TSTP Solution File: GRP381-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP381-1 : 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 299.5s
% Output : Assurance 299.5s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP381-1+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(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% was split for some strategies as:
% -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(inverse(sk_c7),sk_c6).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408)
%
%
% START OF PROOF
% 344349 [] equal(multiply(identity,X),X).
% 344350 [] equal(multiply(inverse(X),X),identity).
% 344351 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344352 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 344353 [?] ?
% 344354 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 344358 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 344359 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 344373 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 344374 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 344378 [?] ?
% 344379 [] equal(inverse(sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 344386 [hyper:344352,344354,binarycut:344353] equal(inverse(sk_c2),sk_c6).
% 344388 [para:344386.1.1,344350.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 344400 [hyper:344352,344379,binarycut:344378] equal(inverse(sk_c7),sk_c6).
% 344403 [para:344400.1.1,344350.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 344407 [hyper:344352,344359,344358] equal(multiply(sk_c2,sk_c6),sk_c7).
% 344421 [hyper:344352,344373,344374] equal(multiply(sk_c6,sk_c5),sk_c7).
% 344423 [para:344388.1.1,344351.1.1.1,demod:344349] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 344429 [para:344407.1.1,344423.1.2.2,demod:344403] equal(sk_c6,identity).
% 344430 [para:344429.1.1,344388.1.1.1,demod:344349] equal(sk_c2,identity).
% 344433 [para:344429.1.1,344421.1.1.1,demod:344349] equal(sk_c5,sk_c7).
% 344435 [para:344430.1.1,344386.1.1.1] equal(inverse(identity),sk_c6).
% 344437 [para:344430.1.1,344407.1.1.1,demod:344349] equal(sk_c6,sk_c7).
% 344452 [para:344437.1.2,344433.1.2] equal(sk_c5,sk_c6).
% 344469 [hyper:344352,344435,demod:344349,cut:344452] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414)
%
%
% START OF PROOF
% 344575 [?] ?
% 344616 [] equal(X,X).
% 344620 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 344623 [?] ?
% 344624 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 344628 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 344629 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 344654 [hyper:344620,344624,binarycut:344623] equal(inverse(sk_c2),sk_c6).
% 344678 [hyper:344620,344628,demod:344654,cut:344575] equal(multiply(sk_c3,sk_c6),sk_c7).
% 344684 [hyper:344620,344629,demod:344654,cut:344575] equal(inverse(sk_c3),sk_c7).
% 344686 [hyper:344620,344684,demod:344678,cut:344616] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414,344685,50,29414,344685,30,29414,344685,40,29414,344720,0,29414)
%
%
% START OF PROOF
% 344687 [] equal(multiply(identity,X),X).
% 344688 [] equal(multiply(inverse(X),X),identity).
% 344689 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344690 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 344691 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 344692 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 344693 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 344694 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 344695 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 344696 [?] ?
% 344697 [?] ?
% 344698 [?] ?
% 344699 [?] ?
% 344700 [?] ?
% 344723 [hyper:344690,344692,binarycut:344697] equal(inverse(sk_c4),sk_c6).
% 344726 [para:344723.1.1,344688.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 344730 [hyper:344690,344694,binarycut:344699] equal(inverse(sk_c3),sk_c7).
% 344731 [para:344730.1.1,344688.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 344734 [hyper:344690,344691,binarycut:344696] equal(multiply(sk_c4,sk_c5),sk_c6).
% 344738 [hyper:344690,344693,binarycut:344698] equal(multiply(sk_c3,sk_c6),sk_c7).
% 344744 [hyper:344690,344695,binarycut:344700] equal(multiply(sk_c6,sk_c7),sk_c5).
% 344745 [para:344688.1.1,344689.1.1.1,demod:344687] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 344746 [para:344726.1.1,344689.1.1.1,demod:344687] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 344747 [para:344731.1.1,344689.1.1.1,demod:344687] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 344748 [para:344734.1.1,344689.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 344749 [para:344738.1.1,344689.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 344751 [para:344734.1.1,344746.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 344752 [para:344751.1.2,344689.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c6,X))).
% 344753 [para:344738.1.1,344747.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 344756 [para:344726.1.1,344745.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 344758 [para:344744.1.1,344745.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 344760 [para:344751.1.2,344745.1.2.2,demod:344758] equal(sk_c6,sk_c7).
% 344762 [para:344760.1.2,344731.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 344764 [para:344760.1.2,344753.1.2.1,demod:344744] equal(sk_c6,sk_c5).
% 344765 [para:344760.1.2,344753.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c6)).
