TSTP Solution File: GRP337-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP337-1 : 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 : art10.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 299.2s
% Output : Assurance 299.2s
% 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/GRP337-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% was split for some strategies as:
% -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7).
% -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% -equal(multiply(sk_c7,sk_c8),sk_c6).
% -equal(multiply(sk_c7,sk_c6),sk_c8).
% -equal(inverse(sk_c8),sk_c6).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700)
%
%
% START OF PROOF
% 373305 [?] ?
% 373316 [] equal(multiply(identity,X),X).
% 373317 [] equal(multiply(inverse(X),X),identity).
% 373318 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 373319 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 373320 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 373321 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 373326 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c6).
% 373327 [?] ?
% 373332 [] equal(multiply(sk_c2,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 373333 [] equal(multiply(sk_c2,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 373338 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 373339 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 373344 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 373345 [?] ?
% 373350 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c5),sk_c6).
% 373351 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 373358 [hyper:373319,373326,binarycut:373327] equal(inverse(sk_c2),sk_c3).
% 373359 [para:373358.1.1,373317.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 373363 [hyper:373319,373344,binarycut:373345] equal(inverse(sk_c1),sk_c8).
% 373364 [para:373363.1.1,373317.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 373370 [hyper:373319,373321,373320] equal(multiply(sk_c3,sk_c8),sk_c7).
% 373376 [hyper:373319,373333,373332] equal(multiply(sk_c2,sk_c3),sk_c7).
% 373393 [hyper:373319,373339,373338] equal(multiply(sk_c1,sk_c7),sk_c8).
% 373396 [hyper:373319,373351,373350] equal(multiply(sk_c7,sk_c8),sk_c6).
% 373398 [para:373359.1.1,373318.1.1.1,demod:373316] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 373399 [para:373364.1.1,373318.1.1.1,demod:373316] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 373400 [para:373370.1.1,373318.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 373404 [para:373376.1.1,373398.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c7)).
% 373406 [para:373393.1.1,373399.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 373422 [para:373406.1.2,373400.1.2.2,demod:373404,373396] equal(sk_c6,sk_c3).
% 373425 [para:373422.1.2,373376.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c7).
% 373431 [hyper:373319,373425,demod:373358,cut:373305] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938)
%
%
% START OF PROOF
% 375502 [?] ?
% 375668 [] equal(X,X).
% 375669 [] equal(multiply(identity,X),X).
% 375670 [] equal(multiply(inverse(X),X),identity).
% 375671 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 375672 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 375717 [para:375670.1.1,375672.1.1,cut:375502] -equal(inverse(inverse(sk_c8)),sk_c8).
% 375816 [para:375670.1.1,375671.1.1.1,demod:375669] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 375885 [para:375670.1.1,375816.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 375980 [para:375816.1.2,375816.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 376057 [para:375980.1.2,375885.1.2] equal(X,multiply(X,identity)).
% 376063 [para:376057.1.2,375885.1.2] equal(X,inverse(inverse(X))).
% 376070 [para:376063.1.2,375717.1.1,cut:375668] 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_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938,376069,50,29939,376069,30,29939,376069,40,29939,376110,0,29939)
%
%
% START OF PROOF
% 376071 [] equal(multiply(identity,X),X).
% 376072 [] equal(multiply(inverse(X),X),identity).
% 376073 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 376074 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(multiply(Y,X),sk_c7) | -equal(inverse(Y),X).
% 376077 [?] ?
% 376078 [?] ?
% 376079 [] equal(multiply(sk_c3,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c8),sk_c7).
% 376080 [?] ?
% 376083 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c6).
% 376084 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 376085 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c2),sk_c3).
% 376086 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c2),sk_c3).
% 376089 [?] ?
% 376090 [?] ?
% 376091 [?] ?
% 376092 [?] ?
% 376123 [hyper:376074,376083,binarycut:376089,binarycut:376077] equal(inverse(sk_c8),sk_c6).
% 376127 [para:376123.1.1,376072.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 376138 [hyper:376074,376084,binarycut:376090,binarycut:376078] equal(inverse(sk_c4),sk_c8).
% 376144 [para:376138.1.1,376072.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 376166 [hyper:376074,376085,binarycut:376091,binarycut:376079] equal(multiply(sk_c4,sk_c8),sk_c7).
% 376175 [hyper:376074,376086,binarycut:376092,binarycut:376080] equal(multiply(sk_c7,sk_c6),sk_c8).
