TSTP Solution File: GRP281-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP281-1 : 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 : art05.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 297.7s
% Output : Assurance 297.7s
% 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/GRP281-1+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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% was split for some strategies as:
% -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c6).
% -equal(multiply(sk_c7,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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522)
%
%
% START OF PROOF
% 301999 [] equal(multiply(identity,X),X).
% 302000 [] equal(multiply(inverse(X),X),identity).
% 302001 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302002 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 302003 [?] ?
% 302004 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 302008 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 302009 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 302013 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 302014 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 302018 [?] ?
% 302019 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 302023 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 302024 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c5),sk_c7).
% 302028 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 302029 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c5),sk_c7).
% 302035 [hyper:302002,302004,binarycut:302003] equal(inverse(sk_c2),sk_c8).
% 302036 [para:302035.1.1,302000.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 302043 [hyper:302002,302019,binarycut:302018] equal(inverse(sk_c1),sk_c8).
% 302047 [hyper:302002,302009,302008] equal(multiply(sk_c2,sk_c8),sk_c3).
% 302057 [hyper:302002,302013,302014] equal(multiply(sk_c8,sk_c3),sk_c7).
% 302065 [hyper:302002,302023,302024] equal(multiply(sk_c1,sk_c8),sk_c7).
% 302068 [hyper:302002,302028,302029] equal(multiply(sk_c8,sk_c7),sk_c6).
% 302069 [para:302000.1.1,302001.1.1.1,demod:301999] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 302070 [para:302036.1.1,302001.1.1.1,demod:301999] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 302076 [para:302047.1.1,302070.1.2.2,demod:302057] equal(sk_c8,sk_c7).
% 302089 [para:302065.1.1,302069.1.2.2,demod:302068,302043] equal(sk_c8,sk_c6).
% 302098 [para:302089.1.1,302065.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c7).
% 302142 [hyper:302002,302098,demod:302043,cut:302076] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,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 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(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522,302141,50,29523,302141,30,29523,302141,40,29523,302176,0,29523,302325,50,29524,302360,0,29529)
%
%
% START OF PROOF
% 302327 [] equal(multiply(identity,X),X).
% 302328 [] equal(multiply(inverse(X),X),identity).
% 302329 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302330 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 302333 [?] ?
% 302334 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 302338 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 302339 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 302343 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 302344 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 302348 [?] ?
% 302349 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 302353 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 302354 [] equal(multiply(sk_c1,sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 302358 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 302359 [] equal(multiply(sk_c8,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c8).
% 302366 [hyper:302330,302334,binarycut:302333] equal(inverse(sk_c2),sk_c8).
% 302369 [para:302366.1.1,302328.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 302378 [hyper:302330,302349,binarycut:302348] equal(inverse(sk_c1),sk_c8).
% 302381 [para:302378.1.1,302328.1.1.1] equal(multiply(sk_c8,sk_c1),identity).
% 302389 [hyper:302330,302339,302338] equal(multiply(sk_c2,sk_c8),sk_c3).
% 302405 [hyper:302330,302343,302344] equal(multiply(sk_c8,sk_c3),sk_c7).
% 302409 [hyper:302330,302353,302354] equal(multiply(sk_c1,sk_c8),sk_c7).
% 302413 [hyper:302330,302358,302359] equal(multiply(sk_c8,sk_c7),sk_c6).
% 302414 [para:302328.1.1,302329.1.1.1,demod:302327] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 302415 [para:302369.1.1,302329.1.1.1,demod:302327] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 302421 [para:302389.1.1,302415.1.2.2,demod:302405] equal(sk_c8,sk_c7).
% 302425 [para:302421.1.1,302405.1.1.1] equal(multiply(sk_c7,sk_c3),sk_c7).
% 302432 [para:302369.1.1,302414.1.2.2] equal(sk_c2,multiply(inverse(sk_c8),identity)).
% 302433 [para:302381.1.1,302414.1.2.2,demod:302432] equal(sk_c1,sk_c2).
% 302434 [para:302405.1.1,302414.1.2.2] equal(sk_c3,multiply(inverse(sk_c8),sk_c7)).
