TSTP Solution File: GRP363-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP363-1 : 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 : art02.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 298.6s
% Output : Assurance 298.6s
% 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/GRP363-1+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 19)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 19)
% (binary-posweight-lex-big-order 30 #f 3 19)
% (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_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% was split for some strategies as:
% -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(inverse(sk_c6),sk_c5).
% -equal(multiply(sk_c6,sk_c7),sk_c5).
%
% Starting a split proof attempt with 6 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675)
%
%
% START OF PROOF
% 342855 [] equal(multiply(identity,X),X).
% 342856 [] equal(multiply(inverse(X),X),identity).
% 342857 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 342858 [] -equal(multiply(sk_c7,X),sk_c6) | -equal(multiply(Y,sk_c7),X) | -equal(inverse(Y),sk_c7).
% 342859 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 342860 [] equal(multiply(sk_c3,sk_c7),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 342861 [?] ?
% 342865 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 342866 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(multiply(sk_c3,sk_c7),sk_c4).
% 342867 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(multiply(sk_c7,sk_c4),sk_c6).
% 342871 [] equal(inverse(sk_c6),sk_c5) | equal(inverse(sk_c3),sk_c7).
% 342872 [] equal(multiply(sk_c3,sk_c7),sk_c4) | equal(inverse(sk_c6),sk_c5).
% 342873 [?] ?
% 342877 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 342878 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c3,sk_c7),sk_c4).
% 342879 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c7,sk_c4),sk_c6).
% 342900 [hyper:342858,342860,342859,binarycut:342861] equal(inverse(sk_c1),sk_c6).
% 342901 [para:342900.1.1,342856.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 342911 [hyper:342858,342872,342871,binarycut:342873] equal(inverse(sk_c6),sk_c5).
% 342915 [para:342911.1.1,342856.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 342928 [hyper:342858,342867,342866,342865] equal(multiply(sk_c1,sk_c6),sk_c5).
% 342936 [hyper:342858,342879,342878,342877] equal(multiply(sk_c6,sk_c5),sk_c7).
% 342938 [para:342856.1.1,342857.1.1.1,demod:342855] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 342940 [para:342901.1.1,342857.1.1.1,demod:342855] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 342941 [para:342915.1.1,342857.1.1.1,demod:342855] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 342942 [para:342928.1.1,342857.1.1.1] equal(multiply(sk_c5,X),multiply(sk_c1,multiply(sk_c6,X))).
% 342946 [para:342856.1.1,342938.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 342950 [para:342928.1.1,342938.1.2.2,demod:342936,342900] equal(sk_c6,sk_c7).
% 342951 [para:342936.1.1,342938.1.2.2,demod:342911] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 342952 [para:342857.1.1,342938.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 342953 [para:342938.1.2,342938.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 342956 [para:342950.1.1,342915.1.1.2,demod:342951] equal(sk_c5,identity).
% 342959 [para:342956.1.1,342915.1.1.1,demod:342855] equal(sk_c6,identity).
% 342963 [para:342959.1.1,342928.1.1.2] equal(multiply(sk_c1,identity),sk_c5).
% 342964 [para:342959.1.1,342936.1.1.1,demod:342855] equal(sk_c5,sk_c7).
% 342969 [para:342940.1.2,342938.1.2.2,demod:342911] equal(multiply(sk_c1,X),multiply(sk_c5,X)).
% 342971 [para:342959.1.1,342940.1.2.1,demod:342855] equal(X,multiply(sk_c1,X)).
% 342978 [para:342950.1.1,342941.1.2.2.1,demod:342971,342969] equal(X,multiply(sk_c7,X)).
% 342984 [para:342901.1.1,342942.1.2.2,demod:342963,342971,342969] equal(sk_c1,sk_c5).
% 342985 [para:342984.1.2,342964.1.1] equal(sk_c1,sk_c7).
% 343024 [para:342953.1.2,342856.1.1] equal(multiply(X,inverse(X)),identity).
