TSTP Solution File: GRP328-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP328-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art01.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 298.5s
% Output : Assurance 298.5s
% 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/GRP328-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -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 6 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(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156)
%
%
% START OF PROOF
% 310382 [] equal(X,X).
% 310386 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 310387 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 310388 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 310389 [?] ?
% 310392 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 310393 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 310394 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 310397 [?] ?
% 310398 [?] ?
% 310399 [?] ?
% 310438 [hyper:310386,310388,310387,binarycut:310389] equal(inverse(sk_c2),sk_c8).
% 310445 [hyper:310386,310392,demod:310438,cut:310382,binarycut:310397] equal(inverse(sk_c4),sk_c8).
% 310465 [hyper:310386,310393,demod:310438,cut:310382,binarycut:310398] equal(multiply(sk_c4,sk_c8),sk_c5).
% 310479 [hyper:310386,310394,demod:310438,cut:310382,binarycut:310399] equal(multiply(sk_c8,sk_c5),sk_c7).
% 310486 [hyper:310386,310479,310465,demod:310445,cut:310382] 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(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156,310485,50,29156,310485,30,29156,310485,40,29156,310520,0,29156)
%
%
% START OF PROOF
% 310486 [] equal(X,X).
% 310490 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 310491 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 310492 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c2),sk_c8).
% 310493 [?] ?
% 310496 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 310497 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c8),sk_c5).
% 310498 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c5),sk_c7).
% 310501 [?] ?
% 310502 [?] ?
% 310503 [?] ?
% 310542 [hyper:310490,310492,310491,binarycut:310493] equal(inverse(sk_c2),sk_c8).
% 310549 [hyper:310490,310496,demod:310542,cut:310486,binarycut:310501] equal(inverse(sk_c4),sk_c8).
% 310569 [hyper:310490,310497,demod:310542,cut:310486,binarycut:310502] equal(multiply(sk_c4,sk_c8),sk_c5).
% 310583 [hyper:310490,310498,demod:310542,cut:310486,binarycut:310503] equal(multiply(sk_c8,sk_c5),sk_c7).
% 310590 [hyper:310490,310583,310569,demod:310549,cut:310486] 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 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(X,sk_c7),sk_c8) | -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
%
%
% 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(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156,310485,50,29156,310485,30,29156,310485,40,29156,310520,0,29156,310589,50,29156,310589,30,29156,310589,40,29156,310624,0,29162,310702,50,29162,310737,0,29162)
%
%
% START OF PROOF
% 310704 [] equal(multiply(identity,X),X).
% 310705 [] equal(multiply(inverse(X),X),identity).
% 310706 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 310707 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 310723 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 310724 [] equal(multiply(sk_c4,sk_c8),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 310725 [] equal(multiply(sk_c8,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 310726 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c8),sk_c6).
% 310727 [] equal(multiply(sk_c7,sk_c6),sk_c8) | equal(inverse(sk_c1),sk_c7).
% 310728 [?] ?
% 310729 [?] ?
% 310730 [?] ?
% 310731 [?] ?
% 310732 [?] ?
% 310743 [hyper:310707,310723,binarycut:310728] equal(inverse(sk_c4),sk_c8).
% 310744 [para:310743.1.1,310705.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 310747 [hyper:310707,310726,binarycut:310731] equal(inverse(sk_c8),sk_c6).
% 310748 [para:310747.1.1,310705.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 310754 [hyper:310707,310724,binarycut:310729] equal(multiply(sk_c4,sk_c8),sk_c5).
% 310757 [hyper:310707,310725,binarycut:310730] equal(multiply(sk_c8,sk_c5),sk_c7).
% 310761 [hyper:310707,310727,binarycut:310732] equal(multiply(sk_c7,sk_c6),sk_c8).
% 310762 [para:310705.1.1,310706.1.1.1,demod:310704] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 310763 [para:310744.1.1,310706.1.1.1,demod:310704] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 310764 [para:310748.1.1,310706.1.1.1,demod:310704] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 310768 [para:310754.1.1,310763.1.2.2,demod:310757] equal(sk_c8,sk_c7).
