TSTP Solution File: GRP347-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP347-1 : 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 : art09.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/GRP347-1+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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% was split for some strategies as:
% -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6).
% -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6).
% -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(inverse(sk_c6),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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338)
%
%
% START OF PROOF
% 283025 [] equal(multiply(identity,X),X).
% 283026 [] equal(multiply(inverse(X),X),identity).
% 283027 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 283028 [] -equal(multiply(X,sk_c7),sk_c5) | -equal(inverse(X),sk_c7).
% 283029 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 283030 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 283035 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 283036 [?] ?
% 283041 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 283042 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 283047 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 283048 [?] ?
% 283053 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c4),sk_c7).
% 283054 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 283061 [hyper:283028,283035,binarycut:283036] equal(inverse(sk_c2),sk_c6).
% 283062 [para:283061.1.1,283026.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 283067 [hyper:283028,283047,binarycut:283048] equal(inverse(sk_c1),sk_c7).
% 283070 [para:283067.1.1,283026.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 283077 [hyper:283028,283030,283029] equal(multiply(sk_c2,sk_c5),sk_c6).
% 283083 [hyper:283028,283042,283041] equal(multiply(sk_c1,sk_c6),sk_c7).
% 283092 [hyper:283028,283054,283053] equal(multiply(sk_c6,sk_c7),sk_c5).
% 283096 [para:283026.1.1,283027.1.1.1,demod:283025] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 283097 [para:283062.1.1,283027.1.1.1,demod:283025] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 283098 [para:283070.1.1,283027.1.1.1,demod:283025] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 283099 [para:283077.1.1,283027.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c2,multiply(sk_c5,X))).
% 283100 [para:283083.1.1,283027.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c6,X))).
% 283102 [para:283077.1.1,283097.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 283104 [para:283083.1.1,283098.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 283107 [para:283026.1.1,283096.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 283108 [para:283062.1.1,283096.1.2.2] equal(sk_c2,multiply(inverse(sk_c6),identity)).
% 283109 [para:283070.1.1,283096.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 283110 [para:283092.1.1,283096.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 283111 [para:283027.1.1,283096.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 283113 [para:283102.1.2,283096.1.2.2,demod:283110] equal(sk_c6,sk_c7).
% 283115 [para:283096.1.2,283096.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 283116 [para:283113.1.1,283062.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 283118 [para:283113.1.1,283092.1.1.1,demod:283104] equal(sk_c6,sk_c5).
% 283119 [para:283113.1.1,283097.1.2.1] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 283127 [para:283118.1.1,283113.1.1] equal(sk_c5,sk_c7).
% 283132 [para:283116.1.1,283096.1.2.2,demod:283109] equal(sk_c2,sk_c1).
% 283134 [para:283097.1.2,283100.1.2.2,demod:283119] equal(X,multiply(sk_c1,X)).
% 283138 [para:283132.1.1,283097.1.2.2.1,demod:283134] equal(X,multiply(sk_c6,X)).
% 283139 [para:283132.1.1,283099.1.2.1,demod:283134,283138] equal(X,multiply(sk_c5,X)).
% 283141 [para:283138.1.2,283097.1.2] equal(X,multiply(sk_c2,X)).
% 283146 [para:283139.1.2,283096.1.2.2] equal(X,multiply(inverse(sk_c5),X)).
% 283151 [para:283146.1.2,283026.1.1] equal(sk_c5,identity).
% 283157 [para:283151.1.1,283110.1.2.2,demod:283108] equal(sk_c7,sk_c2).
% 283158 [para:283157.1.1,283127.1.2] equal(sk_c5,sk_c2).
% 283161 [para:283158.1.2,283061.1.1.1] equal(inverse(sk_c5),sk_c6).
% 283170 [para:283097.1.2,283111.1.2.2.2,demod:283141] equal(X,multiply(inverse(multiply(Y,sk_c6)),multiply(Y,X))).
% 283177 [para:283115.1.2,283107.1.2] equal(X,multiply(X,identity)).
% 283178 [para:283026.1.1,283170.1.2.2,demod:283177] equal(X,inverse(multiply(inverse(X),sk_c6))).