% 343026 [para:342953.1.2,342938.1.2] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 343027 [para:342953.1.2,342946.1.2] equal(X,multiply(X,identity)).
% 343030 [para:343027.1.2,342946.1.2] equal(X,inverse(inverse(X))).
% 343033 [para:343024.1.1,342952.1.2.2.2,demod:343027] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 343038 [para:343026.1.2,342952.1.2.2.2] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 343040 [para:342940.1.2,343033.1.2.1.1,demod:342971] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 343046 [para:343040.1.2,342953.1.2,demod:343030] equal(multiply(X,sk_c6),X).
% 343047 [para:342950.1.1,343046.1.1.2] equal(multiply(X,sk_c7),X).
% 343064 [hyper:342858,343038,342900,demod:343030,342978,343033,343047,cut:342985] 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 19
% 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_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 19
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675,343063,50,29677,343063,30,29677,343063,40,29677,343092,0,29683,343166,50,29683,343195,0,29683)
%
%
% START OF PROOF
% 343168 [] equal(multiply(identity,X),X).
% 343169 [] equal(multiply(inverse(X),X),identity).
% 343170 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 343171 [] -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c6).
% 343175 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 343176 [?] ?
% 343181 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 343182 [] equal(multiply(sk_c1,sk_c6),sk_c5) | equal(multiply(sk_c2,sk_c6),sk_c7).
% 343187 [] equal(inverse(sk_c6),sk_c5) | equal(inverse(sk_c2),sk_c6).
% 343188 [?] ?
% 343193 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c6).
% 343194 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(multiply(sk_c2,sk_c6),sk_c7).
% 343201 [hyper:343171,343175,binarycut:343176] equal(inverse(sk_c1),sk_c6).
% 343204 [para:343201.1.1,343169.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 343210 [hyper:343171,343187,binarycut:343188] equal(inverse(sk_c6),sk_c5).
% 343211 [para:343210.1.1,343169.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 343223 [hyper:343171,343182,343181] equal(multiply(sk_c1,sk_c6),sk_c5).
% 343228 [hyper:343171,343194,343193] equal(multiply(sk_c6,sk_c5),sk_c7).
% 343229 [para:343169.1.1,343170.1.1.1,demod:343168] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 343230 [para:343204.1.1,343170.1.1.1,demod:343168] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 343235 [para:343169.1.1,343229.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 343238 [para:343223.1.1,343229.1.2.2,demod:343228,343201] equal(sk_c6,sk_c7).
% 343239 [para:343228.1.1,343229.1.2.2,demod:343210] equal(sk_c5,multiply(sk_c5,sk_c7)).
% 343240 [para:343170.1.1,343229.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 343241 [para:343229.1.2,343229.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 343243 [para:343238.1.1,343210.1.1.1] equal(inverse(sk_c7),sk_c5).
% 343244 [para:343238.1.1,343211.1.1.2,demod:343239] equal(sk_c5,identity).
% 343247 [para:343244.1.1,343211.1.1.1,demod:343168] equal(sk_c6,identity).
% 343249 [para:343247.1.1,343204.1.1.1,demod:343168] equal(sk_c1,identity).
% 343250 [para:343247.1.1,343210.1.1.1] equal(inverse(identity),sk_c5).
% 343257 [para:343247.1.1,343230.1.2.1,demod:343168] equal(X,multiply(sk_c1,X)).
% 343258 [para:343249.1.1,343201.1.1.1,demod:343250] equal(sk_c5,sk_c6).
% 343283 [para:343241.1.2,343169.1.1] equal(multiply(X,inverse(X)),identity).
% 343285 [para:343241.1.2,343235.1.2] equal(X,multiply(X,identity)).
% 343286 [para:343285.1.2,343235.1.2] equal(X,inverse(inverse(X))).
