295551,cut:295524] equal(inverse(sk_c4),sk_c6).
% 295594 [para:295593.1.1,295522.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 295608 [input:295550,cut:295524] equal(multiply(sk_c4,sk_c5),sk_c6).
% 295610 [input:295554,cut:295524] equal(multiply(sk_c6,sk_c7),sk_c5).
% 295614 [para:295522.1.1,295523.1.1.1,demod:295521] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 295633 [para:295594.1.1,295523.1.1.1,demod:295521] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 295662 [para:295608.1.1,295633.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 295714 [para:295610.1.1,295614.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 295720 [para:295662.1.2,295614.1.2.2,demod:295714] equal(sk_c6,sk_c7).
% 295724 [para:295720.1.2,295524.1.1.1,demod:295662,cut:295520] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(sk_c7),sk_c5).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580,293181,50,29581,293181,30,29581,293181,40,29581,293216,0,29581,293372,50,29581,293372,30,29581,293372,40,29581,293407,0,29586,293518,50,29587,293553,0,29587,293729,50,29589,293764,0,29589,293957,50,29592,293992,0,29597,294198,50,29601,294233,0,29601,294445,50,29608,294480,0,29612,294700,50,29626,294735,0,29626,294963,50,29653,294998,0,29653,295236,50,29711,295271,0,29711,295519,50,29821,295519,40,29821,295554,0,29822,295723,50,29822,295723,30,29822,295723,40,29822,295758,0,29822,295869,50,29823,295904,0,29827,296080,50,29829,296115,0,29829,296308,50,29831,296343,0,29831,296549,50,29835,296584,0,29840,296796,50,29847,296831,0,29847,297051,50,29861,297086,0,29866,297314,50,29894,297349,0,29894,297587,50,29952,297622,0,29952,297870,50,30062,297870,40,30062,297905,0,30062)
%
%
% START OF PROOF
% 297872 [] equal(multiply(identity,X),X).
% 297873 [] equal(multiply(inverse(X),X),identity).
% 297874 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 297875 [] -equal(inverse(sk_c7),sk_c5).
% 297896 [?] ?
% 297897 [?] ?
% 297898 [?] ?
% 297899 [?] ?
% 297900 [?] ?
% 297914 [input:297897,cut:297875] equal(inverse(sk_c4),sk_c6).
% 297915 [para:297914.1.1,297873.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 297916 [input:297899,cut:297875] equal(inverse(sk_c3),sk_c7).
% 297917 [para:297916.1.1,297873.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 297929 [input:297896,cut:297875] equal(multiply(sk_c4,sk_c5),sk_c6).
% 297930 [input:297898,cut:297875] equal(multiply(sk_c3,sk_c6),sk_c7).
% 297931 [input:297900,cut:297875] equal(multiply(sk_c6,sk_c7),sk_c5).
% 297948 [para:297873.1.1,297874.1.1.1,demod:297872] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 297950 [para:297915.1.1,297874.1.1.1,demod:297872] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 297951 [para:297917.1.1,297874.1.1.1,demod:297872] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 297983 [para:297929.1.1,297950.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 297986 [para:297930.1.1,297951.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 298007 [para:297931.1.1,297948.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 298026 [para:297983.1.2,297948.1.2.2,demod:298007] equal(sk_c6,sk_c7).
% 298031 [para:298026.1.2,297875.1.1.1] -equal(inverse(sk_c6),sk_c5).
% 298045 [para:298026.1.2,297986.1.2.1] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 298062 [para:298045.1.2,297931.1.1] equal(sk_c6,sk_c5).
% 298068 [para:298062.1.1,297931.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 298088 [para:298068.1.1,297948.1.2.2,demod:297873] equal(sk_c7,identity).
% 298090 [para:298088.1.1,297917.1.1.1,demod:297872] equal(sk_c3,identity).
% 298097 [para:298088.1.1,298026.1.2] equal(sk_c6,identity).
% 298100 [para:298090.1.1,297916.1.1.1] equal(inverse(identity),sk_c7).
% 298107 [para:298097.1.1,297931.1.1.1,demod:297872] equal(sk_c7,sk_c5).
