TSTP Solution File: GRP294-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP294-1 : 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 : art06.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 298.7s
% Output : Assurance 298.7s
% 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/GRP294-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -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(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6).
% -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c6),sk_c5).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
% -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(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322)
%
%
% START OF PROOF
% 260533 [] equal(multiply(identity,X),X).
% 260534 [] equal(multiply(inverse(X),X),identity).
% 260535 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 260536 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 260537 [?] ?
% 260538 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 260542 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 260543 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 260547 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 260548 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 260552 [?] ?
% 260553 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 260557 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 260558 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c6).
% 260562 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 260563 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(inverse(sk_c4),sk_c6).
% 260569 [hyper:260536,260538,binarycut:260537] equal(inverse(sk_c2),sk_c7).
% 260570 [para:260569.1.1,260534.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 260577 [hyper:260536,260553,binarycut:260552] equal(inverse(sk_c1),sk_c7).
% 260581 [hyper:260536,260543,260542] equal(multiply(sk_c2,sk_c7),sk_c5).
% 260598 [hyper:260536,260547,260548] equal(multiply(sk_c7,sk_c5),sk_c6).
% 260613 [hyper:260536,260557,260558] equal(multiply(sk_c1,sk_c7),sk_c6).
% 260616 [hyper:260536,260562,260563] equal(multiply(sk_c7,sk_c6),sk_c5).
% 260617 [para:260534.1.1,260535.1.1.1,demod:260533] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 260618 [para:260570.1.1,260535.1.1.1,demod:260533] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 260624 [para:260581.1.1,260618.1.2.2,demod:260598] equal(sk_c7,sk_c6).
% 260637 [para:260613.1.1,260617.1.2.2,demod:260616,260577] equal(sk_c7,sk_c5).
% 260646 [para:260637.1.1,260613.1.1.2] equal(multiply(sk_c1,sk_c5),sk_c6).
% 260679 [hyper:260536,260646,demod:260577,cut:260624] 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_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328)
%
%
% START OF PROOF
% 260835 [] equal(multiply(identity,X),X).
% 260836 [] equal(multiply(inverse(X),X),identity).
% 260837 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 260838 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 260841 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 260842 [?] ?
% 260846 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c6).
% 260847 [] equal(multiply(sk_c2,sk_c7),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 260851 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 260852 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 260856 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 260857 [?] ?
% 260861 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 260862 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 260866 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c6).
% 260867 [] equal(multiply(sk_c7,sk_c6),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 260873 [hyper:260838,260841,binarycut:260842] equal(inverse(sk_c2),sk_c7).
% 260875 [para:260873.1.1,260836.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 260882 [hyper:260838,260856,binarycut:260857] equal(inverse(sk_c1),sk_c7).
% 260883 [para:260882.1.1,260836.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 260907 [hyper:260838,260847,260846] equal(multiply(sk_c2,sk_c7),sk_c5).
% 260914 [hyper:260838,260852,260851] equal(multiply(sk_c7,sk_c5),sk_c6).
% 260918 [hyper:260838,260862,260861] equal(multiply(sk_c1,sk_c7),sk_c6).
% 260922 [hyper:260838,260867,260866] equal(multiply(sk_c7,sk_c6),sk_c5).
% 260923 [para:260836.1.1,260837.1.1.1,demod:260835] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 260924 [para:260875.1.1,260837.1.1.1,demod:260835] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 260925 [para:260883.1.1,260837.1.1.1,demod:260835] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 260926 [para:260907.1.1,260837.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c2,multiply(sk_c7,X))).
% 260930 [para:260907.1.1,260924.1.2.2,demod:260914] equal(sk_c7,sk_c6).
% 260934 [para:260930.1.1,260914.1.1.1] equal(multiply(sk_c6,sk_c5),sk_c6).
% 260935 [para:260930.1.1,260918.1.1.2] equal(multiply(sk_c1,sk_c6),sk_c6).
% 260940 [para:260836.1.1,260923.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 260941 [para:260875.1.1,260923.1.2.2] equal(sk_c2,multiply(inverse(sk_c7),identity)).
% 260944 [para:260918.1.1,260923.1.2.2,demod:260922,260882] equal(sk_c7,sk_c5).
% 260945 [para:260837.1.1,260923.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 260946 [para:260922.1.1,260923.1.2.2] equal(sk_c6,multiply(inverse(sk_c7),sk_c5)).