% 343287 [para:343283.1.1,343240.1.2.2.2,demod:343285] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 343290 [para:343230.1.2,343287.1.2.1.1,demod:343257] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 343296 [para:343290.1.2,343241.1.2,demod:343286] equal(multiply(X,sk_c6),X).
% 343297 [hyper:343171,343296,demod:343243,cut:343258] 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 19
% 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_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -equal(inverse(U),sk_c7).
% Split part used next: -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),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 19
% 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 19
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675,343063,50,29677,343063,30,29677,343063,40,29677,343092,0,29683,343166,50,29683,343195,0,29683,343296,50,29684,343296,30,29684,343296,40,29684,343325,0,29684,343431,50,29685,343460,0,29689)
%
%
% START OF PROOF
% 343433 [] equal(multiply(identity,X),X).
% 343434 [] equal(multiply(inverse(X),X),identity).
% 343435 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 343436 [] -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6).
% 343437 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 343438 [] equal(multiply(sk_c3,sk_c7),sk_c4) | equal(inverse(sk_c1),sk_c6).
% 343439 [] equal(multiply(sk_c7,sk_c4),sk_c6) | equal(inverse(sk_c1),sk_c6).
% 343440 [] equal(inverse(sk_c1),sk_c6) | equal(inverse(sk_c2),sk_c6).
% 343441 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c1),sk_c6).
% 343442 [] equal(multiply(sk_c6,sk_c7),sk_c5) | equal(inverse(sk_c1),sk_c6).
% 343443 [?] ?
% 343444 [?] ?
% 343445 [?] ?
% 343446 [?] ?
% 343447 [?] ?
% 343448 [?] ?
% 343463 [hyper:343436,343437,binarycut:343443] equal(inverse(sk_c3),sk_c7).
% 343464 [para:343463.1.1,343434.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 343468 [hyper:343436,343440,binarycut:343446] equal(inverse(sk_c2),sk_c6).
% 343472 [para:343468.1.1,343434.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 343476 [hyper:343436,343438,binarycut:343444] equal(multiply(sk_c3,sk_c7),sk_c4).
% 343479 [hyper:343436,343439,binarycut:343445] equal(multiply(sk_c7,sk_c4),sk_c6).
% 343482 [hyper:343436,343441,binarycut:343447] equal(multiply(sk_c2,sk_c6),sk_c7).
% 343485 [hyper:343436,343442,binarycut:343448] equal(multiply(sk_c6,sk_c7),sk_c5).
% 343486 [para:343434.1.1,343435.1.1.1,demod:343433] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 343487 [para:343464.1.1,343435.1.1.1,demod:343433] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 343488 [para:343472.1.1,343435.1.1.1,demod:343433] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 343489 [para:343476.1.1,343435.1.1.1] equal(multiply(sk_c4,X),multiply(sk_c3,multiply(sk_c7,X))).
% 343490 [para:343479.1.1,343435.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c4,X))).
% 343491 [para:343482.1.1,343435.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c2,multiply(sk_c6,X))).
% 343493 [para:343476.1.1,343487.1.2.2,demod:343479] equal(sk_c7,sk_c6).
% 343494 [para:343493.1.2,343472.1.1.1] equal(multiply(sk_c7,sk_c2),identity).
% 343495 [para:343493.1.2,343482.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c7).
% 343498 [para:343434.1.1,343486.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 343499 [para:343464.1.1,343486.1.2.2] equal(sk_c3,multiply(inverse(sk_c7),identity)).
% 343502 [para:343482.1.1,343486.1.2.2,demod:343485,343468] equal(sk_c6,sk_c5).
% 343503 [para:343435.1.1,343486.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 343506 [para:343486.1.2,343486.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 343509 [para:343502.1.1,343485.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 343514 [para:343494.1.1,343486.1.2.2,demod:343499] equal(sk_c2,sk_c3).
% 343521 [para:343489.1.2,343487.1.2.2,demod:343490] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 343524 [para:343514.1.2,343489.1.2.1] equal(multiply(sk_c4,X),multiply(sk_c2,multiply(sk_c7,X))).