% 344767 [para:344764.1.1,344738.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 344768 [para:344764.1.1,344744.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 344770 [para:344764.1.1,344751.1.2.1] equal(sk_c5,multiply(sk_c5,sk_c6)).
% 344772 [para:344762.1.1,344745.1.2.2,demod:344756] equal(sk_c3,sk_c4).
% 344775 [para:344772.1.2,344748.1.2.1] equal(multiply(sk_c6,X),multiply(sk_c3,multiply(sk_c5,X))).
% 344778 [para:344764.1.1,344749.1.2.2.1,demod:344775] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 344780 [para:344765.1.2,344689.1.1.1,demod:344752,344778] equal(multiply(sk_c6,X),multiply(sk_c5,X)).
% 344785 [para:344768.1.1,344745.1.2.2,demod:344688] equal(sk_c7,identity).
% 344786 [?] ?
% 344788 [para:344785.1.1,344731.1.1.1,demod:344687] equal(sk_c3,identity).
% 344789 [para:344785.1.1,344744.1.1.2,demod:344786,344780] equal(identity,sk_c5).
% 344795 [para:344788.1.1,344767.1.1.1,demod:344687] equal(sk_c5,sk_c7).
% 344802 [para:344789.1.2,344758.1.2.2,demod:344756] equal(sk_c7,sk_c4).
% 344806 [para:344802.1.1,344795.1.2] equal(sk_c5,sk_c4).
% 344810 [para:344806.1.2,344723.1.1.1] equal(inverse(sk_c5),sk_c6).
% 344813 [hyper:344690,344810,demod:344770,cut:344795] 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(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414,344685,50,29414,344685,30,29414,344685,40,29414,344720,0,29414,344812,50,29414,344812,30,29414,344812,40,29414,344847,0,29414)
%
%
% START OF PROOF
% 344814 [] equal(multiply(identity,X),X).
% 344815 [] equal(multiply(inverse(X),X),identity).
% 344816 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 344817 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 344828 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 344829 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 344830 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 344831 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 344832 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 344833 [?] ?
% 344834 [?] ?
% 344835 [?] ?
% 344836 [?] ?
% 344837 [?] ?
% 344854 [hyper:344817,344829,binarycut:344834] equal(inverse(sk_c4),sk_c6).
% 344855 [para:344854.1.1,344815.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 344858 [hyper:344817,344831,binarycut:344836] equal(inverse(sk_c3),sk_c7).
% 344862 [para:344858.1.1,344815.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 344869 [hyper:344817,344828,binarycut:344833] equal(multiply(sk_c4,sk_c5),sk_c6).
% 344872 [hyper:344817,344830,binarycut:344835] equal(multiply(sk_c3,sk_c6),sk_c7).
% 344876 [hyper:344817,344832,binarycut:344837] equal(multiply(sk_c6,sk_c7),sk_c5).
% 344877 [para:344815.1.1,344816.1.1.1,demod:344814] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 344878 [para:344855.1.1,344816.1.1.1,demod:344814] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 344879 [para:344862.1.1,344816.1.1.1,demod:344814] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 344883 [para:344869.1.1,344878.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 344885 [para:344872.1.1,344879.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 344888 [para:344855.1.1,344877.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 344890 [para:344876.1.1,344877.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 344892 [para:344883.1.2,344877.1.2.2,demod:344890] equal(sk_c6,sk_c7).
% 344894 [para:344892.1.2,344862.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 344896 [para:344892.1.2,344885.1.2.1,demod:344876] equal(sk_c6,sk_c5).
% 344900 [para:344896.1.1,344876.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 344904 [para:344894.1.1,344877.1.2.2,demod:344888] equal(sk_c3,sk_c4).
% 344906 [para:344904.1.2,344854.1.1.1,demod:344858] equal(sk_c7,sk_c6).
% 344917 [para:344900.1.1,344877.1.2.2,demod:344815] equal(sk_c7,identity).
% 344920 [para:344917.1.1,344862.1.1.1,demod:344814] equal(sk_c3,identity).
% 344925 [para:344920.1.1,344858.1.1.1] equal(inverse(identity),sk_c7).
% 344933 [hyper:344817,344925,demod:344814,cut:344906] 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(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(inverse(sk_c7),sk_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(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414,344685,50,29414,344685,30,29414,344685,40,29414,344720,0,29414,344812,50,29414,344812,30,29414,344812,40,29414,344847,0,29414,344932,50,29414,344932,30,29414,344932,40,29414,344967,0,29419,345078,50,29419,345113,0,29419,345289,50,29422,345324,0,29426,345517,50,29429,345552,0,29429,345758,50,29434,345793,0,29434,346005,50,29441,346040,0,29446,346260,50,29460,346295,0,29460,346523,50,29486,346558,0,29491,346796,50,29545,346831,0,29545,347079,50,29655,347079,40,29655,347114,0,29655)
%
%
% START OF PROOF
% 346936 [?] ?