% 310769 [para:310768.1.2,310761.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 310771 [para:310744.1.1,310764.1.2.2] equal(sk_c4,multiply(sk_c6,identity)).
% 310773 [para:310763.1.2,310764.1.2.2] equal(multiply(sk_c4,X),multiply(sk_c6,X)).
% 310774 [para:310769.1.1,310764.1.2.2,demod:310748] equal(sk_c6,identity).
% 310775 [para:310774.1.1,310748.1.1.1,demod:310704] equal(sk_c8,identity).
% 310778 [para:310774.1.1,310764.1.2.1,demod:310704] equal(X,multiply(sk_c8,X)).
% 310780 [para:310705.1.1,310762.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 310781 [para:310747.1.1,310762.1.2.1,demod:310778] equal(X,multiply(sk_c6,X)).
% 310784 [para:310706.1.1,310762.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 310786 [para:310762.1.2,310762.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 310787 [para:310775.1.1,310744.1.1.1,demod:310704] equal(sk_c4,identity).
% 310789 [para:310775.1.1,310754.1.1.2,demod:310771,310773] equal(sk_c4,sk_c5).
% 310792 [para:310787.1.1,310754.1.1.1,demod:310704] equal(sk_c8,sk_c5).
% 310793 [para:310789.1.1,310743.1.1.1] equal(inverse(sk_c5),sk_c8).
% 310795 [para:310789.1.1,310754.1.1.1] equal(multiply(sk_c5,sk_c8),sk_c5).
% 310819 [para:310786.1.2,310705.1.1] equal(multiply(X,inverse(X)),identity).
% 310821 [para:310786.1.2,310780.1.2] equal(X,multiply(X,identity)).
% 310825 [para:310821.1.2,310780.1.2] equal(X,inverse(inverse(X))).
% 310829 [para:310757.1.1,310784.1.2.2.2] equal(sk_c5,multiply(inverse(multiply(X,sk_c8)),multiply(X,sk_c7))).
% 310838 [para:310819.1.1,310784.1.2.2.2,demod:310821] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 310841 [para:310763.1.2,310838.1.2.1.1,demod:310781,310773] equal(inverse(X),multiply(inverse(X),sk_c8)).
% 310847 [para:310795.1.1,310838.1.2.1.1,demod:310757,310793,310747] equal(sk_c6,sk_c7).
% 310853 [para:310841.1.2,310786.1.2,demod:310825] equal(multiply(X,sk_c8),X).
% 310855 [para:310792.1.1,310853.1.1.2] equal(multiply(X,sk_c5),X).
% 310857 [para:310829.1.2,310762.1.2.2,demod:310855,310825,310853] equal(multiply(X,sk_c7),X).
% 310858 [hyper:310707,310857,demod:310747,cut:310847] 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 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_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 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156,310485,50,29156,310485,30,29156,310485,40,29156,310520,0,29156,310589,50,29156,310589,30,29156,310589,40,29156,310624,0,29162,310702,50,29162,310737,0,29162,310857,50,29164,310857,30,29164,310857,40,29164,310892,0,29164,310988,50,29164,311023,0,29169,311159,50,29171,311194,0,29171,311338,50,29175,311373,0,29179,311525,50,29184,311560,0,29184,311718,50,29192,311753,0,29192,311919,50,29207,311954,0,29212,312128,50,29239,312163,0,29239,312347,50,29298,312382,0,29298,312576,50,29411,312576,40,29411,312611,0,29411)
%
%
% START OF PROOF
% 312504 [?] ?
% 312578 [] equal(multiply(identity,X),X).
% 312579 [] equal(multiply(inverse(X),X),identity).
% 312580 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 312581 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 312607 [?] ?
% 312608 [?] ?
% 312609 [?] ?
% 312610 [?] ?
% 312611 [?] ?
% 312649 [input:312607,cut:312581] equal(inverse(sk_c4),sk_c8).
% 312650 [para:312649.1.1,312579.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 312652 [input:312610,cut:312581] equal(inverse(sk_c8),sk_c6).
% 312653 [para:312652.1.1,312579.1.1.1] equal(multiply(sk_c6,sk_c8),identity).