% 343525 [para:343495.1.1,343435.1.1.1,demod:343524] equal(multiply(sk_c7,X),multiply(sk_c4,X)).
% 343531 [para:343509.1.1,343486.1.2.2,demod:343434] equal(sk_c7,identity).
% 343532 [para:343531.1.1,343464.1.1.1,demod:343433] equal(sk_c3,identity).
% 343534 [para:343531.1.1,343479.1.1.1,demod:343433] equal(sk_c4,sk_c6).
% 343535 [para:343531.1.1,343485.1.1.2,demod:343521] equal(multiply(sk_c7,identity),sk_c5).
% 343536 [para:343531.1.1,343487.1.2.1,demod:343433] equal(X,multiply(sk_c3,X)).
% 343538 [para:343531.1.1,343489.1.2.2.1,demod:343536,343433,343525] equal(multiply(sk_c7,X),X).
% 343540 [para:343532.1.1,343463.1.1.1] equal(inverse(identity),sk_c7).
% 343544 [para:343493.1.2,343491.1.2.2.1,demod:343538] equal(X,multiply(sk_c2,X)).
% 343546 [para:343534.1.2,343502.1.1] equal(sk_c4,sk_c5).
% 343553 [para:343531.1.1,343499.1.2.1.1,demod:343535,343540] equal(sk_c3,sk_c5).
% 343556 [para:343553.1.2,343546.1.2] equal(sk_c4,sk_c3).
% 343565 [para:343556.1.2,343514.1.2] equal(sk_c2,sk_c4).
% 343568 [para:343565.1.2,343479.1.1.2,demod:343494] equal(identity,sk_c6).
% 343575 [para:343485.1.1,343503.1.2.1.1,demod:343521,343538] equal(X,multiply(inverse(sk_c5),X)).
% 343604 [para:343506.1.2,343434.1.1] equal(multiply(X,inverse(X)),identity).
% 343606 [para:343506.1.2,343498.1.2] equal(X,multiply(X,identity)).
% 343607 [para:343606.1.2,343498.1.2] equal(X,inverse(inverse(X))).
% 343609 [para:343606.1.2,343575.1.2] equal(identity,inverse(sk_c5)).
% 343612 [para:343604.1.1,343503.1.2.2.2,demod:343606] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 343619 [para:343488.1.2,343612.1.2.1.1,demod:343544] equal(inverse(X),multiply(inverse(X),sk_c6)).
% 343628 [para:343619.1.2,343506.1.2,demod:343607] equal(multiply(X,sk_c6),X).
% 343629 [hyper:343436,343628,demod:343609,cut:343568] 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 19
% 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_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675,343063,50,29677,343063,30,29677,343063,40,29677,343092,0,29683,343166,50,29683,343195,0,29683,343296,50,29684,343296,30,29684,343296,40,29684,343325,0,29684,343431,50,29685,343460,0,29689,343628,50,29690,343628,30,29690,343628,40,29690,343657,0,29690,343763,50,29690,343792,0,29696,343954,50,29699,343983,0,29699,344153,50,29703,344182,0,29703,344360,50,29709,344389,0,29713,344573,50,29722,344602,0,29722,344794,50,29739,344823,0,29743,345023,50,29773,345052,0,29773,345262,50,29836,345291,0,29836,345511,50,29954,345511,40,29954,345540,0,29954)
%
%
% START OF PROOF
% 345455 [?] ?
% 345513 [] equal(multiply(identity,X),X).
% 345514 [] equal(multiply(inverse(X),X),identity).
% 345515 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 345516 [] -equal(multiply(sk_c6,sk_c5),sk_c7).
% 345535 [?] ?
% 345536 [?] ?
% 345537 [?] ?
% 345574 [input:345535,cut:345516] equal(inverse(sk_c3),sk_c7).