% 347081 [] equal(multiply(identity,X),X).
% 347082 [] equal(multiply(inverse(X),X),identity).
% 347083 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347084 [] -equal(inverse(sk_c7),sk_c6).
% 347110 [?] ?
% 347111 [?] ?
% 347112 [?] ?
% 347113 [?] ?
% 347114 [?] ?
% 347129 [input:347111,cut:347084] equal(inverse(sk_c4),sk_c6).
% 347130 [para:347129.1.1,347082.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 347133 [input:347113,cut:347084] equal(inverse(sk_c3),sk_c7).
% 347134 [para:347133.1.1,347082.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 347151 [input:347110,cut:347084] equal(multiply(sk_c4,sk_c5),sk_c6).
% 347152 [input:347112,cut:347084] equal(multiply(sk_c3,sk_c6),sk_c7).
% 347153 [input:347114,cut:347084] equal(multiply(sk_c6,sk_c7),sk_c5).
% 347168 [para:347082.1.1,347083.1.1.1,demod:347081] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 347170 [para:347130.1.1,347083.1.1.1,demod:347081] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 347172 [para:347134.1.1,347083.1.1.1,demod:347081] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 347207 [para:347151.1.1,347170.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 347212 [para:347152.1.1,347172.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 347239 [para:347153.1.1,347168.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 347256 [para:347207.1.2,347168.1.2.2,demod:347239] equal(sk_c6,sk_c7).
% 347262 [para:347256.1.2,347084.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 347271 [para:347256.1.2,347212.1.2.1] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 347289 [para:347271.1.2,347153.1.1] equal(sk_c6,sk_c5).
% 347307 [para:347289.1.1,347262.1.1.1,cut:346936] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c5),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414,344685,50,29414,344685,30,29414,344685,40,29414,344720,0,29414,344812,50,29414,344812,30,29414,344812,40,29414,344847,0,29414,344932,50,29414,344932,30,29414,344932,40,29414,344967,0,29419,345078,50,29419,345113,0,29419,345289,50,29422,345324,0,29426,345517,50,29429,345552,0,29429,345758,50,29434,345793,0,29434,346005,50,29441,346040,0,29446,346260,50,29460,346295,0,29460,346523,50,29486,346558,0,29491,346796,50,29545,346831,0,29545,347079,50,29655,347079,40,29655,347114,0,29655,347306,50,29656,347306,30,29656,347306,40,29656,347341,0,29656,347452,50,29657,347487,0,29662,347663,50,29664,347698,0,29664,347891,50,29667,347926,0,29667,348132,50,29672,348167,0,29676,348379,50,29683,348414,0,29683,348634,50,29697,348669,0,29702,348897,50,29728,348932,0,29728,349170,50,29785,349205,0,29785,349453,50,29896,349453,40,29896,349488,0,29896)
%
%
% START OF PROOF
% 349397 [?] ?
% 349455 [] equal(multiply(identity,X),X).
% 349456 [] equal(multiply(inverse(X),X),identity).
% 349457 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349458 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 349479 [?] ?
% 349480 [?] ?
% 349483 [?] ?
% 349528 [input:349480,cut:349458] equal(inverse(sk_c4),sk_c6).
% 349529 [para:349528.1.1,349456.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 349549 [input:349479,cut:349458] equal(multiply(sk_c4,sk_c5),sk_c6).
% 349551 [input:349483,cut:349458] equal(multiply(sk_c6,sk_c7),sk_c5).
% 349565 [para:349456.1.1,349457.1.1.1,demod:349455] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 349578 [para:349529.1.1,349457.1.1.1,demod:349455] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 349607 [para:349549.1.1,349578.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 349664 [para:349551.1.1,349565.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 349667 [para:349607.1.2,349565.1.2.2,demod:349664] equal(sk_c6,sk_c7).