% 283180 [para:283177.1.2,283107.1.2] equal(X,inverse(inverse(X))).
% 283189 [para:283178.1.2,283107.1.2.1.1,demod:283177] equal(multiply(inverse(X),sk_c6),inverse(X)).
% 283204 [para:283189.1.1,283115.1.2,demod:283180] equal(multiply(X,sk_c6),X).
% 283205 [para:283113.1.1,283204.1.1.2] equal(multiply(X,sk_c7),X).
% 283206 [hyper:283028,283205,demod:283161,cut:283113] 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 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% 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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343)
%
%
% START OF PROOF
% 283207 [] equal(multiply(identity,X),X).
% 283208 [] equal(multiply(inverse(X),X),identity).
% 283209 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 283210 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 283213 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 283214 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 283219 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 283220 [?] ?
% 283225 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 283226 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 283231 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 283232 [?] ?
% 283237 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c3),sk_c6).
% 283238 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 283246 [hyper:283210,283219,binarycut:283220] equal(inverse(sk_c2),sk_c6).
% 283249 [para:283246.1.1,283208.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 283254 [hyper:283210,283231,binarycut:283232] equal(inverse(sk_c1),sk_c7).
% 283255 [para:283254.1.1,283208.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 283280 [hyper:283210,283214,283213] equal(multiply(sk_c2,sk_c5),sk_c6).
% 283287 [hyper:283210,283226,283225] equal(multiply(sk_c1,sk_c6),sk_c7).
% 283294 [hyper:283210,283238,283237] equal(multiply(sk_c6,sk_c7),sk_c5).
% 283295 [para:283208.1.1,283209.1.1.1,demod:283207] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 283296 [para:283249.1.1,283209.1.1.1,demod:283207] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 283299 [para:283287.1.1,283209.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c1,multiply(sk_c6,X))).
% 283301 [para:283280.1.1,283296.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 283307 [para:283255.1.1,283295.1.2.2] equal(sk_c1,multiply(inverse(sk_c7),identity)).
% 283308 [para:283294.1.1,283295.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 283310 [para:283301.1.2,283295.1.2.2,demod:283308] equal(sk_c6,sk_c7).
% 283312 [para:283310.1.1,283249.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 283315 [para:283310.1.1,283296.1.2.1] equal(X,multiply(sk_c7,multiply(sk_c2,X))).
% 283328 [para:283312.1.1,283295.1.2.2,demod:283307] equal(sk_c2,sk_c1).
% 283330 [para:283296.1.2,283299.1.2.2,demod:283315] equal(X,multiply(sk_c1,X)).
% 283334 [para:283328.1.1,283296.1.2.2.1,demod:283330] equal(X,multiply(sk_c6,X)).
% 283336 [para:283334.1.2,283249.1.1] equal(sk_c2,identity).
% 283339 [para:283336.1.1,283246.1.1.1] equal(inverse(identity),sk_c6).
% 283342 [hyper:283210,283339,demod:283207,cut:283310] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(Y),sk_c6) | -equal(multiply(Y,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
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343,283341,50,29343,283341,30,29343,283341,40,29343,283376,0,29343,283468,50,29344,283503,0,29344,283640,50,29346,283675,0,29351)
%
%
% START OF PROOF
% 283632 [?] ?
% 283642 [] equal(multiply(identity,X),X).
% 283643 [] equal(multiply(inverse(X),X),identity).
% 283644 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 283645 [] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c6).
% 283646 [?] ?
% 283647 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c7),sk_c5).
% 283648 [?] ?
% 283649 [] equal(multiply(sk_c2,sk_c5),sk_c6) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 283650 [?] ?
% 283652 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c4),sk_c7).
% 283653 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 283654 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c3),sk_c6).
% 283655 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 283656 [] equal(inverse(sk_c2),sk_c6) | equal(inverse(sk_c6),sk_c5).
% 283678 [hyper:283645,283652,binarycut:283646] equal(inverse(sk_c4),sk_c7).
% 283679 [para:283678.1.1,283643.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 283683 [hyper:283645,283654,binarycut:283648] equal(inverse(sk_c3),sk_c6).