% 345575 [para:345574.1.1,345514.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 345585 [input:345536,cut:345516] equal(multiply(sk_c3,sk_c7),sk_c4).
% 345586 [input:345537,cut:345516] equal(multiply(sk_c7,sk_c4),sk_c6).
% 345603 [para:345575.1.1,345515.1.1.1,demod:345513] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 345623 [para:345585.1.1,345603.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c4)).
% 345629 [para:345623.1.2,345586.1.1] equal(sk_c7,sk_c6).
% 345631 [para:345629.1.2,345516.1.1.1,cut:345455] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675,343063,50,29677,343063,30,29677,343063,40,29677,343092,0,29683,343166,50,29683,343195,0,29683,343296,50,29684,343296,30,29684,343296,40,29684,343325,0,29684,343431,50,29685,343460,0,29689,343628,50,29690,343628,30,29690,343628,40,29690,343657,0,29690,343763,50,29690,343792,0,29696,343954,50,29699,343983,0,29699,344153,50,29703,344182,0,29703,344360,50,29709,344389,0,29713,344573,50,29722,344602,0,29722,344794,50,29739,344823,0,29743,345023,50,29773,345052,0,29773,345262,50,29836,345291,0,29836,345511,50,29954,345511,40,29954,345540,0,29954,345630,50,29954,345630,30,29954,345630,40,29954,345659,0,29954,345765,50,29955,345794,0,29959,345956,50,29962,345985,0,29962,346155,50,29966,346184,0,29966,346362,50,29972,346391,0,29977,346575,50,29986,346604,0,29986,346796,50,30002,346825,0,30007,347025,50,30036,347054,0,30036,347264,50,30100,347293,0,30100,347513,50,30218,347513,40,30218,347542,0,30218)
%
%
% START OF PROOF
% 347380 [?] ?
% 347515 [] equal(multiply(identity,X),X).
% 347516 [] equal(multiply(inverse(X),X),identity).
% 347517 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 347518 [] -equal(inverse(sk_c6),sk_c5).
% 347531 [?] ?
% 347532 [?] ?
% 347533 [?] ?
% 347534 [?] ?
% 347535 [?] ?
% 347536 [?] ?
% 347551 [input:347531,cut:347518] equal(inverse(sk_c3),sk_c7).
% 347552 [para:347551.1.1,347516.1.1.1] equal(multiply(sk_c7,sk_c3),identity).
% 347553 [input:347534,cut:347518] equal(inverse(sk_c2),sk_c6).
% 347554 [para:347553.1.1,347516.1.1.1] equal(multiply(sk_c6,sk_c2),identity).
% 347563 [input:347532,cut:347518] equal(multiply(sk_c3,sk_c7),sk_c4).
% 347565 [input:347533,cut:347518] equal(multiply(sk_c7,sk_c4),sk_c6).
% 347566 [input:347535,cut:347518] equal(multiply(sk_c2,sk_c6),sk_c7).
% 347567 [input:347536,cut:347518] equal(multiply(sk_c6,sk_c7),sk_c5).
% 347580 [para:347516.1.1,347517.1.1.1,demod:347515] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 347582 [para:347552.1.1,347517.1.1.1,demod:347515] equal(X,multiply(sk_c7,multiply(sk_c3,X))).
% 347583 [para:347554.1.1,347517.1.1.1,demod:347515] equal(X,multiply(sk_c6,multiply(sk_c2,X))).
% 347591 [para:347565.1.1,347517.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c4,X))).
% 347607 [para:347563.1.1,347582.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c4)).
% 347609 [para:347607.1.2,347565.1.1] equal(sk_c7,sk_c6).
% 347610 [para:347607.1.2,347517.1.1.1,demod:347591] equal(multiply(sk_c7,X),multiply(sk_c6,X)).
% 347611 [para:347609.1.2,347518.1.1.1] -equal(inverse(sk_c7),sk_c5).
