TSTP Solution File: GRP358-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP358-1 : 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 : art04.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 298.1s
% Output : Assurance 298.1s
% 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/GRP358-1+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_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% was split for some strategies as:
% -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7).
% -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8).
% -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(inverse(sk_c8),sk_c6).
%
% Starting a split proof attempt with 6 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_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421)
%
%
% START OF PROOF
% 403997 [?] ?
% 404003 [] equal(multiply(identity,X),X).
% 404004 [] equal(multiply(inverse(X),X),identity).
% 404005 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 404006 [] -equal(multiply(X,sk_c8),sk_c6) | -equal(inverse(X),sk_c6).
% 404007 [?] ?
% 404008 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 404013 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 404014 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 404019 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 404020 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 404025 [?] ?
% 404026 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 404031 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 404032 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 404039 [hyper:404006,404008,binarycut:404007] equal(inverse(sk_c1),sk_c8).
% 404040 [para:404039.1.1,404004.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 404048 [hyper:404006,404026,binarycut:404025] equal(inverse(sk_c8),sk_c6).
% 404051 [para:404048.1.1,404004.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 404055 [hyper:404006,404014,404013] equal(multiply(sk_c1,sk_c8),sk_c2).
% 404061 [hyper:404006,404019,404020] equal(multiply(sk_c8,sk_c2),sk_c7).
% 404067 [hyper:404006,404031,404032] equal(multiply(sk_c7,sk_c6),sk_c8).
% 404069 [para:404040.1.1,404005.1.1.1,demod:404003] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 404070 [para:404051.1.1,404005.1.1.1,demod:404003] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 404074 [para:404055.1.1,404069.1.2.2,demod:404061] equal(sk_c8,sk_c7).
% 404075 [para:404074.1.2,404067.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 404080 [para:404075.1.1,404070.1.2.2,demod:404051] equal(sk_c6,identity).
% 404081 [para:404080.1.1,404051.1.1.1,demod:404003] equal(sk_c8,identity).
% 404094 [para:404081.1.1,404048.1.1.1] equal(inverse(identity),sk_c6).
% 404108 [hyper:404006,404094,demod:404003,cut:403997] 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 4
% 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_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),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 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 12
% 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 13
% 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 14
% 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 15
% 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 16
% 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 17
% 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 18
% 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 19
% 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 20
% 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 21
% 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(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421,404107,50,29421,404107,30,29421,404107,40,29421,404142,0,29426,404230,50,29426,404265,0,29427,404370,50,29427,404405,0,29427,404512,50,29428,404547,0,29432,404656,50,29432,404691,0,29432,404800,50,29432,404835,0,29437,404944,50,29438,404979,0,29438,405088,50,29439,405123,0,29439,405232,50,29440,405267,0,29444,405376,50,29445,405411,0,29445,405520,50,29446,405555,0,29450,405664,50,29450,405699,0,29450,405808,50,29450,405843,0,29450,405952,50,29451,405987,0,29456,406096,50,29457,406131,0,29457,406240,50,29457,406275,0,29462,406384,50,29463,406419,0,29463,406528,50,29463,406563,0,29463,406672,50,29464,406707,0,29469,406816,50,29470,406816,40,29470,406851,0,29470)
%
%
% START OF PROOF
% 406795 [?] ?
% 406813 [?] ?
% 406818 [] equal(multiply(identity,X),X).
% 406819 [] equal(multiply(inverse(X),X),identity).
% 406820 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 406821 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 406935 [para:406819.1.1,406820.1.1.1,demod:406818] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 406996 [para:406819.1.1,406935.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 407076 [para:406935.1.2,406935.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 407144 [para:407076.1.2,406996.1.2] equal(X,multiply(X,identity)).
% 407145 [para:407144.1.2,406819.1.1] equal(inverse(identity),identity).
% 407147 [para:407145.1.1,406821.2.1,demod:406818,cut:406795,cut:406813] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% 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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421,404107,50,29421,404107,30,29421,404107,40,29421,404142,0,29426,404230,50,29426,404265,0,29427,404370,50,29427,404405,0,29427,404512,50,29428,404547,0,29432,404656,50,29432,404691,0,29432,404800,50,29432,404835,0,29437,404944,50,29438,404979,0,29438,405088,50,29439,405123,0,29439,405232,50,29440,405267,0,29444,405376,50,29445,405411,0,29445,405520,50,29446,405555,0,29450,405664,50,29450,405699,0,29450,405808,50,29450,405843,0,29450,405952,50,29451,405987,0,29456,406096,50,29457,406131,0,29457,406240,50,29457,406275,0,29462,406384,50,29463,406419,0,29463,406528,50,29463,406563,0,29463,406672,50,29464,406707,0,29469,406816,50,29470,406816,40,29470,406851,0,29470,407146,50,29471,407146,30,29471,407146,40,29471,407181,0,29476)
%
%
% START OF PROOF
% 407148 [] equal(multiply(identity,X),X).