% 283687 [para:283683.1.1,283643.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 283694 [hyper:283645,283656,binarycut:283650] equal(inverse(sk_c6),sk_c5).
% 283695 [para:283694.1.1,283643.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 283698 [hyper:283645,283653,binarycut:283647] equal(multiply(sk_c4,sk_c7),sk_c5).
% 283704 [hyper:283645,283655,binarycut:283649] equal(multiply(sk_c3,sk_c6),sk_c7).
% 283708 [para:283643.1.1,283644.1.1.1,demod:283642] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 283709 [para:283679.1.1,283644.1.1.1,demod:283642] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 283710 [para:283687.1.1,283644.1.1.1,demod:283642] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 283715 [para:283698.1.1,283709.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 283717 [para:283704.1.1,283710.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 283721 [para:283687.1.1,283708.1.2.2,demod:283694] equal(sk_c3,multiply(sk_c5,identity)).
% 283726 [para:283710.1.2,283708.1.2.2,demod:283694] equal(multiply(sk_c3,X),multiply(sk_c5,X)).
% 283729 [para:283717.1.2,283708.1.2.2,demod:283695,283694] equal(sk_c7,identity).
% 283732 [para:283729.1.1,283709.1.2.1,demod:283642] equal(X,multiply(sk_c4,X)).
% 283733 [para:283729.1.1,283715.1.2.1,demod:283642] equal(sk_c7,sk_c5).
% 283739 [para:283733.1.1,283709.1.2.1,demod:283732] equal(X,multiply(sk_c5,X)).
% 283741 [para:283733.1.1,283729.1.1] equal(sk_c5,identity).
% 283747 [para:283741.1.1,283695.1.1.1,demod:283642] equal(sk_c6,identity).
% 283750 [para:283747.1.1,283704.1.1.2,demod:283721,283726] equal(sk_c3,sk_c7).
% 283752 [para:283750.1.2,283698.1.1.2,demod:283732] equal(sk_c3,sk_c5).
% 283755 [para:283752.1.1,283683.1.1.1] equal(inverse(sk_c5),sk_c6).
% 283757 [hyper:283645,283755,demod:283739,cut:283632] 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 5
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343,283341,50,29343,283341,30,29343,283341,40,29343,283376,0,29343,283468,50,29344,283503,0,29344,283640,50,29346,283675,0,29351,283756,50,29351,283756,30,29351,283756,40,29351,283791,0,29351)
%
%
% START OF PROOF
% 283758 [] equal(multiply(identity,X),X).
% 283759 [] equal(multiply(inverse(X),X),identity).
% 283760 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 283761 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 283774 [?] ?
% 283775 [?] ?
% 283776 [?] ?
% 283777 [] equal(multiply(sk_c1,sk_c6),sk_c7) | equal(multiply(sk_c3,sk_c6),sk_c7).
% 283778 [?] ?
% 283779 [?] ?
% 283780 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c7).
% 283781 [] equal(multiply(sk_c4,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c7).
% 283782 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c6).
% 283783 [] equal(multiply(sk_c3,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 283784 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c6),sk_c5).
% 283785 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c1),sk_c7).
% 283799 [hyper:283761,283780,binarycut:283774] equal(inverse(sk_c4),sk_c7).
% 283803 [para:283799.1.1,283759.1.1.1] equal(multiply(sk_c7,sk_c4),identity).
% 283808 [hyper:283761,283782,binarycut:283776] equal(inverse(sk_c3),sk_c6).
% 283809 [para:283808.1.1,283759.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 283812 [hyper:283761,283784,binarycut:283778] equal(inverse(sk_c6),sk_c5).
% 283816 [para:283812.1.1,283759.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 283825 [hyper:283761,283781,binarycut:283775] equal(multiply(sk_c4,sk_c7),sk_c5).
% 283834 [hyper:283761,283783,binarycut:283777] equal(multiply(sk_c3,sk_c6),sk_c7).
% 283840 [hyper:283761,283785,binarycut:283779] equal(multiply(sk_c6,sk_c5),sk_c7).