% 298109 [para:298097.1.1,298031.1.1.1,demod:298100,cut:298107] 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(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c5,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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 *********
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580,293181,50,29581,293181,30,29581,293181,40,29581,293216,0,29581,293372,50,29581,293372,30,29581,293372,40,29581,293407,0,29586,293518,50,29587,293553,0,29587,293729,50,29589,293764,0,29589,293957,50,29592,293992,0,29597,294198,50,29601,294233,0,29601,294445,50,29608,294480,0,29612,294700,50,29626,294735,0,29626,294963,50,29653,294998,0,29653,295236,50,29711,295271,0,29711,295519,50,29821,295519,40,29821,295554,0,29822,295723,50,29822,295723,30,29822,295723,40,29822,295758,0,29822,295869,50,29823,295904,0,29827,296080,50,29829,296115,0,29829,296308,50,29831,296343,0,29831,296549,50,29835,296584,0,29840,296796,50,29847,296831,0,29847,297051,50,29861,297086,0,29866,297314,50,29894,297349,0,29894,297587,50,29952,297622,0,29952,297870,50,30062,297870,40,30062,297905,0,30062,298108,50,30063,298108,30,30063,298108,40,30063,298143,0,30063,298254,50,30064,298289,0,30069,298465,50,30071,298500,0,30071,298693,50,30074,298728,0,30074,298934,50,30079,298969,0,30083,299181,50,30090,299216,0,30090,299436,50,30104,299471,0,30109,299699,50,30135,299734,0,30135,299972,50,30192,300007,0,30192,300255,50,30303,300255,40,30303,300290,0,30303)
%
%
% START OF PROOF
% 300256 [] equal(X,X).
% 300257 [] equal(multiply(identity,X),X).
% 300258 [] equal(multiply(inverse(X),X),identity).
% 300259 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 300260 [] -equal(multiply(sk_c5,sk_c6),sk_c7).
% 300276 [?] ?
% 300277 [?] ?
% 300278 [?] ?
% 300279 [?] ?
% 300280 [?] ?
% 300318 [input:300277,cut:300260] equal(inverse(sk_c4),sk_c6).
% 300319 [para:300318.1.1,300258.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 300321 [input:300279,cut:300260] equal(inverse(sk_c3),sk_c7).
% 300322 [para:300321.1.1,300258.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 300339 [input:300276,cut:300260] equal(multiply(sk_c4,sk_c5),sk_c6).
% 300340 [input:300278,cut:300260] equal(multiply(sk_c3,sk_c6),sk_c7).
% 300341 [input:300280,cut:300260] equal(multiply(sk_c6,sk_c7),sk_c5).
% 300348 [para:300258.1.1,300259.1.1.1,demod:300257] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 300360 [para:300319.1.1,300259.1.1.1,demod:300257] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 300361 [para:300322.1.1,300259.1.1.1,demod:300257] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 300392 [para:300339.1.1,300360.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 300398 [para:300340.1.1,300361.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 300437 [para:300341.1.1,300348.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 300446 [para:300392.1.2,300348.1.2.2,demod:300437] equal(sk_c6,sk_c7).
% 300450 [para:300446.1.2,300260.1.2] -equal(multiply(sk_c5,sk_c6),sk_c6).
% 300471 [para:300446.1.2,300398.1.2.1] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 300497 [para:300471.1.2,300341.1.1] equal(sk_c6,sk_c5).
% 300510 [para:300497.1.1,300392.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 300512 [para:300497.1.1,300450.1.2,demod:300510,cut:300256] 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(multiply(sk_c7,sk_c6),sk_c5) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(sk_c5,sk_c6),sk_c7) | -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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 21
% 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(35,40,1,74,0,1,643,50,5,682,0,6,1741,50,18,1780,0,18,3084,50,35,3123,0,35,4553,50,50,4592,0,50,6149,50,69,6188,0,69,7933,50,97,7972,0,97,9905,50,141,9944,0,141,12127,50,220,12166,0,220,14599,50,369,14638,0,369,17383,50,625,17422,0,625,20479,50,1051,20479,40,1051,20518,0,1051,31273,3,1352,32025,4,1502,32697,5,1652,32697,1,1652,32697,50,1652,32697,40,1652,32736,0,1652,32978,3,1954,32989,4,2114,32998,5,2253,32998,1,2253,32998,50,2253,32998,40,2253,33037,0,2253,57562,3,3754,58805,4,4504,59943,1,5254,59943,50,5254,59943,40,5254,59982,0,5254,75336,3,6005,76307,4,6380,77300,1,6755,77300,50,6755,77300,40,6755,77339,0,6755,85095,3,7