% 376176 [para:376072.1.1,376073.1.1.1,demod:376071] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 376178 [para:376127.1.1,376073.1.1.1,demod:376071] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 376189 [para:376144.1.1,376178.1.2.2] equal(sk_c4,multiply(sk_c6,identity)).
% 376195 [para:376166.1.1,376176.1.2.2,demod:376138] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 376201 [para:376189.1.2,376073.1.1.1,demod:376071] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 376203 [para:376195.1.2,376178.1.2.2,demod:376127] equal(sk_c7,identity).
% 376205 [para:376203.1.1,376175.1.1.1,demod:376071] equal(sk_c6,sk_c8).
% 376208 [para:376205.1.2,376123.1.1.1] equal(inverse(sk_c6),sk_c6).
% 376209 [para:376205.1.2,376127.1.1.2] equal(multiply(sk_c6,sk_c6),identity).
% 376211 [para:376205.1.2,376166.1.1.2,demod:376209,376201] equal(identity,sk_c7).
% 376219 [hyper:376074,376208,demod:376127,376209,cut:376211,cut:376211] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938,376069,50,29939,376069,30,29939,376069,40,29939,376110,0,29939,376218,50,29939,376218,30,29939,376218,40,29939,376259,0,29944,376339,50,29945,376380,0,29945)
%
%
% START OF PROOF
% 376341 [] equal(multiply(identity,X),X).
% 376342 [] equal(multiply(inverse(X),X),identity).
% 376343 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 376344 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 376363 [?] ?
% 376364 [?] ?
% 376365 [?] ?
% 376366 [?] ?
% 376367 [?] ?
% 376368 [?] ?
% 376369 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 376370 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 376371 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c8),sk_c6).
% 376372 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 376373 [] equal(multiply(sk_c4,sk_c8),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 376374 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 376389 [hyper:376344,376369,binarycut:376363] equal(inverse(sk_c5),sk_c6).
% 376390 [para:376389.1.1,376342.1.1.1] equal(multiply(sk_c6,sk_c5),identity).
% 376394 [hyper:376344,376371,binarycut:376365] equal(inverse(sk_c8),sk_c6).
% 376395 [para:376394.1.1,376342.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 376398 [hyper:376344,376372,binarycut:376366] equal(inverse(sk_c4),sk_c8).
% 376402 [para:376398.1.1,376342.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 376410 [hyper:376344,376370,binarycut:376364] equal(multiply(sk_c5,sk_c6),sk_c7).
% 376413 [hyper:376344,376373,binarycut:376367] equal(multiply(sk_c4,sk_c8),sk_c7).
% 376416 [hyper:376344,376374,binarycut:376368] equal(multiply(sk_c7,sk_c6),sk_c8).
% 376417 [para:376342.1.1,376343.1.1.1,demod:376341] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 376419 [para:376395.1.1,376343.1.1.1,demod:376341] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 376420 [para:376402.1.1,376343.1.1.1,demod:376341] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 376421 [para:376410.1.1,376343.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 376426 [para:376402.1.1,376419.1.2.2] equal(sk_c4,multiply(sk_c6,identity)).
% 376428 [para:376342.1.1,376417.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 376429 [para:376390.1.1,376417.1.2.2] equal(sk_c5,multiply(inverse(sk_c6),identity)).
% 376430 [para:376395.1.1,376417.1.2.2,demod:376429] equal(sk_c8,sk_c5).
% 376431 [para:376413.1.1,376417.1.2.2,demod:376398] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 376433 [para:376343.1.1,376417.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 376436 [para:376417.1.2,376417.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 376439 [para:376426.1.2,376343.1.1.1,demod:376341] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 376441 [para:376431.1.2,376419.1.2.2,demod:376395] equal(sk_c7,identity).
% 376443 [para:376441.1.1,376416.1.1.1,demod:376341] equal(sk_c6,sk_c8).
% 376454 [para:376430.1.1,376420.1.2.1,demod:376421,376439] equal(X,multiply(sk_c7,X)).
% 376475 [para:376436.1.2,376342.1.1] equal(multiply(X,inverse(X)),identity).
% 376477 [para:376436.1.2,376428.1.2] equal(X,multiply(X,identity)).
% 376480 [para:376477.1.2,376428.1.2] equal(X,inverse(inverse(X))).
% 376481 [para:376475.1.1,376433.1.2.2.2,demod:376477] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 376487 [para:376454.1.2,376481.1.2.1.1] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 376491 [para:376487.1.2,376436.1.2,demod:376480] equal(multiply(X,sk_c7),X).
% 376492 [hyper:376344,376491,demod:376394,cut:376443] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),sk_c6).