% 407149 [] equal(multiply(inverse(X),X),identity).
% 407150 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 407151 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 407156 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 407157 [?] ?
% 407162 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 407163 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 407168 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c8).
% 407169 [] equal(multiply(sk_c8,sk_c2),sk_c7) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 407174 [] equal(inverse(sk_c8),sk_c6) | equal(inverse(sk_c3),sk_c8).
% 407175 [?] ?
% 407180 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 407181 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 407190 [hyper:407151,407156,binarycut:407157] equal(inverse(sk_c1),sk_c8).
% 407193 [para:407190.1.1,407149.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 407200 [hyper:407151,407174,binarycut:407175] equal(inverse(sk_c8),sk_c6).
% 407201 [para:407200.1.1,407149.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 407220 [hyper:407151,407163,407162] equal(multiply(sk_c1,sk_c8),sk_c2).
% 407225 [hyper:407151,407169,407168] equal(multiply(sk_c8,sk_c2),sk_c7).
% 407230 [hyper:407151,407181,407180] equal(multiply(sk_c7,sk_c6),sk_c8).
% 407231 [para:407149.1.1,407150.1.1.1,demod:407148] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 407232 [para:407193.1.1,407150.1.1.1,demod:407148] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 407233 [para:407201.1.1,407150.1.1.1,demod:407148] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 407234 [para:407220.1.1,407150.1.1.1] equal(multiply(sk_c2,X),multiply(sk_c1,multiply(sk_c8,X))).
% 407237 [para:407220.1.1,407232.1.2.2,demod:407225] equal(sk_c8,sk_c7).
% 407238 [para:407237.1.2,407230.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 407240 [para:407193.1.1,407233.1.2.2] equal(sk_c1,multiply(sk_c6,identity)).
% 407241 [para:407225.1.1,407233.1.2.2] equal(sk_c2,multiply(sk_c6,sk_c7)).
% 407242 [para:407232.1.2,407233.1.2.2] equal(multiply(sk_c1,X),multiply(sk_c6,X)).
% 407243 [para:407238.1.1,407233.1.2.2,demod:407201] equal(sk_c6,identity).
% 407244 [para:407243.1.1,407201.1.1.1,demod:407148] equal(sk_c8,identity).
% 407247 [para:407243.1.1,407233.1.2.1,demod:407148] equal(X,multiply(sk_c8,X)).
% 407249 [para:407200.1.1,407231.1.2.1,demod:407242,407247] equal(X,multiply(sk_c1,X)).
% 407255 [para:407244.1.1,407220.1.1.2,demod:407249] equal(identity,sk_c2).
% 407264 [para:407225.1.1,407234.1.2.2,demod:407249] equal(multiply(sk_c2,sk_c2),sk_c7).
% 407267 [para:407232.1.2,407234.1.2.2,demod:407249] equal(multiply(sk_c2,X),X).
% 407277 [para:407255.1.2,407264.1.1.2,demod:407267] equal(identity,sk_c7).
% 407278 [para:407277.1.2,407241.1.2.2,demod:407240] equal(sk_c2,sk_c1).
% 407279 [para:407278.1.2,407190.1.1.1] equal(inverse(sk_c2),sk_c8).
% 407281 [hyper:407151,407279,demod:407267,cut:407237] 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_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),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 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421,404107,50,29421,404107,30,29421,404107,40,29421,404142,0,29426,404230,50,29426,404265,0,29427,404370,50,29427,404405,0,29427,404512,50,29428,404547,0,29432,404656,50,29432,404691,0,29432,404800,50,29432,404835,0,29437,404944,50,29438,404979,0,29438,405088,50,29439,405123,0,29439,405232,50,29440,405267,0,29444,405376,50,29445,405411,0,29445,405520,50,29446,405555,0,29450,405664,50,29450,405699,0,29450,405808,50,29450,405843,0,29450,405952,50,29451,405987,0,29456,406096,50,29457,406131,0,29457,406240,50,29457,406275,0,29462,406384,50,29463,406419,0,29463,406528,50,29463,406563,0,29463,406672,50,29464,406707,0,29469,406816,50,29470,406816,40,29470,406851,0,29470,407146,50,29471,407146,30,29471,407146,40,29471,407181,0,29476,407280,50,29477,407280,30,29477,407280,40,29477,407315,0,29477)
%
%
% START OF PROOF
% 407281 [] equal(X,X).