% 347618 [para:347609.1.2,347566.1.1.2] equal(multiply(sk_c2,sk_c7),sk_c7).
% 347619 [para:347609.1.2,347567.1.1.1] equal(multiply(sk_c7,sk_c7),sk_c5).
% 347637 [para:347566.1.1,347583.1.2.2,demod:347619,347610] equal(sk_c6,sk_c5).
% 347638 [para:347618.1.1,347583.1.2.2,demod:347619,347610] equal(sk_c7,sk_c5).
% 347647 [para:347637.1.1,347567.1.1.1] equal(multiply(sk_c5,sk_c7),sk_c5).
% 347664 [para:347638.1.2,347611.1.2] -equal(inverse(sk_c7),sk_c7).
% 347712 [para:347647.1.1,347580.1.2.2,demod:347516] equal(sk_c7,identity).
% 347726 [para:347712.1.1,347664.1.1.1,cut:347380] 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_c5),sk_c7) | -equal(inverse(sk_c6),sk_c5) | -equal(multiply(X,sk_c6),sk_c5) | -equal(inverse(X),sk_c6) | -equal(multiply(sk_c6,sk_c7),sk_c5) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(inverse(Y),sk_c6) | -equal(multiply(sk_c7,Z),sk_c6) | -equal(multiply(U,sk_c7),Z) | -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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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 19
% 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(29,40,0,62,0,0,505,50,3,538,0,3,1445,50,12,1478,0,12,2802,50,30,2835,0,30,4355,50,47,4388,0,47,6132,50,67,6165,0,68,8091,50,97,8124,0,97,10291,50,146,10324,0,146,12733,50,233,12766,0,233,15476,50,402,15509,0,402,18521,50,665,18554,0,665,21927,50,1155,21927,40,1155,21960,0,1155,32553,3,1456,33267,4,1606,33928,5,1756,33929,1,1756,33929,50,1756,33929,40,1756,33962,0,1756,34151,3,2057,34161,4,2219,34169,5,2357,34169,1,2357,34169,50,2357,34169,40,2357,34202,0,2357,61766,3,3863,62875,4,4608,63762,5,5358,63763,1,5358,63763,50,5359,63763,40,5359,63796,0,5359,82375,3,6110,83097,4,6485,83814,5,6860,83815,1,6860,83815,50,6860,83815,40,6860,83848,0,6860,94368,3,7623,95440,4,7986,96404,5,8361,96405,5,8361,96405,1,8361,96405,50,8361,96405,40,8361,96438,0,8361,156874,3,12265,158062,4,14213,158257,1,16162,158257,50,16164,158257,40,16164,158290,0,16164,213392,3,18716,214167,4,19990,214762,1,21265,214762,50,21267,214762,40,21267,214795,0,21267,260453,3,22769,261116,4,23518,261807,5,24268,261808,1,24268,261808,50,24270,261808,40,24270,261841,0,24270,274773,3,25026,275677,4,25396,276671,5,25771,276671,1,25771,276671,50,25771,276671,40,25771,276704,0,25771,313628,3,26973,314294,4,27572,314805,5,28172,314806,1,28172,314806,50,28173,314806,40,28173,314839,0,28173,341657,3,28924,342243,4,29299,342702,5,29674,342703,1,29674,342703,50,29675,342703,40,29675,342703,40,29675,342732,0,29675,342853,50,29675,342882,0,29675,343063,50,29677,343063,30,29677,343063,40,29677,343092,0,29683,343166,50,29683,343195,0,29683,343296,50,29684,343296,30,29684,343296,40,29684,343325,0,29684,343431,50,29685,343460,0,29689,343628,50,29690,343628,30,29690,343628,40,29690,343657,0,29690,343763,50,29690,343792,0,29696,343954,50,29699,343983,0,29699,344153,50,29703,344182,0,29703,344360,50,29709,344389,0,29713,344573,50,29722,344602,0,29722,344794,50,29739,344823,0,29743,345023,50,29773,345052,0,29773,345262,50,29836,345291,0,29836,345511,50,29954,345511,40,29954,345540,0,29954,345630,50,29954,345630,30,29954,345630,40,29954,345659,0,29954,345765,50,29955,345794,0,29959,345956,50,29962,345985,0,29962,346155,50,29966,346184,0,29966,346362,50,29972,346391,0,29977,346575,50,29986,346604,0,29986,346796,50,30002,346825,0,30007,347025,50,30036,347054,0,30036,347264,50,30100,347293,0,30100,347513,50,30218,347513,40,30218,347542,0,30218,347725,50,30218,347725,30,30218,347725,40,30218,347754,0,30218,347835,50,30219,347864,0,30223,347978,50,30224,348007,0,30224,348129,50,30227,348158,0,30227,348288,50,30232,348317,0,30236,348453,50,30244,348482,0,30244,348626,50,30257,348655,0,30261,348807,50,30287,348836,0,30287,348998,50,30345,349027,0,30345,349199,50,30454,349199,40,30454,349228,0,30454)
%
%
% START OF PROOF
% 349100 [?] ?