% 349673 [para:349667.1.2,349458.1.2,cut:349397] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c7),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(Z),sk_c7) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c6,sk_c7),sk_c5).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,689,50,4,729,0,4,1358,50,9,1398,0,9,2038,50,15,2078,0,15,2725,50,20,2765,0,20,3419,50,28,3459,0,28,4121,50,43,4161,0,43,4832,50,71,4872,0,71,5553,50,133,5593,0,133,6285,50,260,6325,0,260,7029,50,470,7069,0,470,7786,50,888,7786,40,888,7826,0,888,18202,3,1189,18963,4,1339,19689,5,1489,19690,1,1489,19690,50,1489,19690,40,1489,19730,0,1489,19957,3,1797,19966,4,1949,19973,5,2090,19973,1,2090,19973,50,2090,19973,40,2090,20013,0,2090,42603,3,3597,44057,4,4341,45393,5,5091,45394,1,5091,45394,50,5092,45394,40,5092,45434,0,5092,60541,3,5845,61609,4,6218,62555,5,6593,62556,1,6593,62556,50,6593,62556,40,6593,62596,0,6593,72713,3,7349,73699,4,7719,75007,1,8094,75007,50,8094,75007,40,8094,75047,0,8094,169848,3,11997,170802,4,13945,171754,1,15895,171754,50,15898,171754,40,15898,171794,0,15898,244535,3,18449,245341,4,19724,245937,5,20999,245938,1,20999,245938,50,21001,245938,40,21001,245978,0,21001,280519,3,22509,281474,4,23252,282375,5,24002,282376,1,24002,282376,50,24003,282376,40,24003,282416,0,24003,290689,3,24795,291952,4,25130,292277,5,25504,292277,1,25504,292277,50,25504,292277,40,25504,292317,0,25504,320494,3,26705,321371,4,27305,321925,5,27905,321926,1,27905,321926,50,27906,321926,40,27906,321966,0,27906,343166,3,28657,343867,4,29032,344347,1,29407,344347,50,29408,344347,40,29408,344347,40,29408,344382,0,29408,344468,50,29409,344468,30,29409,344468,40,29409,344503,0,29409,344615,50,29409,344650,0,29414,344685,50,29414,344685,30,29414,344685,40,29414,344720,0,29414,344812,50,29414,344812,30,29414,344812,40,29414,344847,0,29414,344932,50,29414,344932,30,29414,344932,40,29414,344967,0,29419,345078,50,29419,345113,0,29419,345289,50,29422,345324,0,29426,345517,50,29429,345552,0,29429,345758,50,29434,345793,0,29434,346005,50,29441,346040,0,29446,346260,50,29460,346295,0,29460,346523,50,29486,346558,0,29491,346796,50,29545,346831,0,29545,347079,50,29655,347079,40,29655,347114,0,29655,347306,50,29656,347306,30,29656,347306,40,29656,347341,0,29656,347452,50,29657,347487,0,29662,347663,50,29664,347698,0,29664,347891,50,29667,347926,0,29667,348132,50,29672,348167,0,29676,348379,50,29683,348414,0,29683,348634,50,29697,348669,0,29702,348897,50,29728,348932,0,29728,349170,50,29785,349205,0,29785,349453,50,29896,349453,40,29896,349488,0,29896,349672,50,29896,349672,30,29896,349672,40,29896,349707,0,29896,349793,50,29896,349828,0,29901,349962,50,29902,349997,0,29902,350142,50,29905,350177,0,29905,350331,50,29910,350366,0,29914,350527,50,29921,350562,0,29921,350731,50,29935,350766,0,29939,350944,50,29966,350979,0,29966,351167,50,30025,351202,0,30025,351401,50,30137,351401,40,30137,351436,0,30137)
%
%
% START OF PROOF
% 351286 [?] ?
% 351404 [] equal(multiply(inverse(X),X),identity).
% 351406 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 351436 [?] ?
% 351485 [input:351436,cut:351406] equal(inverse(sk_c7),sk_c6).
% 351486 [para:351485.1.1,351404.1.1.1] equal(multiply(sk_c6,sk_c7),identity).
% 351488 [para:351486.1.1,351406.1.1,cut:351286] 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: 37288
% derived clauses: 6343616
% kept clauses: 287940
% kept size sum: 891688
% kept mid-nuclei: 4065
% kept new demods: 5095
% forw unit-subs: 2226687
% forw double-subs: 3451501
% forw overdouble-subs: 309378
% backward subs: 9373
% fast unit cutoff: 23479
% full unit cutoff: 0
% dbl unit cutoff: 5934
% real runtime : 302.14
% process. runtime: 301.37
% specific non-discr-tree subsumption statistics:
% tried: 39572657
% length fails: 4746155
% strength fails: 10719200
% predlist fails: 1845207
% aux str. fails: 4559487
% by-lit fails: 8954983
% full subs tried: 1391630
% full subs fail: 1294630
%
% ; 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/GRP381-1+eq_r.in")
%
%------------------------------------------------------------------------------