% 407282 [] equal(multiply(identity,X),X).
% 407283 [] equal(multiply(inverse(X),X),identity).
% 407284 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 407285 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 407286 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 407287 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 407288 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c7).
% 407289 [] equal(multiply(sk_c4,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 407290 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c3),sk_c8).
% 407291 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 407292 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 407293 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c5),sk_c6).
% 407294 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c4),sk_c7).
% 407295 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c4,sk_c7),sk_c6).
% 407296 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(inverse(sk_c3),sk_c8).
% 407297 [] equal(multiply(sk_c1,sk_c8),sk_c2) | equal(multiply(sk_c3,sk_c8),sk_c7).
% 407298 [?] ?
% 407299 [?] ?
% 407300 [?] ?
% 407301 [?] ?
% 407302 [?] ?
% 407303 [?] ?
% 407363 [hyper:407285,407293,binarycut:407299,binarycut:407287] equal(inverse(sk_c5),sk_c6).
% 407364 [para:407363.1.1,407283.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 407367 [hyper:407285,407294,binarycut:407300,binarycut:407288] equal(inverse(sk_c4),sk_c7).
% 407372 [hyper:407285,407292,407286,binarycut:407298] equal(multiply(sk_c5,sk_c8),sk_c6).
% 407375 [para:407367.1.1,407283.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 407380 [hyper:407285,407296,binarycut:407302,binarycut:407290] equal(inverse(sk_c3),sk_c8).
% 407397 [hyper:407285,407295,407289,binarycut:407301] equal(multiply(sk_c4,sk_c7),sk_c6).
% 407404 [hyper:407285,407297,407291,binarycut:407303] equal(multiply(sk_c3,sk_c8),sk_c7).
% 407409 [para:407283.1.1,407284.1.1.1,demod:407282] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 407410 [para:407364.1.1,407284.1.1.1,demod:407282] equal(X,multiply(sk_c6,multiply(sk_c5,X))).
% 407412 [para:407375.1.1,407284.1.1.1,demod:407282] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 407418 [para:407372.1.1,407410.1.2.2] equal(sk_c8,multiply(sk_c6,sk_c6)).
% 407426 [para:407397.1.1,407409.1.2.2,demod:407367] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 407430 [para:407426.1.2,407409.1.2.2,demod:407283] equal(sk_c6,identity).
% 407432 [para:407430.1.1,407410.1.2.1,demod:407282] equal(X,multiply(sk_c5,X)).
% 407433 [para:407430.1.1,407418.1.2.1,demod:407282] equal(sk_c8,sk_c6).
% 407440 [para:407433.1.2,407410.1.2.1,demod:407432] equal(X,multiply(sk_c8,X)).
% 407454 [hyper:407285,407412,407404,demod:407440,407412,demod:407380,cut:407281] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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 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
%
% old unit clauses discarded
%
% 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(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421,404107,50,29421,404107,30,29421,404107,40,29421,404142,0,29426,404230,50,29426,404265,0,29427,404370,50,29427,404405,0,29427,404512,50,29428,404547,0,29432,404656,50,29432,404691,0,29432,404800,50,29432,404835,0,29437,404944,50,29438,404979,0,29438,405088,50,29439,405123,0,29439,405232,50,29440,405267,0,29444,405376,50,29445,405411,0,29445,405520,50,29446,405555,0,29450,405664,50,29450,405699,0,29450,405808,50,29450,405843,0,29450,405952,50,29451,405987,0,29456,406096,50,29457,406131,0,29457,406240,50,29457,406275,0,29462,406384,50,29463,406419,0,29463,406528,50,29463,406563,0,29463,406672,50,29464,406707,0,29469,406816,50,29470,406816,40,29470,406851,0,29470,407146,50,29471,407146,30,29471,407146,40,29471,407181,0,29476,407280,50,29477,407280,30,29477,407280,40,29477,407315,0,29477,407453,50,29477,407453,30,29477,407453,40,29477,407488,0,29477,407608,50,29478,407643,0,29482,407825,50,29485,407860,0,29485,408050,50,29490,408085,0,29494,408283,50,29501,408318,0,29501,408522,50,29511,408557,0,29511,408769,50,29529,408804,0,29533,409024,50,29566,409059,0,29566,409289,50,29633,409324,0,29634,409564,50,29759,409564,40,29759,409599,0,29759)
%
%
% START OF PROOF
% 409419 [?] ?