% 302435 [para:302409.1.1,302414.1.2.2,demod:302413,302378] equal(sk_c8,sk_c6).
% 302436 [para:302329.1.1,302414.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 302441 [para:302433.1.2,302389.1.1.1,demod:302409] equal(sk_c7,sk_c3).
% 302442 [para:302435.1.1,302369.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 302444 [para:302435.1.1,302389.1.1.2] equal(multiply(sk_c2,sk_c6),sk_c3).
% 302447 [para:302435.1.1,302413.1.1.1] equal(multiply(sk_c6,sk_c7),sk_c6).
% 302449 [para:302435.1.1,302421.1.1] equal(sk_c6,sk_c7).
% 302454 [para:302449.1.2,302441.1.1] equal(sk_c6,sk_c3).
% 302461 [para:302425.1.1,302414.1.2.2,demod:302328] equal(sk_c3,identity).
% 302464 [para:302461.1.1,302405.1.1.2] equal(multiply(sk_c8,identity),sk_c7).
% 302465 [para:302461.1.1,302454.1.2] equal(sk_c6,identity).
% 302480 [para:302465.1.1,302442.1.1.1,demod:302327] equal(sk_c2,identity).
% 302482 [para:302480.1.1,302369.1.1.2,demod:302464] equal(sk_c7,identity).
% 302498 [para:302482.1.1,302434.1.2.2,demod:302432] equal(sk_c3,sk_c2).
% 302500 [para:302498.1.2,302433.1.2] equal(sk_c1,sk_c3).
% 302502 [para:302500.1.2,302454.1.2] equal(sk_c6,sk_c1).
% 302506 [para:302389.1.1,302436.1.2.2.2] equal(sk_c8,multiply(inverse(multiply(X,sk_c2)),multiply(X,sk_c3))).
% 302519 [para:302444.1.1,302436.1.2.2.2,demod:302506] equal(sk_c6,sk_c8).
% 302522 [para:302502.1.2,302378.1.1.1] equal(inverse(sk_c6),sk_c8).
% 302530 [hyper:302330,302522,demod:302447,cut:302519] 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(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% 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(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522,302141,50,29523,302141,30,29523,302141,40,29523,302176,0,29523,302325,50,29524,302360,0,29529,302529,50,29530,302529,30,29530,302529,40,29530,302564,0,29530)
%
%
% START OF PROOF
% 302530 [] equal(X,X).
% 302531 [] equal(multiply(identity,X),X).
% 302532 [] equal(multiply(inverse(X),X),identity).
% 302533 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302534 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 302535 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c8).
% 302536 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 302537 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c8).
% 302538 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 302539 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 302540 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c6),sk_c7).
% 302541 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c7).
% 302542 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 302543 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 302544 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c7,sk_c8),sk_c6).
% 302545 [?] ?
% 302546 [?] ?
% 302547 [?] ?
% 302548 [?] ?
% 302549 [?] ?
% 302613 [hyper:302534,302540,302535,binarycut:302545] equal(multiply(sk_c5,sk_c6),sk_c7).
% 302616 [hyper:302534,302541,binarycut:302546,binarycut:302536] equal(inverse(sk_c5),sk_c7).
% 302617 [para:302616.1.1,302532.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 302620 [hyper:302534,302543,binarycut:302548,binarycut:302538] equal(inverse(sk_c4),sk_c8).
% 302628 [hyper:302534,302542,302537,binarycut:302547] equal(multiply(sk_c4,sk_c7),sk_c8).
% 302631 [para:302620.1.1,302532.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 302644 [hyper:302534,302544,302539,binarycut:302549] equal(multiply(sk_c7,sk_c8),sk_c6).
% 302647 [para:302532.1.1,302533.1.1.1,demod:302531] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 302648 [para:302613.1.1,302533.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c5,multiply(sk_c6,X))).
% 302649 [para:302617.1.1,302533.1.1.1,demod:302531] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 302650 [para:302628.1.1,302533.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c4,multiply(sk_c7,X))).