% 283841 [para:283759.1.1,283760.1.1.1,demod:283758] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 283842 [para:283803.1.1,283760.1.1.1,demod:283758] equal(X,multiply(sk_c7,multiply(sk_c4,X))).
% 283843 [para:283809.1.1,283760.1.1.1,demod:283758] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 283848 [para:283825.1.1,283842.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c5)).
% 283850 [para:283834.1.1,283843.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 283859 [para:283850.1.2,283841.1.2.2,demod:283816,283812] equal(sk_c7,identity).
% 283860 [para:283859.1.1,283803.1.1.1,demod:283758] equal(sk_c4,identity).
% 283863 [para:283859.1.1,283848.1.2.1,demod:283758] equal(sk_c7,sk_c5).
% 283865 [para:283860.1.1,283799.1.1.1] equal(inverse(identity),sk_c7).
% 283870 [para:283863.1.1,283850.1.2.2,demod:283840] equal(sk_c6,sk_c7).
% 283886 [hyper:283761,283865,demod:283758,cut:283870] 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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% 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(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343,283341,50,29343,283341,30,29343,283341,40,29343,283376,0,29343,283468,50,29344,283503,0,29344,283640,50,29346,283675,0,29351,283756,50,29351,283756,30,29351,283756,40,29351,283791,0,29351,283885,50,29352,283885,30,29352,283885,40,29352,283920,0,29356,284023,50,29357,284058,0,29357,284200,50,29360,284235,0,29360,284385,50,29363,284420,0,29368,284578,50,29373,284613,0,29373,284777,50,29381,284812,0,29386,284984,50,29401,285019,0,29401,285199,50,29429,285234,0,29429,285424,50,29489,285459,0,29489,285659,50,29601,285659,40,29601,285694,0,29601)
%
%
% START OF PROOF
% 285541 [?] ?
% 285661 [] equal(multiply(identity,X),X).
% 285662 [] equal(multiply(inverse(X),X),identity).
% 285663 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 285664 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 285691 [?] ?
% 285692 [?] ?
% 285742 [input:285691,cut:285664] equal(inverse(sk_c3),sk_c6).
% 285743 [para:285742.1.1,285662.1.1.1] equal(multiply(sk_c6,sk_c3),identity).
% 285756 [input:285692,cut:285664] equal(multiply(sk_c3,sk_c6),sk_c7).
% 285779 [para:285743.1.1,285663.1.1.1,demod:285661] equal(X,multiply(sk_c6,multiply(sk_c3,X))).
% 285807 [para:285756.1.1,285779.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c7)).
% 285808 [para:285807.1.2,285664.1.1,cut:285541] 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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(sk_c6,sk_c5),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 21
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343,283341,50,29343,283341,30,29343,283341,40,29343,283376,0,29343,283468,50,29344,283503,0,29344,283640,50,29346,283675,0,29351,283756,50,29351,283756,30,29351,283756,40,29351,283791,0,29351,283885,50,29352,283885,30,29352,283885,40,29352,283920,0,29356,284023,50,29357,284058,0,29357,284200,50,29360,284235,0,29360,284385,50,29363,284420,0,29368,284578,50,29373,284613,0,29373,284777,50,29381,284812,0,29386,284984,50,29401,285019,0,29401,285199,50,29429,285234,0,29429,285424,50,29489,285459,0,29489,285659,50,29601,285659,40,29601,285694,0,29601,285807,50,29602,285807,30,29602,285807,40,29602,285842,0,29602,285947,50,29602,285982,0,29608,286131,50,29610,286166,0,29610,286323,50,29614,286358,0,29614,286523,50,29620,286558,0,29624,286729,50,29633,286764,0,29633,286943,50,29649,286978,0,29653,287165,50,29683,287200,0,29683,287397,50,29745,287432,0,29745,287639,50,29863,287639,40,29863,287674,0,29863)
%
%
% START OF PROOF
% 287584 [?] ?
% 287641 [] equal(multiply(identity,X),X).
% 287642 [] equal(multiply(inverse(X),X),identity).
% 287643 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 287644 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 287650 [?] ?
% 287656 [?] ?
% 287674 [?] ?
% 287704 [input:287656,cut:287644] equal(inverse(sk_c2),sk_c6).