% 260947 [para:260924.1.2,260923.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c7),X)).
% 260949 [para:260923.1.2,260923.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 260960 [para:260925.1.2,260923.1.2.2,demod:260947] equal(multiply(sk_c1,X),multiply(sk_c2,X)).
% 260961 [para:260944.1.1,260925.1.2.1] equal(X,multiply(sk_c5,multiply(sk_c1,X))).
% 260963 [para:260934.1.1,260923.1.2.2,demod:260836] equal(sk_c5,identity).
% 260973 [para:260924.1.2,260926.1.2.2,demod:260961,260960] equal(X,multiply(sk_c1,X)).
% 260989 [para:260963.1.1,260946.1.2.2,demod:260941] equal(sk_c6,sk_c2).
% 260991 [para:260989.1.1,260935.1.1.2,demod:260973] equal(sk_c2,sk_c6).
% 261008 [para:260949.1.2,260836.1.1] equal(multiply(X,inverse(X)),identity).
% 261010 [para:260949.1.2,260940.1.2] equal(X,multiply(X,identity)).
% 261014 [para:261010.1.2,260941.1.2] equal(sk_c2,inverse(sk_c7)).
% 261015 [para:261010.1.2,260940.1.2] equal(X,inverse(inverse(X))).
% 261018 [para:261008.1.1,260945.1.2.2.2,demod:261010] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 261021 [para:260924.1.2,261018.1.2.1.1,demod:260973,260960] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 261032 [para:261021.1.2,260949.1.2,demod:261015] equal(multiply(X,sk_c7),X).
% 261033 [para:260930.1.1,261032.1.1.2] equal(multiply(X,sk_c6),X).
% 261037 [hyper:260838,261033,demod:261014,cut:260991] 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_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328,261036,50,29329,261036,30,29329,261036,40,29329,261071,0,29329,261155,50,29329,261190,0,29330)
%
%
% START OF PROOF
% 261157 [] equal(multiply(identity,X),X).
% 261158 [] equal(multiply(inverse(X),X),identity).
% 261159 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 261160 [] -equal(multiply(X,sk_c7),sk_c5) | -equal(inverse(X),sk_c7).
% 261161 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c2),sk_c7).
% 261162 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 261163 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 261164 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 261165 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c7).
% 261166 [?] ?
% 261167 [?] ?
% 261168 [?] ?
% 261169 [?] ?
% 261170 [?] ?
% 261193 [hyper:261160,261162,binarycut:261167] equal(inverse(sk_c4),sk_c6).
% 261194 [para:261193.1.1,261158.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 261198 [hyper:261160,261163,binarycut:261168] equal(inverse(sk_c3),sk_c6).
% 261199 [para:261198.1.1,261158.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 261202 [hyper:261160,261161,binarycut:261166] equal(multiply(sk_c4,sk_c5),sk_c6).
% 261205 [hyper:261160,261164,binarycut:261169] equal(multiply(sk_c3,sk_c6),sk_c7).
% 261209 [hyper:261160,261165,binarycut:261170] equal(multiply(sk_c6,sk_c7),sk_c5).
% 261213 [para:261158.1.1,261159.1.1.1,demod:261157] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 261214 [para:261194.1.1,261159.1.1.1,demod:261157] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 261215 [para:261199.1.1,261159.1.1.1,demod:261157] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 261216 [para:261202.1.1,261159.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 261217 [para:261205.1.1,261159.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 261219 [para:261202.1.1,261214.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 261221 [para:261205.1.1,261215.1.2.2,demod:261209] equal(sk_c6,sk_c5).
% 261224 [para:261221.1.1,261205.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 261225 [para:261221.1.1,261209.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 261231 [para:261158.1.1,261213.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 261232 [para:261194.1.1,261213.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 261233 [para:261199.1.1,261213.1.2.2,demod:261232] equal(sk_c3,sk_c4).
% 261234 [para:261209.1.1,261213.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 261235 [para:261159.1.1,261213.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 261236 [para:261214.1.2,261213.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c6),X)).
% 261237 [para:261219.1.2,261213.1.2.2,demod:261234] equal(sk_c6,sk_c7).
% 261238 [para:261215.1.2,261213.1.2.2,demod:261236] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 261240 [para:261213.1.2,261213.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 261242 [para:261224.1.1,261159.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c5,X))).
% 261244 [para:261233.1.2,261216.1.2.1,demod:261242] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 261248 [para:261225.1.1,261213.1.2.2,demod:261158] equal(sk_c7,identity).