% 302651 [para:302631.1.1,302533.1.1.1,demod:302531] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 302657 [para:302613.1.1,302649.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 302661 [para:302628.1.1,302651.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 302666 [para:302617.1.1,302647.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 302668 [para:302644.1.1,302647.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 302669 [para:302649.1.2,302647.1.2.2] equal(multiply(sk_c5,X),multiply(inverse(sk_c7),X)).
% 302670 [para:302657.1.2,302647.1.2.2,demod:302668] equal(sk_c7,sk_c8).
% 302672 [para:302670.1.2,302631.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 302674 [para:302670.1.2,302661.1.2.1,demod:302644] equal(sk_c7,sk_c6).
% 302677 [para:302674.1.1,302628.1.1.2] equal(multiply(sk_c4,sk_c6),sk_c8).
% 302682 [para:302672.1.1,302647.1.2.2,demod:302666] equal(sk_c4,sk_c5).
% 302687 [para:302682.1.2,302648.1.2.1] equal(multiply(sk_c7,X),multiply(sk_c4,multiply(sk_c6,X))).
% 302692 [para:302677.1.1,302533.1.1.1,demod:302687] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 302697 [para:302649.1.2,302650.1.2.2,demod:302649,302692] equal(X,multiply(sk_c4,X)).
% 302700 [para:302697.1.2,302651.1.2.2,demod:302692] equal(X,multiply(sk_c7,X)).
% 302707 [para:302700.1.2,302649.1.2] equal(X,multiply(sk_c5,X)).
% 302733 [hyper:302534,302669,demod:302616,302661,302707,302669,cut:302530,cut:302670] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522,302141,50,29523,302141,30,29523,302141,40,29523,302176,0,29523,302325,50,29524,302360,0,29529,302529,50,29530,302529,30,29530,302529,40,29530,302564,0,29530,302732,50,29530,302732,30,29530,302732,40,29530,302767,0,29530)
%
%
% START OF PROOF
% 302734 [] equal(multiply(identity,X),X).
% 302735 [] equal(multiply(inverse(X),X),identity).
% 302736 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 302737 [] -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8).
% 302753 [] equal(multiply(sk_c5,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c8).
% 302754 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c5),sk_c7).
% 302755 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c8).
% 302756 [] equal(inverse(sk_c1),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 302757 [] equal(multiply(sk_c7,sk_c8),sk_c6) | equal(inverse(sk_c1),sk_c8).
% 302758 [?] ?
% 302759 [?] ?
% 302760 [?] ?
% 302761 [?] ?
% 302762 [?] ?
% 302776 [hyper:302737,302754,binarycut:302759] equal(inverse(sk_c5),sk_c7).
% 302777 [para:302776.1.1,302735.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 302780 [hyper:302737,302756,binarycut:302761] equal(inverse(sk_c4),sk_c8).
% 302784 [para:302780.1.1,302735.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 302797 [hyper:302737,302753,binarycut:302758] equal(multiply(sk_c5,sk_c6),sk_c7).
% 302800 [hyper:302737,302755,binarycut:302760] equal(multiply(sk_c4,sk_c7),sk_c8).
% 302804 [hyper:302737,302757,binarycut:302762] equal(multiply(sk_c7,sk_c8),sk_c6).
% 302805 [para:302735.1.1,302736.1.1.1,demod:302734] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 302806 [para:302777.1.1,302736.1.1.1,demod:302734] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 302807 [para:302784.1.1,302736.1.1.1,demod:302734] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 302811 [para:302797.1.1,302806.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 302813 [para:302800.1.1,302807.1.2.2] equal(sk_c7,multiply(sk_c8,sk_c8)).
% 302816 [para:302777.1.1,302805.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),identity)).
% 302818 [para:302804.1.1,302805.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 302820 [para:302811.1.2,302805.1.2.2,demod:302818] equal(sk_c7,sk_c8).
% 302822 [para:302820.1.2,302784.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 302824 [para:302820.1.2,302813.1.2.1,demod:302804] equal(sk_c7,sk_c6).
% 302828 [para:302824.1.1,302804.1.1.1] equal(multiply(sk_c6,sk_c8),sk_c6).