% 409566 [] equal(multiply(identity,X),X).
% 409567 [] equal(multiply(inverse(X),X),identity).
% 409568 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 409569 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 409596 [?] ?
% 409597 [?] ?
% 409646 [input:409596,cut:409569] equal(inverse(sk_c4),sk_c7).
% 409647 [para:409646.1.1,409567.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 409661 [input:409597,cut:409569] equal(multiply(sk_c4,sk_c7),sk_c6).
% 409684 [para:409647.1.1,409568.1.1.1,demod:409566] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 409716 [para:409661.1.1,409684.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c6)).
% 409717 [para:409716.1.2,409569.1.1,cut:409419] 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_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(inverse(Z),sk_c8) | -equal(multiply(U,sk_c7),sk_c6) | -equal(inverse(U),sk_c7) | -equal(inverse(V),sk_c6) | -equal(multiply(V,sk_c8),sk_c6).
% Split part used next: -equal(inverse(sk_c8),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 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(35,40,1,75,0,1,4486,50,79,4526,0,79,9602,50,170,9642,0,170,15051,50,239,15091,0,239,20670,50,300,20710,0,300,26460,50,368,26500,0,368,32504,50,448,32544,0,448,38802,50,546,38842,0,547,45438,50,683,45478,0,683,52412,50,897,52412,40,897,52452,0,897,63109,3,1198,63837,4,1348,64550,5,1498,64551,1,1498,64551,50,1498,64551,40,1498,64591,0,1498,64848,3,1809,64857,4,1953,64868,5,2099,64868,1,2099,64868,50,2099,64868,40,2099,64908,0,2100,97180,3,3602,97914,4,4351,98469,5,5101,98470,1,5101,98470,50,5102,98470,40,5102,98510,0,5102,120233,3,5853,120807,4,6228,121205,5,6603,121206,1,6603,121206,50,6604,121206,40,6604,121246,0,6604,138470,3,7375,139152,4,7730,139696,5,8105,139697,1,8105,139697,50,8105,139697,40,8105,139737,0,8105,208841,3,12012,209592,4,13956,210221,1,15906,210221,50,15909,210221,40,15909,210261,0,15909,262878,3,18461,263442,4,19735,263860,5,21010,263861,1,21010,263861,50,21011,263861,40,21011,263901,0,21011,308496,3,22512,309151,4,23262,309619,5,24012,309620,1,24012,309620,50,24013,309620,40,24013,309660,0,24013,323530,3,24823,324445,4,25139,325472,5,25515,325472,1,25515,325472,50,25515,325472,40,25515,325512,0,25515,371138,3,26716,371636,4,27316,371994,5,27916,371995,1,27916,371995,50,27918,371995,40,27918,372035,0,27918,403109,3,28669,403576,4,29044,403882,5,29419,403883,1,29419,403883,50,29420,403883,40,29420,403883,40,29420,403918,0,29420,404001,50,29421,404036,0,29421,404107,50,29421,404107,30,29421,404107,40,29421,404142,0,29426,404230,50,29426,404265,0,29427,404370,50,29427,404405,0,29427,404512,50,29428,404547,0,29432,404656,50,29432,404691,0,29432,404800,50,29432,404835,0,29437,404944,50,29438,404979,0,29438,405088,50,29439,405123,0,29439,405232,50,29440,405267,0,29444,405376,50,29445,405411,0,29445,405520,50,29446,405555,0,29450,405664,50,29450,405699,0,29450,405808,50,29450,405843,0,29450,405952,50,29451,405987,0,29456,406096,50,29457,406131,0,29457,406240,50,29457,406275,0,29462,406384,50,29463,406419,0,29463,406528,50,29463,406563,0,29463,406672,50,29464,406707,0,29469,406816,50,29470,406816,40,29470,406851,0,29470,407146,50,29471,407146,30,29471,407146,40,29471,407181,0,29476,407280,50,29477,407280,30,29477,407280,40,29477,407315,0,29477,407453,50,29477,407453,30,29477,407453,40,29477,407488,0,29477,407608,50,29478,407643,0,29482,407825,50,29485,407860,0,29485,408050,50,29490,408085,0,29494,408283,50,29501,408318,0,29501,408522,50,29511,408557,0,29511,408769,50,29529,408804,0,29533,409024,50,29566,409059,0,29566,409289,50,29633,409324,0,29634,409564,50,29759,409564,40,29759,409599,0,29759,409716,50,29759,409716,30,29759,409716,40,29759,409751,0,29759,409871,50,29760,409906,0,29764,410088,50,29768,410123,0,29768,410313,50,29772,410348,0,29772,410546,50,29778,410581,0,29783,410785,50,29793,410820,0,29793,411032,50,29811,411067,0,29816,411287,50,29848,411322,0,29849,411552,50,29916,411587,0,29916,411827,50,30042,411827,40,30042,411862,0,30042)
%
%
% START OF PROOF
% 411828 [] equal(X,X).