% 261250 [para:261248.1.1,261209.1.1.2] equal(multiply(sk_c6,identity),sk_c5).
% 261251 [para:261248.1.1,261237.1.2] equal(sk_c6,identity).
% 261254 [para:261251.1.1,261194.1.1.1,demod:261157] equal(sk_c4,identity).
% 261258 [para:261251.1.1,261214.1.2.1,demod:261157,261238] equal(X,multiply(sk_c3,X)).
% 261262 [para:261214.1.2,261217.1.2.2,demod:261244,261258,261238] equal(multiply(sk_c6,X),X).
% 261263 [para:261254.1.1,261193.1.1.1] equal(inverse(identity),sk_c6).
% 261268 [para:261251.1.1,261232.1.2.1.1,demod:261250,261263] equal(sk_c4,sk_c5).
% 261269 [para:261268.1.1,261193.1.1.1] equal(inverse(sk_c5),sk_c6).
% 261289 [para:261240.1.2,261158.1.1] equal(multiply(X,inverse(X)),identity).
% 261291 [para:261240.1.2,261231.1.2] equal(X,multiply(X,identity)).
% 261292 [para:261291.1.2,261231.1.2] equal(X,inverse(inverse(X))).
% 261295 [para:261289.1.1,261235.1.2.2.2,demod:261291] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 261304 [para:261244.1.2,261295.1.2.1.1,demod:261262] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 261314 [para:261304.1.2,261240.1.2,demod:261292] equal(multiply(X,sk_c7),X).
% 261315 [hyper:261160,261314,demod:261269,cut:261237] 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_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -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
%
%
% 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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328,261036,50,29329,261036,30,29329,261036,40,29329,261071,0,29329,261155,50,29329,261190,0,29330,261314,50,29331,261314,30,29331,261314,40,29331,261349,0,29336,261441,50,29336,261476,0,29336)
%
%
% START OF PROOF
% 261443 [] equal(multiply(identity,X),X).
% 261444 [] equal(multiply(inverse(X),X),identity).
% 261445 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 261446 [] -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 261462 [] equal(multiply(sk_c4,sk_c5),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 261463 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c6).
% 261464 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 261465 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 261466 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 261467 [?] ?
% 261468 [?] ?
% 261469 [?] ?
% 261470 [?] ?
% 261471 [?] ?
% 261484 [hyper:261446,261463,binarycut:261468] equal(inverse(sk_c4),sk_c6).
% 261485 [para:261484.1.1,261444.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 261488 [hyper:261446,261464,binarycut:261469] equal(inverse(sk_c3),sk_c6).
% 261489 [para:261488.1.1,261444.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 261501 [hyper:261446,261462,binarycut:261467] equal(multiply(sk_c4,sk_c5),sk_c6).
% 261504 [hyper:261446,261465,binarycut:261470] equal(multiply(sk_c3,sk_c6),sk_c7).
% 261508 [hyper:261446,261466,binarycut:261471] equal(multiply(sk_c6,sk_c7),sk_c5).
% 261509 [para:261444.1.1,261445.1.1.1,demod:261443] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 261510 [para:261485.1.1,261445.1.1.1,demod:261443] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 261511 [para:261489.1.1,261445.1.1.1,demod:261443] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 261512 [para:261501.1.1,261445.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 261513 [para:261504.1.1,261445.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c6,X))).
% 261515 [para:261501.1.1,261510.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 261517 [para:261504.1.1,261511.1.2.2,demod:261508] equal(sk_c6,sk_c5).
% 261520 [para:261517.1.1,261504.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 261521 [para:261517.1.1,261508.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 261527 [para:261444.1.1,261509.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 261528 [para:261485.1.1,261509.1.2.2] equal(sk_c4,multiply(inverse(sk_c6),identity)).
% 261529 [para:261489.1.1,261509.1.2.2,demod:261528] equal(sk_c3,sk_c4).
% 261530 [para:261508.1.1,261509.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 261531 [para:261445.1.1,261509.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 261532 [para:261510.1.2,261509.1.2.2] equal(multiply(sk_c4,X),multiply(inverse(sk_c6),X)).
% 261533 [para:261515.1.2,261509.1.2.2,demod:261530] equal(sk_c6,sk_c7).
% 261534 [para:261511.1.2,261509.1.2.2,demod:261532] equal(multiply(sk_c3,X),multiply(sk_c4,X)).