% 302832 [para:302822.1.1,302805.1.2.2,demod:302816] equal(sk_c4,sk_c5).
% 302834 [para:302832.1.2,302776.1.1.1,demod:302780] equal(sk_c8,sk_c7).
% 302845 [para:302828.1.1,302805.1.2.2,demod:302735] equal(sk_c8,identity).
% 302848 [para:302845.1.1,302784.1.1.1,demod:302734] equal(sk_c4,identity).
% 302853 [para:302848.1.1,302780.1.1.1] equal(inverse(identity),sk_c8).
% 302861 [hyper:302737,302853,demod:302734,cut:302834] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% Split part used next: -equal(multiply(sk_c8,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(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522,302141,50,29523,302141,30,29523,302141,40,29523,302176,0,29523,302325,50,29524,302360,0,29529,302529,50,29530,302529,30,29530,302529,40,29530,302564,0,29530,302732,50,29530,302732,30,29530,302732,40,29530,302767,0,29530,302860,50,29530,302860,30,29530,302860,40,29530,302895,0,29535,302998,50,29536,303033,0,29536,303179,50,29538,303214,0,29543,303368,50,29547,303403,0,29547,303565,50,29552,303600,0,29552,303768,50,29561,303803,0,29565,303979,50,29580,304014,0,29580,304198,50,29609,304233,0,29613,304427,50,29671,304462,0,29671,304666,50,29787,304666,40,29787,304701,0,29787)
%
%
% START OF PROOF
% 304667 [] equal(X,X).
% 304668 [] equal(multiply(identity,X),X).
% 304669 [] equal(multiply(inverse(X),X),identity).
% 304670 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 304671 [] -equal(multiply(sk_c8,sk_c7),sk_c6).
% 304697 [?] ?
% 304698 [?] ?
% 304701 [?] ?
% 304740 [input:304698,cut:304671] equal(inverse(sk_c5),sk_c7).
% 304741 [para:304740.1.1,304669.1.1.1] equal(multiply(sk_c7,sk_c5),identity).
% 304755 [input:304697,cut:304671] equal(multiply(sk_c5,sk_c6),sk_c7).
% 304757 [input:304701,cut:304671] equal(multiply(sk_c7,sk_c8),sk_c6).
% 304761 [para:304669.1.1,304670.1.1.1,demod:304668] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 304780 [para:304741.1.1,304670.1.1.1,demod:304668] equal(X,multiply(sk_c7,multiply(sk_c5,X))).
% 304809 [para:304755.1.1,304780.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 304861 [para:304757.1.1,304761.1.2.2] equal(sk_c8,multiply(inverse(sk_c7),sk_c6)).
% 304867 [para:304809.1.2,304761.1.2.2,demod:304861] equal(sk_c7,sk_c8).
% 304871 [para:304867.1.2,304671.1.1.1,demod:304809,cut:304667] 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_c8,sk_c7),sk_c6) | -equal(multiply(X,sk_c8),sk_c7) | -equal(inverse(X),sk_c8) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(multiply(sk_c7,sk_c8),sk_c6) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(inverse(V),sk_c7) | -equal(multiply(V,sk_c6),sk_c7).