% 312665 [input:312608,cut:312581] equal(multiply(sk_c4,sk_c8),sk_c5).
% 312666 [input:312609,cut:312581] equal(multiply(sk_c8,sk_c5),sk_c7).
% 312667 [input:312611,cut:312581] equal(multiply(sk_c7,sk_c6),sk_c8).
% 312686 [para:312650.1.1,312580.1.1.1,demod:312578] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 312689 [para:312653.1.1,312580.1.1.1,demod:312578] equal(X,multiply(sk_c6,multiply(sk_c8,X))).
% 312709 [para:312666.1.1,312580.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c5,X))).
% 312719 [para:312665.1.1,312686.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c5)).
% 312725 [para:312719.1.2,312666.1.1] equal(sk_c8,sk_c7).
% 312726 [para:312719.1.2,312580.1.1.1,demod:312709] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 312739 [para:312725.1.2,312667.1.1.1] equal(multiply(sk_c8,sk_c6),sk_c8).
% 312755 [para:312719.1.2,312689.1.2.2,demod:312653] equal(sk_c5,identity).
% 312756 [para:312739.1.1,312689.1.2.2,demod:312653] equal(sk_c6,identity).
% 312762 [para:312755.1.1,312666.1.1.2] equal(multiply(sk_c8,identity),sk_c7).
% 312766 [para:312756.1.1,312653.1.1.1,demod:312578] equal(sk_c8,identity).
% 312772 [para:312766.1.1,312581.1.1.2,demod:312762,312726,cut:312504] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(multiply(sk_c7,sk_c6),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156,310485,50,29156,310485,30,29156,310485,40,29156,310520,0,29156,310589,50,29156,310589,30,29156,310589,40,29156,310624,0,29162,310702,50,29162,310737,0,29162,310857,50,29164,310857,30,29164,310857,40,29164,310892,0,29164,310988,50,29164,311023,0,29169,311159,50,29171,311194,0,29171,311338,50,29175,311373,0,29179,311525,50,29184,311560,0,29184,311718,50,29192,311753,0,29192,311919,50,29207,311954,0,29212,312128,50,29239,312163,0,29239,312347,50,29298,312382,0,29298,312576,50,29411,312576,40,29411,312611,0,29411,312771,50,29411,312771,30,29411,312771,40,29411,312806,0,29411,312925,50,29411,312960,0,29416,313131,50,29419,313166,0,29419,313345,50,29423,313380,0,29423,313567,50,29429,313602,0,29433,313795,50,29442,313830,0,29442,314031,50,29459,314066,0,29464,314275,50,29495,314310,0,29495,314529,50,29560,314564,0,29560,314793,50,29681,314793,40,29681,314828,0,29681)
%
%
% START OF PROOF
% 314736 [?] ?
% 314795 [] equal(multiply(identity,X),X).
% 314796 [] equal(multiply(inverse(X),X),identity).
% 314797 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 314798 [] -equal(multiply(sk_c7,sk_c6),sk_c8).
% 314803 [?] ?
% 314808 [?] ?
% 314813 [?] ?
% 314845 [input:314803,cut:314798] equal(inverse(sk_c2),sk_c8).
% 314846 [para:314845.1.1,314796.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 314872 [input:314808,cut:314798] equal(multiply(sk_c2,sk_c8),sk_c3).
% 314878 [input:314813,cut:314798] equal(multiply(sk_c8,sk_c3),sk_c7).
% 314890 [para:314846.1.1,314797.1.1.1,demod:314795] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 314930 [para:314872.1.1,314890.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 314935 [para:314930.1.2,314878.1.1] equal(sk_c8,sk_c7).
% 314937 [para:314935.1.2,314798.1.1.1,cut:314736] 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(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c6),sk_c8) | -equal(inverse(sk_c8),sk_c6) | -equal(multiply(sk_c8,U),sk_c7) | -equal(multiply(V,sk_c8),U) | -equal(inverse(V),sk_c8).