% 287705 [para:287704.1.1,287642.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 287715 [input:287650,cut:287644] equal(multiply(sk_c2,sk_c5),sk_c6).
% 287737 [input:287674,cut:287644] equal(multiply(sk_c6,sk_c7),sk_c5).
% 287741 [para:287642.1.1,287643.1.1.1,demod:287641] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 287751 [para:287705.1.1,287643.1.1.1,demod:287641] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 287786 [para:287715.1.1,287751.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 287838 [para:287737.1.1,287741.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 287844 [para:287786.1.2,287741.1.2.2,demod:287838] equal(sk_c6,sk_c7).
% 287849 [para:287844.1.1,287644.1.1.1,cut:287584] 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_c6,sk_c7),sk_c5) | -equal(inverse(X),sk_c7) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(Y,sk_c5),sk_c6) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(Z,sk_c6),sk_c7) | -equal(inverse(Z),sk_c6) | -equal(multiply(U,sk_c7),sk_c5) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(inverse(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(35,40,0,75,0,0,661,50,4,701,0,4,1302,50,8,1342,0,8,1949,50,14,1989,0,14,2602,50,20,2642,0,20,3262,50,27,3302,0,27,3930,50,40,3970,0,40,4607,50,65,4647,0,65,5294,50,120,5334,0,120,5991,50,240,6031,0,240,6700,50,440,6740,0,440,7421,50,818,7421,40,818,7461,0,818,17924,3,1119,18677,4,1269,19400,5,1419,19401,1,1419,19401,50,1419,19401,40,1419,19441,0,1419,19649,3,1729,19657,4,1871,19665,5,2020,19665,1,2020,19665,50,2020,19665,40,2020,19705,0,2020,44112,3,3524,45432,4,4271,46695,1,5021,46695,50,5022,46695,40,5022,46735,0,5022,62330,3,5775,63212,4,6148,64097,1,6523,64097,50,6523,64097,40,6523,64137,0,6523,72763,3,7293,73993,4,7649,75181,5,8024,75182,1,8024,75182,50,8024,75182,40,8024,75222,0,8024,132970,3,11926,134211,4,13875,135348,1,15825,135348,50,15827,135348,40,15827,135388,0,15827,183074,3,18378,184006,4,19654,184854,5,20928,184855,1,20928,184855,50,20930,184855,40,20930,184895,0,20930,221138,3,22433,222053,4,23181,222901,5,23931,222902,1,23931,222902,50,23932,222902,40,23932,222942,0,23932,230472,3,24743,231423,4,25062,231700,5,25433,231700,1,25433,231700,50,25434,231700,40,25434,231740,0,25434,260522,3,26635,261365,4,27235,261776,1,27835,261776,50,27836,261776,40,27836,261816,0,27836,281901,3,28587,282635,4,28962,282886,1,29337,282886,50,29338,282886,40,29338,282886,40,29338,282921,0,29338,283023,50,29338,283058,0,29338,283205,50,29339,283205,30,29339,283205,40,29339,283240,0,29343,283341,50,29343,283341,30,29343,283341,40,29343,283376,0,29343,283468,50,29344,283503,0,29344,283640,50,29346,283675,0,29351,283756,50,29351,283756,30,29351,283756,40,29351,283791,0,29351,283885,50,29352,283885,30,29352,283885,40,29352,283920,0,29356,284023,50,29357,284058,0,29357,284200,50,29360,284235,0,29360,284385,50,29363,284420,0,29368,284578,50,29373,284613,0,29373,284777,50,29381,284812,0,29386,284984,50,29401,285019,0,29401,285199,50,29429,285234,0,29429,285424,50,29489,285459,0,29489,285659,50,29601,285659,40,29601,285694,0,29601,285807,50,29602,285807,30,29602,285807,40,29602,285842,0,29602,285947,50,29602,285982,0,29608,286131,50,29610,286166,0,29610,286323,50,29614,286358,0,29614,286523,50,29620,286558,0,29624,286729,50,29633,286764,0,29633,286943,50,29649,286978,0,29653,287165,50,29683,287200,0,29683,287397,50,29745,287432,0,29745,287639,50,29863,287639,40,29863,287674,0,29863,287848,50,29864,287848,30,29864,287848,40,29864,287883,0,29864,287988,50,29864,288023,0,29870,288172,50,29872,288207,0,29872,288364,50,29876,288399,0,29876,288564,50,29882,288599,0,29886,288770,50,29895,288805,0,29895,288984,50,29911,289019,0,29915,289206,50,29944,289241,0,29944,289438,50,30007,289473,0,30007,289680,50,30123,289680,40,30123,289715,0,30124)
%
%
% START OF PROOF
% 289682 [] equal(multiply(identity,X),X).