% 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(35,40,1,75,0,1,747,50,7,787,0,7,1662,50,18,1702,0,18,2678,50,33,2718,0,33,3748,50,45,3788,0,46,4873,50,62,4913,0,62,6078,50,86,6118,0,86,7364,50,127,7404,0,127,8756,50,201,8796,0,201,10254,50,344,10294,0,345,11884,50,573,11924,0,573,13646,50,1000,13646,40,1000,13686,0,1000,24039,3,1301,24790,4,1451,25504,5,1601,25505,1,1601,25505,50,1601,25505,40,1601,25545,0,1603,25857,3,1904,25868,4,2065,25882,5,2204,25882,1,2204,25882,50,2204,25882,40,2204,25922,0,2204,50521,3,3705,51375,4,4455,52175,1,5205,52175,50,5206,52175,40,5206,52215,0,5206,70970,3,5957,71583,4,6332,72275,1,6707,72275,50,6707,72275,40,6707,72315,0,6708,82617,3,7461,84022,4,7834,85490,5,8209,85491,1,8209,85491,50,8209,85491,40,8209,85531,0,8209,142516,3,12116,143869,4,14060,144753,1,16010,144753,50,16012,144753,40,16012,144793,0,16012,196604,3,18563,197566,4,19838,198193,5,21113,198194,1,21113,198194,50,21115,198194,40,21115,198234,0,21115,239080,3,22617,239848,4,23366,240681,5,24116,240682,1,24116,240682,50,24118,240682,40,24118,240722,0,24118,249892,3,24870,250820,4,25247,251202,5,25619,251202,1,25619,251202,50,25619,251202,40,25619,251242,0,25619,278140,3,26820,278910,4,27420,279537,1,28020,279537,50,28021,279537,40,28021,279577,0,28021,300774,3,28772,301510,4,29147,301996,5,29522,301997,1,29522,301997,50,29522,301997,40,29522,301997,40,29522,302032,0,29522,302141,50,29523,302141,30,29523,302141,40,29523,302176,0,29523,302325,50,29524,302360,0,29529,302529,50,29530,302529,30,29530,302529,40,29530,302564,0,29530,302732,50,29530,302732,30,29530,302732,40,29530,302767,0,29530,302860,50,29530,302860,30,29530,302860,40,29530,302895,0,29535,302998,50,29536,303033,0,29536,303179,50,29538,303214,0,29543,303368,50,29547,303403,0,29547,303565,50,29552,303600,0,29552,303768,50,29561,303803,0,29565,303979,50,29580,304014,0,29580,304198,50,29609,304233,0,29613,304427,50,29671,304462,0,29671,304666,50,29787,304666,40,29787,304701,0,29787,304870,50,29787,304870,30,29787,304870,40,29787,304905,0,29787,305039,50,29788,305074,0,29792,305256,50,29795,305291,0,29795,305481,50,29799,305516,0,29799,305714,50,29806,305749,0,29810,305953,50,29821,305988,0,29821,306200,50,29840,306235,0,29845,306455,50,29878,306490,0,29878,306720,50,29947,306755,0,29947,306995,50,30073,306995,40,30073,307030,0,30073)
%
%
% START OF PROOF
% 306815 [?] ?
% 306997 [] equal(multiply(identity,X),X).
% 306998 [] equal(multiply(inverse(X),X),identity).
% 306999 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 307000 [] -equal(multiply(sk_c7,sk_c8),sk_c6).
% 307005 [?] ?
% 307010 [?] ?
% 307015 [?] ?
% 307047 [input:307005,cut:307000] equal(inverse(sk_c2),sk_c8).
% 307048 [para:307047.1.1,306998.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 307067 [input:307010,cut:307000] equal(multiply(sk_c2,sk_c8),sk_c3).
% 307080 [input:307015,cut:307000] equal(multiply(sk_c8,sk_c3),sk_c7).
% 307093 [para:307048.1.1,306999.1.1.1,demod:306997] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 307132 [para:307067.1.1,307093.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c3)).
% 307137 [para:307132.1.2,307080.1.1] equal(sk_c8,sk_c7).
% 307139 [para:307137.1.1,307000.1.1.2,cut:306815] 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: 34459
% derived clauses: 6055276
% kept clauses: 257869
% kept size sum: 307321
% kept mid-nuclei: 10425
% kept new demods: 4372
% forw unit-subs: 2408010
% forw double-subs: 3124420
% forw overdouble-subs: 216008
% backward subs: 9839
% fast unit cutoff: 18645
% full unit cutoff: 0
% dbl unit cutoff: 6022
% real runtime : 303.40
% process. runtime: 300.73
% specific non-discr-tree subsumption statistics:
% tried: 42525446
% length fails: 5423134
% strength fails: 14180495
% predlist fails: 2758028
% aux str. fails: 6367938
% by-lit fails: 7208931
% full subs tried: 1597454
% full subs fail: 1501079
%
% ; 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/GRP281-1+eq_r.in")
%
%------------------------------------------------------------------------------