% Split part used next: -equal(multiply(sk_c7,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 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938,376069,50,29939,376069,30,29939,376069,40,29939,376110,0,29939,376218,50,29939,376218,30,29939,376218,40,29939,376259,0,29944,376339,50,29945,376380,0,29945,376491,50,29945,376491,30,29945,376491,40,29945,376532,0,29946,376619,50,29946,376660,0,29951,376794,50,29954,376835,0,29954,376989,50,29960,377030,0,29965,377196,50,29975,377237,0,29975,377415,50,29993,377456,0,29993,377648,50,30026,377689,0,30031,377903,50,30101,377944,0,30101,378182,50,30245,378182,40,30245,378223,0,30245)
%
%
% START OF PROOF
% 378029 [?] ?
% 378184 [] equal(multiply(identity,X),X).
% 378185 [] equal(multiply(inverse(X),X),identity).
% 378186 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 378187 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 378220 [?] ?
% 378221 [?] ?
% 378222 [?] ?
% 378278 [input:378220,cut:378187] equal(inverse(sk_c8),sk_c6).
% 378279 [para:378278.1.1,378185.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 378280 [input:378221,cut:378187] equal(inverse(sk_c4),sk_c8).
% 378281 [para:378280.1.1,378185.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 378294 [input:378222,cut:378187] equal(multiply(sk_c4,sk_c8),sk_c7).
% 378322 [para:378279.1.1,378186.1.1.1,demod:378184] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 378323 [para:378281.1.1,378186.1.1.1,demod:378184] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 378361 [para:378294.1.1,378323.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c7)).
% 378366 [para:378361.1.2,378322.1.2.2,demod:378279] equal(sk_c7,identity).
% 378367 [para:378366.1.1,378187.1.1.1,demod:378184,cut:378029] 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_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938,376069,50,29939,376069,30,29939,376069,40,29939,376110,0,29939,376218,50,29939,376218,30,29939,376218,40,29939,376259,0,29944,376339,50,29945,376380,0,29945,376491,50,29945,376491,30,29945,376491,40,29945,376532,0,29946,376619,50,29946,376660,0,29951,376794,50,29954,376835,0,29954,376989,50,29960,377030,0,29965,377196,50,29975,377237,0,29975,377415,50,29993,377456,0,29993,377648,50,30026,377689,0,30031,377903,50,30101,377944,0,30101,378182,50,30245,378182,40,30245,378223,0,30245,378366,50,30246,378366,30,30246,378366,40,30246,378407,0,30246,378539,50,30247,378580,0,30251,378769,50,30256,378810,0,30256,379009,50,30263,379050,0,30263,379261,50,30275,379302,0,30280,379525,50,30297,379566,0,30297,379805,50,30329,379846,0,30333,380101,50,30389,380142,0,30389,380417,50,30504,380417,40,30504,380458,0,30504)
%
%
% START OF PROOF
% 380274 [?] ?
% 380419 [] equal(multiply(identity,X),X).
% 380420 [] equal(multiply(inverse(X),X),identity).
% 380421 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 380422 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 380428 [?] ?
% 380434 [?] ?
% 380440 [?] ?
% 380446 [?] ?
% 380452 [?] ?
% 380458 [?] ?
% 380488 [input:380434,cut:380422] equal(inverse(sk_c2),sk_c3).
% 380489 [para:380488.1.1,380420.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 380499 [input:380428,cut:380422] equal(multiply(sk_c3,sk_c8),sk_c7).
% 380508 [input:380452,cut:380422] equal(inverse(sk_c1),sk_c8).
% 380509 [para:380508.1.1,380420.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 380520 [input:380440,cut:380422] equal(multiply(sk_c2,sk_c3),sk_c7).
% 380527 [input:380446,cut:380422] equal(multiply(sk_c1,sk_c7),sk_c8).
% 380530 [input:380458,cut:380422] equal(multiply(sk_c7,sk_c8),sk_c6).
% 380534 [para:380420.1.1,380421.1.1.1,demod:380419] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 380544 [para:380489.1.1,380421.1.1.1,demod:380419] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 380549 [para:380499.1.1,380421.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c8,X))).
% 380556 [para:380509.1.1,380421.1.1.1,demod:380419] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 380578 [para:380530.1.1,380421.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c8,X))).
% 380587 [para:380520.1.1,380544.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c7)).
% 380594 [para:380527.1.1,380556.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 380601 [para:380594.1.2,380549.1.2.2,demod:380587] equal(multiply(sk_c7,sk_c8),sk_c3).