% 261536 [para:261509.1.2,261509.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 261538 [para:261520.1.1,261445.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c3,multiply(sk_c5,X))).
% 261540 [para:261529.1.2,261512.1.2.1,demod:261538] equal(multiply(sk_c6,X),multiply(sk_c7,X)).
% 261542 [para:261521.1.1,261509.1.2.2,demod:261444] equal(sk_c7,identity).
% 261545 [para:261542.1.1,261533.1.2] equal(sk_c6,identity).
% 261552 [para:261545.1.1,261510.1.2.1,demod:261443,261534] equal(X,multiply(sk_c3,X)).
% 261553 [para:261545.1.1,261517.1.1] equal(identity,sk_c5).
% 261556 [para:261510.1.2,261513.1.2.2,demod:261540,261552,261534] equal(multiply(sk_c6,X),X).
% 261566 [para:261553.1.2,261530.1.2.2,demod:261528] equal(sk_c7,sk_c4).
% 261568 [para:261566.1.1,261533.1.2] equal(sk_c6,sk_c4).
% 261570 [para:261568.1.1,261504.1.1.2,demod:261552] equal(sk_c4,sk_c7).
% 261583 [para:261536.1.2,261444.1.1] equal(multiply(X,inverse(X)),identity).
% 261585 [para:261536.1.2,261527.1.2] equal(X,multiply(X,identity)).
% 261586 [para:261585.1.2,261527.1.2] equal(X,inverse(inverse(X))).
% 261587 [para:261585.1.2,261528.1.2] equal(sk_c4,inverse(sk_c6)).
% 261589 [para:261583.1.1,261531.1.2.2.2,demod:261585] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 261598 [para:261540.1.2,261589.1.2.1.1,demod:261556] equal(inverse(X),multiply(inverse(X),sk_c7)).
% 261608 [para:261598.1.2,261536.1.2,demod:261586] equal(multiply(X,sk_c7),X).
% 261609 [hyper:261446,261608,demod:261587,cut:261570] 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 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c6),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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328,261036,50,29329,261036,30,29329,261036,40,29329,261071,0,29329,261155,50,29329,261190,0,29330,261314,50,29331,261314,30,29331,261314,40,29331,261349,0,29336,261441,50,29336,261476,0,29336,261608,50,29337,261608,30,29337,261608,40,29337,261643,0,29342,261739,50,29343,261774,0,29343,261914,50,29345,261949,0,29345,262097,50,29348,262132,0,29352,262288,50,29358,262323,0,29358,262485,50,29366,262520,0,29370,262690,50,29386,262725,0,29386,262903,50,29414,262938,0,29414,263126,50,29474,263161,0,29474,263359,50,29588,263359,40,29588,263394,0,29588)
%
%
% START OF PROOF
% 263360 [] equal(X,X).
% 263361 [] equal(multiply(identity,X),X).
% 263362 [] equal(multiply(inverse(X),X),identity).
% 263363 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 263364 [] -equal(multiply(sk_c7,sk_c6),sk_c5).
% 263390 [?] ?
% 263391 [?] ?
% 263394 [?] ?
% 263433 [input:263391,cut:263364] equal(inverse(sk_c4),sk_c6).
% 263434 [para:263433.1.1,263362.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 263448 [input:263390,cut:263364] equal(multiply(sk_c4,sk_c5),sk_c6).
% 263450 [input:263394,cut:263364] equal(multiply(sk_c6,sk_c7),sk_c5).
% 263454 [para:263362.1.1,263363.1.1.1,demod:263361] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 263473 [para:263434.1.1,263363.1.1.1,demod:263361] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 263502 [para:263448.1.1,263473.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 263553 [para:263450.1.1,263454.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 263556 [para:263502.1.2,263454.1.2.2,demod:263553] equal(sk_c6,sk_c7).
% 263566 [para:263556.1.2,263364.1.1.1,demod:263502,cut:263360] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(inverse(U),sk_c6) | -equal(multiply(U,sk_c5),sk_c6).