% 349201 [] equal(multiply(identity,X),X).
% 349202 [] equal(multiply(inverse(X),X),identity).
% 349203 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 349204 [] -equal(multiply(sk_c6,sk_c7),sk_c5).
% 349210 [?] ?
% 349216 [?] ?
% 349222 [?] ?
% 349228 [?] ?
% 349247 [input:349210,cut:349204] equal(inverse(sk_c1),sk_c6).
% 349248 [para:349247.1.1,349202.1.1.1] equal(multiply(sk_c6,sk_c1),identity).
% 349260 [input:349222,cut:349204] equal(inverse(sk_c6),sk_c5).
% 349261 [para:349260.1.1,349202.1.1.1] equal(multiply(sk_c5,sk_c6),identity).
% 349272 [input:349216,cut:349204] equal(multiply(sk_c1,sk_c6),sk_c5).
% 349276 [input:349228,cut:349204] equal(multiply(sk_c6,sk_c5),sk_c7).
% 349281 [para:349248.1.1,349203.1.1.1,demod:349201] equal(X,multiply(sk_c6,multiply(sk_c1,X))).
% 349289 [para:349261.1.1,349203.1.1.1,demod:349201] equal(X,multiply(sk_c5,multiply(sk_c6,X))).
% 349313 [para:349272.1.1,349281.1.2.2] equal(sk_c6,multiply(sk_c6,sk_c5)).
% 349319 [para:349313.1.2,349276.1.1] equal(sk_c6,sk_c7).
% 349334 [para:349319.1.1,349261.1.1.2] equal(multiply(sk_c5,sk_c7),identity).
% 349360 [para:349276.1.1,349289.1.2.2,demod:349334] equal(sk_c5,identity).
% 349365 [para:349360.1.1,349261.1.1.1,demod:349201] equal(sk_c6,identity).
% 349374 [para:349365.1.1,349204.1.1.1,demod:349201,cut:349100] 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: 32937
% derived clauses: 6075817
% kept clauses: 292470
% kept size sum: 903975
% kept mid-nuclei: 14178
% kept new demods: 5532
% forw unit-subs: 1846080
% forw double-subs: 3531592
% forw overdouble-subs: 349509
% backward subs: 10925
% fast unit cutoff: 11743
% full unit cutoff: 0
% dbl unit cutoff: 12882
% real runtime : 306.28
% process. runtime: 304.55
% specific non-discr-tree subsumption statistics:
% tried: 39661142
% length fails: 4443206
% strength fails: 9678559
% predlist fails: 1981201
% aux str. fails: 7212483
% by-lit fails: 8822337
% full subs tried: 1187124
% full subs fail: 1091148
%
% ; 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/GRP363-1+eq_r.in")
%
%------------------------------------------------------------------------------