% 380614 [para:380601.1.1,380530.1.1] equal(sk_c3,sk_c6).
% 380616 [para:380601.1.1,380421.1.1.1,demod:380578] equal(multiply(sk_c3,X),multiply(sk_c6,X)).
% 380629 [para:380614.1.1,380520.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c7).
% 380642 [para:380629.1.1,380421.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c6,X))).
% 380681 [para:380544.1.2,380534.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 380690 [para:380616.1.1,380534.1.2.2,demod:380642,380681] equal(X,multiply(sk_c7,X)).
% 380694 [para:380690.1.2,380422.1.1,cut:380274] 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_c8),sk_c6) | -equal(inverse(X),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,Z),sk_c7) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c8),sk_c7) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(multiply(U,sk_c8),sk_c7) | -equal(inverse(U),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(V,sk_c6),sk_c7) | -equal(inverse(V),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 23
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(41,40,0,87,0,0,1026,50,9,1072,0,9,2553,50,34,2599,0,34,4186,50,55,4232,0,55,5921,50,77,5967,0,77,7711,50,105,7757,0,105,9653,50,144,9699,0,144,11699,50,203,11745,0,203,13947,50,303,13993,0,303,16349,50,472,16395,0,472,19003,50,722,19049,0,722,21861,50,1178,21861,40,1178,21907,0,1178,32426,3,1482,33109,4,1629,33770,5,1779,33771,1,1779,33771,50,1779,33771,40,1779,33817,0,1779,34175,3,2081,34186,4,2239,34212,5,2380,34212,1,2380,34212,50,2380,34212,40,2380,34258,0,2380,87682,3,3883,88153,4,4631,88562,5,5381,88563,1,5382,88563,50,5383,88563,40,5383,88609,0,5383,112856,3,6136,113289,4,6509,113650,1,6884,113650,50,6884,113650,40,6884,113696,0,6884,123348,3,7648,124510,4,8010,125764,5,8385,125765,1,8385,125765,50,8385,125765,40,8385,125811,0,8385,188813,3,12287,189901,4,14236,190394,5,16186,190395,1,16186,190395,50,16188,190395,40,16188,190441,0,16188,247509,3,18740,248322,4,20014,248439,1,21289,248439,50,21290,248439,40,21290,248485,0,21291,294983,3,22800,295811,4,23542,296383,5,24292,296384,1,24292,296384,50,24294,296384,40,24294,296430,0,24294,305125,3,25046,306110,4,25422,306333,5,25795,306334,5,25795,306335,1,25795,306335,50,25795,306335,40,25795,306381,0,25795,343398,3,26998,344020,4,27596,344486,5,28196,344487,1,28196,344487,50,28197,344487,40,28197,344533,0,28197,372239,3,28951,372788,4,29323,373140,5,29698,373141,1,29698,373141,50,29699,373141,40,29699,373141,40,29699,373182,0,29699,373314,50,29700,373355,0,29700,373430,50,29700,373430,30,29700,373430,40,29700,373471,0,29707,373631,50,29708,373672,0,29708,373886,50,29712,373927,0,29712,374151,50,29718,374192,0,29723,374426,50,29733,374467,0,29733,374712,50,29750,374753,0,29754,375013,50,29781,375054,0,29781,375330,50,29835,375371,0,29835,375667,50,29938,375667,40,29938,375708,0,29938,376069,50,29939,376069,30,29939,376069,40,29939,376110,0,29939,376218,50,29939,376218,30,29939,376218,40,29939,376259,0,29944,376339,50,29945,376380,0,29945,376491,50,29945,376491,30,29945,376491,40,29945,376532,0,29946,376619,50,29946,376660,0,29951,376794,50,29954,376835,0,29954,376989,50,29960,377030,0,29965,377196,50,29975,377237,0,29975,377415,50,29993,377456,0,29993,377648,50,30026,377689,0,30031,377903,50,30101,377944,0,30101,378182,50,30245,378182,40,30245,378223,0,30245,378366,50,30246,378366,30,30246,378366,40,30246,378407,0,30246,378539,50,30247,378580,0,30251,378769,50,30256,378810,0,30256,379009,50,30263,379050,0,30263,379261,50,30275,379302,0,30280,379525,50,30297,379566,0,30297,379805,50,30329,379846,0,30333,380101,50,30389,380142,0,30389,380417,50,30504,380417,40,30504,380458,0,30504,380693,50,30505,380693,30,30505,380693,40,30505,380734,0,30505,380862,50,30506,380903,0,30511,381088,50,30516,381129,0,30516,381324,50,30523,381365,0,30523,381570,50,30534,381611,0,30538,381828,50,30554,381869,0,30554,382101,50,30584,382142,0,30589,382390,50,30641,382431,0,30641,382699,50,30749,382699,40,30749,382740,0,30749)
%
%
% START OF PROOF
% 382701 [] equal(multiply(identity,X),X).