% 411829 [] equal(multiply(identity,X),X).
% 411830 [] equal(multiply(inverse(X),X),identity).
% 411831 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 411832 [] -equal(inverse(sk_c8),sk_c6).
% 411851 [?] ?
% 411852 [?] ?
% 411853 [?] ?
% 411854 [?] ?
% 411874 [input:411852,cut:411832] equal(inverse(sk_c5),sk_c6).
% 411875 [para:411874.1.1,411830.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 411876 [input:411853,cut:411832] equal(inverse(sk_c4),sk_c7).
% 411877 [para:411876.1.1,411830.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 411892 [input:411851,cut:411832] equal(multiply(sk_c5,sk_c8),sk_c6).
% 411893 [input:411854,cut:411832] equal(multiply(sk_c4,sk_c7),sk_c6).
% 411911 [para:411830.1.1,411831.1.1.1,demod:411829] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 411950 [para:411875.1.1,411911.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 411952 [para:411877.1.1,411911.1.2.2] equal(sk_c4,multiply(inverse(sk_c7),identity)).
% 411965 [para:411892.1.1,411911.1.2.2] equal(sk_c8,multiply(inverse(sk_c5),sk_c6)).
% 411966 [para:411893.1.1,411911.1.2.2] equal(sk_c7,multiply(inverse(sk_c4),sk_c6)).
% 411985 [para:411911.1.2,411911.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 411986 [para:411950.1.2,411831.1.1.1,demod:411829] equal(multiply(sk_c5,X),multiply(inverse(sk_c6),X)).
% 411987 [para:411952.1.2,411831.1.1.1,demod:411829] equal(multiply(sk_c4,X),multiply(inverse(sk_c7),X)).
% 411997 [para:411966.1.2,411911.1.2.2,demod:411985] equal(sk_c6,multiply(sk_c4,sk_c7)).
% 412064 [para:411986.1.2,411830.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 412068 [para:412064.1.1,411911.1.2.2] equal(sk_c6,multiply(inverse(sk_c5),identity)).
% 412071 [para:411987.1.2,411830.1.1,demod:411997] equal(sk_c6,identity).
% 412078 [para:412071.1.1,411875.1.1.1,demod:411829] equal(sk_c5,identity).
% 412082 [para:412071.1.1,411965.1.2.2,demod:412068] equal(sk_c8,sk_c6).
% 412087 [para:412078.1.1,411874.1.1.1] equal(inverse(identity),sk_c6).
% 412105 [para:412082.1.2,412071.1.1] equal(sk_c8,identity).
% 412115 [para:412105.1.1,411832.1.1.1,demod:412087,cut:411828] 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: 31084
% derived clauses: 6131559
% kept clauses: 326052
% kept size sum: 25371
% kept mid-nuclei: 42124
% kept new demods: 5725
% forw unit-subs: 2430790
% forw double-subs: 2809263
% forw overdouble-subs: 458682
% backward subs: 11842
% fast unit cutoff: 28240
% full unit cutoff: 0
% dbl unit cutoff: 14456
% real runtime : 302.63
% process. runtime: 300.43
% specific non-discr-tree subsumption statistics:
% tried: 33907828
% length fails: 3769885
% strength fails: 9213557
% predlist fails: 1475768
% aux str. fails: 3945848
% by-lit fails: 5011522
% full subs tried: 2978503
% full subs fail: 2798840
%
% ; 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/GRP358-1+eq_r.in")
%
%------------------------------------------------------------------------------