% Split part used next: -equal(inverse(sk_c8),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,74,0,1,827,50,8,866,0,8,2402,50,29,2441,0,29,4660,50,64,4699,0,64,7213,50,94,7252,0,94,10158,50,135,10197,0,135,13399,50,191,13438,0,191,17034,50,274,17073,0,274,21063,50,407,21102,0,407,25583,50,632,25622,0,633,30595,50,939,30595,40,939,30634,0,939,42556,3,1240,43169,4,1390,43819,5,1540,43820,1,1540,43820,50,1540,43820,40,1540,43859,0,1540,44055,3,1847,44064,4,1999,44071,5,2141,44071,1,2141,44071,50,2141,44071,40,2141,44110,0,2141,61054,3,3642,62537,4,4392,64216,1,5142,64216,50,5142,64216,40,5142,64255,0,5142,74685,3,5893,75980,4,6268,76561,50,6342,76561,40,6342,76600,0,6342,87323,3,7093,88432,4,7468,90053,5,7843,90054,1,7843,90054,50,7843,90054,40,7843,90093,0,7843,142206,3,11745,143376,4,13694,143913,5,15644,143914,1,15644,143914,50,15646,143914,40,15646,143953,0,15646,188926,3,18197,189795,4,19472,190371,1,20747,190371,50,20748,190371,40,20748,190410,0,20748,232974,3,22251,233578,4,22999,234248,5,23749,234249,1,23749,234249,50,23751,234249,40,23751,234288,0,23751,252809,3,24502,253474,4,24877,254239,5,25252,254240,1,25252,254240,50,25252,254240,40,25252,254279,0,25252,286237,3,26453,286897,4,27053,287499,1,27653,287499,50,27654,287499,40,27654,287538,0,27654,309441,3,28405,309925,4,28780,310380,5,29155,310381,1,29155,310381,50,29156,310381,40,29156,310381,40,29156,310416,0,29156,310485,50,29156,310485,30,29156,310485,40,29156,310520,0,29156,310589,50,29156,310589,30,29156,310589,40,29156,310624,0,29162,310702,50,29162,310737,0,29162,310857,50,29164,310857,30,29164,310857,40,29164,310892,0,29164,310988,50,29164,311023,0,29169,311159,50,29171,311194,0,29171,311338,50,29175,311373,0,29179,311525,50,29184,311560,0,29184,311718,50,29192,311753,0,29192,311919,50,29207,311954,0,29212,312128,50,29239,312163,0,29239,312347,50,29298,312382,0,29298,312576,50,29411,312576,40,29411,312611,0,29411,312771,50,29411,312771,30,29411,312771,40,29411,312806,0,29411,312925,50,29411,312960,0,29416,313131,50,29419,313166,0,29419,313345,50,29423,313380,0,29423,313567,50,29429,313602,0,29433,313795,50,29442,313830,0,29442,314031,50,29459,314066,0,29464,314275,50,29495,314310,0,29495,314529,50,29560,314564,0,29560,314793,50,29681,314793,40,29681,314828,0,29681,314936,50,29681,314936,30,29681,314936,40,29681,314971,0,29681,315090,50,29681,315125,0,29686,315296,50,29689,315331,0,29689,315510,50,29693,315545,0,29693,315732,50,29699,315767,0,29703,315960,50,29712,315995,0,29712,316196,50,29729,316231,0,29734,316440,50,29766,316475,0,29766,316694,50,29831,316729,0,29831,316958,50,29953,316958,40,29953,316993,0,29953)
%
%
% START OF PROOF
% 316960 [] equal(multiply(identity,X),X).
% 316961 [] equal(multiply(inverse(X),X),identity).
% 316962 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 316963 [] -equal(inverse(sk_c8),sk_c6).
% 316967 [?] ?
% 316972 [?] ?
% 316977 [?] ?
% 316982 [?] ?
% 316987 [?] ?
% 316992 [?] ?
% 316999 [input:316967,cut:316963] equal(inverse(sk_c2),sk_c8).
% 317000 [para:316999.1.1,316961.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 317004 [input:316982,cut:316963] equal(inverse(sk_c1),sk_c7).
% 317005 [para:317004.1.1,316961.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 317010 [input:316972,cut:316963] equal(multiply(sk_c2,sk_c8),sk_c3).
% 317013 [input:316977,cut:316963] equal(multiply(sk_c8,sk_c3),sk_c7).