517,87341,4,7881,89574,5,8256,89575,1,8256,89575,50,8256,89575,40,8256,89614,0,8256,136517,3,12158,138190,4,14107,139227,5,16057,139228,1,16057,139228,50,16059,139228,40,16059,139267,0,16059,181746,3,18611,182927,4,19885,183643,5,21160,183644,1,21160,183644,50,21162,183644,40,21162,183683,0,21162,223934,3,22664,224740,4,23413,225565,5,24163,225566,1,24163,225566,50,24165,225566,40,24165,225605,0,24165,236654,3,24916,237957,4,25291,238870,5,25666,238870,1,25666,238870,50,25666,238870,40,25666,238909,0,25666,268546,3,26868,269388,4,27467,270007,5,28067,270008,1,28067,270008,50,28068,270008,40,28068,270047,0,28068,290876,3,28819,291583,4,29194,292291,5,29569,292292,1,29569,292292,50,29569,292292,40,29569,292292,40,29569,292327,0,29569,292413,50,29569,292448,0,29569,292544,50,29570,292579,0,29574,292703,50,29575,292703,30,29575,292703,40,29575,292738,0,29575,292845,50,29575,292880,0,29575,292997,50,29575,293032,0,29580,293181,50,29581,293181,30,29581,293181,40,29581,293216,0,29581,293372,50,29581,293372,30,29581,293372,40,29581,293407,0,29586,293518,50,29587,293553,0,29587,293729,50,29589,293764,0,29589,293957,50,29592,293992,0,29597,294198,50,29601,294233,0,29601,294445,50,29608,294480,0,29612,294700,50,29626,294735,0,29626,294963,50,29653,294998,0,29653,295236,50,29711,295271,0,29711,295519,50,29821,295519,40,29821,295554,0,29822,295723,50,29822,295723,30,29822,295723,40,29822,295758,0,29822,295869,50,29823,295904,0,29827,296080,50,29829,296115,0,29829,296308,50,29831,296343,0,29831,296549,50,29835,296584,0,29840,296796,50,29847,296831,0,29847,297051,50,29861,297086,0,29866,297314,50,29894,297349,0,29894,297587,50,29952,297622,0,29952,297870,50,30062,297870,40,30062,297905,0,30062,298108,50,30063,298108,30,30063,298108,40,30063,298143,0,30063,298254,50,30064,298289,0,30069,298465,50,30071,298500,0,30071,298693,50,30074,298728,0,30074,298934,50,30079,298969,0,30083,299181,50,30090,299216,0,30090,299436,50,30104,299471,0,30109,299699,50,30135,299734,0,30135,299972,50,30192,300007,0,30192,300255,50,30303,300255,40,30303,300290,0,30303,300511,50,30303,300511,30,30303,300511,40,30304,300546,0,30304,300642,50,30304,300677,0,30309,300821,50,30311,300856,0,30312,301010,50,30315,301045,0,30315,301211,50,30321,301246,0,30325,301418,50,30334,301453,0,30334,301633,50,30351,301668,0,30355,301857,50,30386,301892,0,30386,302091,50,30452,302126,0,30452,302336,50,30577,302336,40,30577,302371,0,30577)
%
%
% START OF PROOF
% 302338 [] equal(multiply(identity,X),X).
% 302339 [] equal(multiply(inverse(X),X),identity).
% 302340 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302341 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 302346 [?] ?
% 302351 [?] ?
% 302356 [?] ?
% 302371 [?] ?
% 302388 [input:302346,cut:302341] equal(inverse(sk_c1),sk_c7).
% 302389 [para:302388.1.1,302339.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 302410 [input:302351,cut:302341] equal(multiply(sk_c1,sk_c7),sk_c2).
% 302421 [input:302356,cut:302341] equal(multiply(sk_c7,sk_c2),sk_c6).
% 302427 [input:302371,cut:302341] equal(multiply(sk_c7,sk_c6),sk_c5).
% 302434 [para:302389.1.1,302340.1.1.1,demod:302338] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 302473 [para:302410.1.1,302434.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c2)).
% 302478 [para:302473.1.2,302421.1.1] equal(sk_c7,sk_c6).
% 302480 [para:302478.1.1,302341.1.1.2] -equal(multiply(sk_c6,sk_c6),sk_c5).
% 302504 [para:302478.1.1,302427.1.1.1,cut:302480] 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: 40751
% derived clauses: 6852824
% kept clauses: 241291
% kept size sum: 905326
% kept mid-nuclei: 11773
% kept new demods: 6717
% forw unit-subs: 2842507
% forw double-subs: 3496527
% forw overdouble-subs: 209482
% backward subs: 7320
% fast unit cutoff: 12661
% full unit cutoff: 0
% dbl unit cutoff: 11303
% real runtime : 308.63
% process. runtime: 305.76
% specific non-discr-tree subsumption statistics:
% tried: 39294440
% length fails: 4953417
% strength fails: 10398449
% predlist fails: 2370555
% aux str. fails: 6075995
% by-lit fails: 7658306
% full subs tried: 1808655
% full subs fail: 1722016
%
% ; 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/GRP311-1+eq_r.in")
%
%------------------------------------------------------------------------------