% Split part used next: -equal(multiply(sk_c7,sk_c5),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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328,261036,50,29329,261036,30,29329,261036,40,29329,261071,0,29329,261155,50,29329,261190,0,29330,261314,50,29331,261314,30,29331,261314,40,29331,261349,0,29336,261441,50,29336,261476,0,29336,261608,50,29337,261608,30,29337,261608,40,29337,261643,0,29342,261739,50,29343,261774,0,29343,261914,50,29345,261949,0,29345,262097,50,29348,262132,0,29352,262288,50,29358,262323,0,29358,262485,50,29366,262520,0,29370,262690,50,29386,262725,0,29386,262903,50,29414,262938,0,29414,263126,50,29474,263161,0,29474,263359,50,29588,263359,40,29588,263394,0,29588,263565,50,29589,263565,30,29589,263565,40,29589,263600,0,29589,263696,50,29590,263731,0,29594,263871,50,29596,263906,0,29596,264054,50,29600,264089,0,29600,264245,50,29605,264280,0,29610,264442,50,29618,264477,0,29618,264647,50,29633,264682,0,29638,264860,50,29666,264895,0,29666,265083,50,29727,265118,0,29727,265316,50,29841,265316,40,29841,265351,0,29841)
%
%
% START OF PROOF
% 265318 [] equal(multiply(identity,X),X).
% 265319 [] equal(multiply(inverse(X),X),identity).
% 265320 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 265321 [] -equal(multiply(sk_c7,sk_c5),sk_c6).
% 265332 [?] ?
% 265333 [?] ?
% 265334 [?] ?
% 265335 [?] ?
% 265336 [?] ?
% 265375 [input:265333,cut:265321] equal(inverse(sk_c4),sk_c6).
% 265376 [para:265375.1.1,265319.1.1.1] equal(multiply(sk_c6,sk_c4),identity).
% 265377 [input:265334,cut:265321] equal(inverse(sk_c3),sk_c6).
% 265378 [para:265377.1.1,265319.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 265392 [input:265332,cut:265321] equal(multiply(sk_c4,sk_c5),sk_c6).
% 265396 [input:265335,cut:265321] equal(multiply(sk_c3,sk_c6),sk_c7).
% 265397 [input:265336,cut:265321] equal(multiply(sk_c6,sk_c7),sk_c5).
% 265407 [para:265319.1.1,265320.1.1.1,demod:265318] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 265415 [para:265376.1.1,265320.1.1.1,demod:265318] equal(X,multiply(sk_c6,multiply(sk_c4,X))).
% 265418 [para:265378.1.1,265320.1.1.1,demod:265318] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 265434 [para:265397.1.1,265320.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c6,multiply(sk_c7,X))).
% 265447 [para:265392.1.1,265415.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 265452 [para:265396.1.1,265418.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 265456 [para:265452.1.2,265397.1.1] equal(sk_c6,sk_c5).
% 265457 [para:265452.1.2,265320.1.1.1,demod:265434] equal(multiply(sk_c6,X),multiply(sk_c5,X)).
% 265469 [para:265456.1.1,265396.1.1.2] equal(multiply(sk_c3,sk_c5),sk_c7).
% 265475 [para:265456.1.1,265447.1.2.2,demod:265457] equal(sk_c5,multiply(sk_c5,sk_c5)).
% 265478 [para:265469.1.1,265418.1.2.2,demod:265452] equal(sk_c5,sk_c6).
% 265488 [para:265397.1.1,265407.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 265491 [para:265447.1.2,265407.1.2.2,demod:265488] equal(sk_c6,sk_c7).