% 382702 [] equal(multiply(inverse(X),X),identity).
% 382703 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 382704 [] -equal(inverse(sk_c8),sk_c6).
% 382707 [?] ?
% 382713 [?] ?
% 382719 [?] ?
% 382725 [?] ?
% 382731 [?] ?
% 382737 [?] ?
% 382746 [input:382713,cut:382704] equal(inverse(sk_c2),sk_c3).
% 382747 [para:382746.1.1,382702.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 382753 [input:382731,cut:382704] equal(inverse(sk_c1),sk_c8).
% 382754 [para:382753.1.1,382702.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 382758 [input:382707,cut:382704] equal(multiply(sk_c3,sk_c8),sk_c7).
% 382767 [input:382719,cut:382704] equal(multiply(sk_c2,sk_c3),sk_c7).
% 382773 [input:382725,cut:382704] equal(multiply(sk_c1,sk_c7),sk_c8).
% 382782 [input:382737,cut:382704] equal(multiply(sk_c7,sk_c8),sk_c6).
% 382802 [para:382702.1.1,382703.1.1.1,demod:382701] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 382804 [para:382747.1.1,382703.1.1.1,demod:382701] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 382807 [para:382754.1.1,382703.1.1.1,demod:382701] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 382814 [para:382767.1.1,382703.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c3,X))).
% 382842 [para:382767.1.1,382804.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c7)).
% 382845 [para:382773.1.1,382807.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 382850 [para:382747.1.1,382802.1.2.2] equal(sk_c2,multiply(inverse(sk_c3),identity)).
% 382853 [para:382754.1.1,382802.1.2.2] equal(sk_c1,multiply(inverse(sk_c8),identity)).
% 382854 [para:382758.1.1,382802.1.2.2] equal(sk_c8,multiply(inverse(sk_c3),sk_c7)).
% 382860 [para:382767.1.1,382802.1.2.2] equal(sk_c3,multiply(inverse(sk_c2),sk_c7)).
% 382891 [para:382804.1.2,382802.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 382892 [para:382842.1.2,382802.1.2.2,demod:382891] equal(sk_c7,multiply(sk_c2,sk_c3)).
% 382893 [para:382807.1.2,382802.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c8),X)).
% 382894 [para:382845.1.2,382802.1.2.2,demod:382893] equal(sk_c8,multiply(sk_c1,sk_c7)).
% 382914 [para:382891.1.2,382702.1.1,demod:382892] equal(sk_c7,identity).
% 382915 [para:382891.1.2,382802.1.2,demod:382814] equal(X,multiply(sk_c7,X)).
% 382925 [para:382914.1.1,382854.1.2.2,demod:382850] equal(sk_c8,sk_c2).
% 382926 [para:382914.1.1,382860.1.2.2] equal(sk_c3,multiply(inverse(sk_c2),identity)).
% 382942 [para:382925.1.1,382704.1.1.1] -equal(inverse(sk_c2),sk_c6).
% 382956 [para:382925.1.1,382853.1.2.1.1,demod:382926] equal(sk_c1,sk_c3).
% 382970 [para:382956.1.2,382842.1.2.1,demod:382894] equal(sk_c3,sk_c8).
% 382982 [para:382970.1.2,382782.1.1.2,demod:382915] equal(sk_c3,sk_c6).
% 383019 [para:382746.1.1,382942.1.1,cut:382982] 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: 34125
% derived clauses: 5458734
% kept clauses: 326723
% kept size sum: 61159
% kept mid-nuclei: 15948
% kept new demods: 7094
% forw unit-subs: 2155668
% forw double-subs: 2624676
% forw overdouble-subs: 289363
% backward subs: 12338
% fast unit cutoff: 27233
% full unit cutoff: 0
% dbl unit cutoff: 9189
% real runtime : 308.69
% process. runtime: 307.50
% specific non-discr-tree subsumption statistics:
% tried: 40508349
% length fails: 3010583
% strength fails: 17198775
% predlist fails: 1606754
% aux str. fails: 3931500
% by-lit fails: 8525970
% full subs tried: 977244
% full subs fail: 873510
%
% ; 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/GRP337-1+eq_r.in")
%
%------------------------------------------------------------------------------