% 289683 [] equal(multiply(inverse(X),X),identity).
% 289684 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 289685 [] -equal(inverse(sk_c6),sk_c5).
% 289690 [?] ?
% 289696 [?] ?
% 289702 [?] ?
% 289708 [?] ?
% 289714 [?] ?
% 289724 [input:289696,cut:289685] equal(inverse(sk_c2),sk_c6).
% 289725 [para:289724.1.1,289683.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 289733 [input:289708,cut:289685] equal(inverse(sk_c1),sk_c7).
% 289734 [para:289733.1.1,289683.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 289737 [input:289690,cut:289685] equal(multiply(sk_c2,sk_c5),sk_c6).
% 289746 [input:289702,cut:289685] equal(multiply(sk_c1,sk_c6),sk_c7).
% 289756 [input:289714,cut:289685] equal(multiply(sk_c6,sk_c7),sk_c5).
% 289769 [para:289683.1.1,289684.1.1.1,demod:289682] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 289771 [para:289725.1.1,289684.1.1.1,demod:289682] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 289774 [para:289734.1.1,289684.1.1.1,demod:289682] equal(X,multiply(sk_c7,multiply(sk_c1,X))).
% 289807 [para:289737.1.1,289771.1.2.2] equal(sk_c5,multiply(sk_c6,sk_c6)).
% 289811 [para:289746.1.1,289774.1.2.2] equal(sk_c6,multiply(sk_c7,sk_c7)).
% 289839 [para:289756.1.1,289769.1.2.2] equal(sk_c7,multiply(inverse(sk_c6),sk_c5)).
% 289854 [para:289807.1.2,289769.1.2.2,demod:289839] equal(sk_c6,sk_c7).
% 289872 [para:289854.1.1,289756.1.1.1,demod:289811] equal(sk_c6,sk_c5).
% 289881 [para:289872.1.1,289685.1.1.1] -equal(inverse(sk_c5),sk_c5).
% 289894 [para:289872.1.1,289756.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 289901 [para:289872.1.1,289854.1.1] equal(sk_c5,sk_c7).
% 289902 [para:289854.1.1,289872.1.1] equal(sk_c7,sk_c5).
% 289930 [para:289894.1.1,289769.1.2.2,demod:289683] equal(sk_c7,identity).
% 289933 [para:289930.1.1,289734.1.1.1,demod:289682] equal(sk_c1,identity).
% 289942 [para:289930.1.1,289901.1.2] equal(sk_c5,identity).
% 289950 [para:289933.1.1,289733.1.1.1] equal(inverse(identity),sk_c7).
% 289960 [para:289942.1.1,289881.1.1.1,demod:289950,cut:289902] 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: 38275
% derived clauses: 6663154
% kept clauses: 245219
% kept size sum: 281635
% kept mid-nuclei: 4048
% kept new demods: 5507
% forw unit-subs: 2548214
% forw double-subs: 3529160
% forw overdouble-subs: 293853
% backward subs: 11653
% fast unit cutoff: 19956
% full unit cutoff: 0
% dbl unit cutoff: 5006
% real runtime : 303.80
% process. runtime: 301.24
% specific non-discr-tree subsumption statistics:
% tried: 40842588
% length fails: 5194554
% strength fails: 10752834
% predlist fails: 1736628
% aux str. fails: 5602502
% by-lit fails: 10453950
% full subs tried: 1568197
% full subs fail: 1471222
%
% ; 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/GRP347-1+eq_r.in")
%
%------------------------------------------------------------------------------