% 265501 [para:265491.1.2,265321.1.1.1,demod:265475,265457,cut:265478] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c7,sk_c6),sk_c5) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(multiply(Y,sk_c7),sk_c5) | -equal(inverse(Y),sk_c7) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -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(35,40,0,75,0,0,645,50,4,685,0,4,1270,50,9,1310,0,9,1900,50,14,1940,0,15,2536,50,22,2576,0,22,3179,50,28,3219,0,28,3830,50,41,3870,0,41,4489,50,64,4529,0,64,5158,50,116,5198,0,116,5837,50,227,5877,0,227,6528,50,423,6568,0,423,7231,50,805,7231,40,805,7271,0,805,17592,3,1106,18325,4,1256,19029,1,1406,19029,50,1406,19029,40,1406,19069,0,1406,19275,3,1709,19285,4,1871,19292,5,2007,19292,1,2007,19292,50,2007,19292,40,2007,19332,0,2007,41537,3,3508,42540,4,4258,43211,1,5008,43211,50,5008,43211,40,5008,43251,0,5008,60433,3,5760,61046,4,6134,61504,5,6509,61505,1,6509,61505,50,6509,61505,40,6509,61545,0,6509,70750,3,7263,71732,4,7635,72995,5,8010,72996,1,8010,72996,50,8010,72996,40,8010,73036,0,8010,123877,3,11913,125119,4,13862,125891,1,15811,125891,50,15813,125891,40,15813,125931,0,15813,170522,3,18374,171567,4,19640,172244,1,20914,172244,50,20916,172244,40,20916,172284,0,20916,206398,3,22429,207203,4,23167,208087,5,23917,208088,1,23917,208088,50,23918,208088,40,23918,208128,0,23918,215167,3,24727,216184,4,25048,216441,5,25419,216441,1,25419,216441,50,25419,216441,40,25419,216481,0,25419,240077,3,26624,241088,4,27220,241953,5,27820,241954,1,27820,241954,50,27821,241954,40,27821,241994,0,27821,259072,3,28573,259848,4,28947,260531,1,29322,260531,50,29322,260531,40,29322,260531,40,29322,260566,0,29322,260678,50,29323,260678,30,29323,260678,40,29323,260713,0,29323,260833,50,29323,260868,0,29328,261036,50,29329,261036,30,29329,261036,40,29329,261071,0,29329,261155,50,29329,261190,0,29330,261314,50,29331,261314,30,29331,261314,40,29331,261349,0,29336,261441,50,29336,261476,0,29336,261608,50,29337,261608,30,29337,261608,40,29337,261643,0,29342,261739,50,29343,261774,0,29343,261914,50,29345,261949,0,29345,262097,50,29348,262132,0,29352,262288,50,29358,262323,0,29358,262485,50,29366,262520,0,29370,262690,50,29386,262725,0,29386,262903,50,29414,262938,0,29414,263126,50,29474,263161,0,29474,263359,50,29588,263359,40,29588,263394,0,29588,263565,50,29589,263565,30,29589,263565,40,29589,263600,0,29589,263696,50,29590,263731,0,29594,263871,50,29596,263906,0,29596,264054,50,29600,264089,0,29600,264245,50,29605,264280,0,29610,264442,50,29618,264477,0,29618,264647,50,29633,264682,0,29638,264860,50,29666,264895,0,29666,265083,50,29727,265118,0,29727,265316,50,29841,265316,40,29841,265351,0,29841,265500,50,29841,265500,30,29841,265500,40,29841,265535,0,29841,265635,50,29842,265670,0,29846,265822,50,29849,265857,0,29849,266019,50,29853,266054,0,29853,266228,50,29860,266263,0,29865,266443,50,29876,266478,0,29876,266666,50,29894,266701,0,29898,266898,50,29933,266933,0,29933,267140,50,30003,267175,0,30003,267393,50,30133,267393,40,30133,267428,0,30133)
%
%
% START OF PROOF
% 267235 [?] ?
% 267395 [] equal(multiply(identity,X),X).
% 267396 [] equal(multiply(inverse(X),X),identity).
% 267397 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 267398 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 267403 [?] ?
% 267408 [?] ?
% 267413 [?] ?
% 267445 [input:267403,cut:267398] equal(inverse(sk_c2),sk_c7).
% 267446 [para:267445.1.1,267396.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 267465 [input:267408,cut:267398] equal(multiply(sk_c2,sk_c7),sk_c5).
% 267478 [input:267413,cut:267398] equal(multiply(sk_c7,sk_c5),sk_c6).
% 267491 [para:267446.1.1,267397.1.1.1,demod:267395] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 267530 [para:267465.1.1,267491.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 267535 [para:267530.1.2,267478.1.1] equal(sk_c7,sk_c6).
% 267537 [para:267535.1.1,267398.1.1.2,cut:267235] 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: 36714
% derived clauses: 7067473
% kept clauses: 223578
% kept size sum: 260263
% kept mid-nuclei: 3756
% kept new demods: 5545
% forw unit-subs: 2867951
% forw double-subs: 3771891
% forw overdouble-subs: 161417
% backward subs: 14165
% fast unit cutoff: 30780
% full unit cutoff: 0
% dbl unit cutoff: 6127
% real runtime : 302.94
% process. runtime: 301.34
% specific non-discr-tree subsumption statistics:
% tried: 36872037
% length fails: 4666777
% strength fails: 10688489
% predlist fails: 2533977
% aux str. fails: 3634121
% by-lit fails: 9511980
% full subs tried: 1077994
% full subs fail: 982870
%
% ; 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/GRP294-1+eq_r.in")
%
%------------------------------------------------------------------------------