% 317020 [input:316987,cut:316963] equal(multiply(sk_c1,sk_c7),sk_c8).
% 317024 [input:316992,cut:316963] equal(multiply(sk_c7,sk_c8),sk_c6).
% 317037 [para:316961.1.1,316962.1.1.1,demod:316960] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 317039 [para:317000.1.1,316962.1.1.1,demod:316960] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 317040 [para:317005.1.1,316962.1.1.1,demod:316960] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 317046 [para:317013.1.1,316962.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c3,X))).
% 317069 [para:317010.1.1,317039.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 317071 [para:317069.1.2,317013.1.1] equal(sk_c8,sk_c7).
% 317072 [para:317069.1.2,316962.1.1.1,demod:317046] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 317073 [para:317071.1.2,317005.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 317077 [para:317071.1.2,317020.1.1.2] equal(multiply(sk_c1,sk_c8),sk_c8).
% 317079 [para:317071.1.2,317024.1.1.1] equal(multiply(sk_c8,sk_c8),sk_c6).
% 317082 [para:317073.1.1,316962.1.1.1,demod:316960] equal(X,multiply(sk_c8,multiply(sk_c1,X))).
% 317088 [para:317020.1.1,317040.1.2.2,demod:317079,317072] equal(sk_c7,sk_c6).
% 317089 [para:317077.1.1,317040.1.2.2,demod:317079,317072] equal(sk_c8,sk_c6).
% 317094 [para:317088.1.1,317020.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c8).
% 317096 [para:317088.1.1,317024.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 317100 [para:317089.1.1,316963.1.1.1] -equal(inverse(sk_c6),sk_c6).
% 317105 [para:317089.1.1,317010.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 317121 [para:317094.1.1,316962.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c1,multiply(sk_c6,X))).
% 317132 [para:317088.1.1,317072.1.2.1] equal(multiply(sk_c8,X),multiply(sk_c6,X)).
% 317174 [para:317039.1.2,317037.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c8),X)).
% 317177 [para:317079.1.1,317037.1.2.2,demod:317105,317174] equal(sk_c8,sk_c3).
% 317178 [para:317040.1.2,317037.1.2.2] equal(multiply(sk_c1,X),multiply(inverse(sk_c7),X)).
% 317180 [para:317096.1.1,317037.1.2.2,demod:316961] equal(sk_c8,identity).
% 317186 [para:317072.1.2,317037.1.2.2,demod:317121,317178,317132] equal(X,multiply(sk_c6,X)).
% 317187 [para:317082.1.2,317037.1.2.2,demod:317174] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 317189 [para:317132.1.1,317037.1.2.2,demod:317187,317174,317186] equal(X,multiply(sk_c1,X)).
% 317203 [para:317177.1.1,317039.1.2.1,demod:317189,317187] equal(X,multiply(sk_c3,X)).
% 317204 [para:317177.1.1,317073.1.1.1,demod:317203] equal(sk_c1,identity).
% 317217 [para:317180.1.1,317024.1.1.2,demod:317186,317132,317072] equal(identity,sk_c6).
% 317239 [para:317204.1.1,317004.1.1.1] equal(inverse(identity),sk_c7).
% 317246 [para:317217.1.2,317100.1.1.1,demod:317239,cut:317088] 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: 43126
% derived clauses: 4926242
% kept clauses: 242633
% kept size sum: 37058
% kept mid-nuclei: 23664
% kept new demods: 5378
% forw unit-subs: 1957440
% forw double-subs: 2485943
% forw overdouble-subs: 157329
% backward subs: 30971
% fast unit cutoff: 27662
% full unit cutoff: 0
% dbl unit cutoff: 10875
% real runtime : 301.32
% process. runtime: 299.53
% specific non-discr-tree subsumption statistics:
% tried: 30532536
% length fails: 3107602
% strength fails: 7715076
% predlist fails: 1105697
% aux str. fails: 5621850
% by-lit fails: 6974507
% full subs tried: 1204968
% full subs fail: 1125118
%
% ; 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/GRP328-1+eq_r.in")
%
%------------------------------------------------------------------------------