TSTP Solution File: GRP241-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP241-1 : 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 : art10.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 289.2s
% Output : Assurance 289.2s
% 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/GRP241-1+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 23)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 23)
% (binary-posweight-lex-big-order 30 #f 3 23)
% (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(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% was split for some strategies as:
% -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% -equal(inverse(sk_c8),sk_c7).
% -equal(inverse(sk_c7),sk_c8).
%
% 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(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968)
%
%
% START OF PROOF
% 679790 [] equal(X,X).
% 679794 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 679795 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 679796 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 679797 [?] ?
% 679800 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 679801 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 679802 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 679805 [?] ?
% 679806 [?] ?
% 679807 [?] ?
% 679880 [hyper:679794,679796,679795,binarycut:679797] equal(inverse(sk_c2),sk_c8).
% 679897 [hyper:679794,679800,demod:679880,cut:679790,binarycut:679805] equal(inverse(sk_c5),sk_c8).
% 679921 [hyper:679794,679801,demod:679880,cut:679790,binarycut:679806] equal(multiply(sk_c5,sk_c8),sk_c6).
% 679939 [hyper:679794,679802,demod:679880,cut:679790,binarycut:679807] equal(multiply(sk_c8,sk_c6),sk_c7).
% 679951 [hyper:679794,679939,679921,demod:679897,cut:679790] 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968,679950,50,28968,679950,30,28968,679950,40,28968,679990,0,28968)
%
%
% START OF PROOF
% 679952 [] equal(multiply(identity,X),X).
% 679953 [] equal(multiply(inverse(X),X),identity).
% 679954 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 679955 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c8).
% 679959 [?] ?
% 679960 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 679964 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 679965 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c4),sk_c8).
% 679969 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 679970 [] equal(multiply(sk_c8,sk_c3),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 679974 [?] ?
% 679975 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 679979 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(multiply(sk_c4,sk_c7),sk_c8).
% 679980 [] equal(multiply(sk_c1,sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 679984 [?] ?
% 679985 [] equal(inverse(sk_c7),sk_c8) | equal(inverse(sk_c4),sk_c8).
% 679989 [?] ?
% 679990 [] equal(inverse(sk_c8),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 679997 [hyper:679955,679960,binarycut:679959] equal(inverse(sk_c2),sk_c8).
% 680000 [para:679997.1.1,679953.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 680010 [hyper:679955,679975,binarycut:679974] equal(inverse(sk_c1),sk_c7).
% 680011 [para:680010.1.1,679953.1.1.1] equal(multiply(sk_c7,sk_c1),identity).
% 680021 [hyper:679955,679985,binarycut:679984] equal(inverse(sk_c7),sk_c8).
% 680031 [hyper:679955,679990,binarycut:679989] equal(inverse(sk_c8),sk_c7).
% 680033 [para:680031.1.1,679953.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 680045 [hyper:679955,679964,679965] equal(multiply(sk_c2,sk_c8),sk_c3).
% 680060 [hyper:679955,679969,679970] equal(multiply(sk_c8,sk_c3),sk_c7).
% 680070 [hyper:679955,679979,679980] equal(multiply(sk_c1,sk_c7),sk_c8).
% 680074 [para:679953.1.1,679954.1.1.1,demod:679952] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 680075 [para:680000.1.1,679954.1.1.1,demod:679952] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 680082 [para:680045.1.1,680075.1.2.2,demod:680060] equal(sk_c8,sk_c7).
% 680090 [para:680011.1.1,680074.1.2.2,demod:680021] equal(sk_c1,multiply(sk_c8,identity)).
% 680092 [para:680033.1.1,680074.1.2.2,demod:680090,680021] equal(sk_c8,sk_c1).
% 680094 [para:680070.1.1,680074.1.2.2,demod:680033,680010] equal(sk_c7,identity).
% 680102 [para:680092.1.1,680082.1.1] equal(sk_c1,sk_c7).
% 680105 [para:680094.1.1,680021.1.1.1] equal(inverse(identity),sk_c8).
% 680116 [para:680102.1.2,680021.1.1.1,demod:680010] equal(sk_c7,sk_c8).
% 680130 [hyper:679955,680105,demod:679952,cut:680116] 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 23
% 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(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968,679950,50,28968,679950,30,28968,679950,40,28968,679990,0,28968,680129,50,28968,680129,30,28968,680129,40,28968,680169,0,28973)
%
%
% START OF PROOF
% 680130 [] equal(X,X).
% 680134 [] -equal(multiply(sk_c8,X),sk_c7) | -equal(multiply(Y,sk_c8),X) | -equal(inverse(Y),sk_c8).
% 680135 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 680136 [] equal(multiply(sk_c5,sk_c8),sk_c6) | equal(inverse(sk_c2),sk_c8).
% 680137 [?] ?
% 680140 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 680141 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c6).
% 680142 [] equal(multiply(sk_c2,sk_c8),sk_c3) | equal(multiply(sk_c8,sk_c6),sk_c7).
% 680145 [?] ?
% 680146 [?] ?
% 680147 [?] ?
% 680220 [hyper:680134,680136,680135,binarycut:680137] equal(inverse(sk_c2),sk_c8).
% 680237 [hyper:680134,680140,demod:680220,cut:680130,binarycut:680145] equal(inverse(sk_c5),sk_c8).
% 680261 [hyper:680134,680141,demod:680220,cut:680130,binarycut:680146] equal(multiply(sk_c5,sk_c8),sk_c6).
% 680279 [hyper:680134,680142,demod:680220,cut:680130,binarycut:680147] equal(multiply(sk_c8,sk_c6),sk_c7).
% 680291 [hyper:680134,680279,680261,demod:680237,cut:680130] 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 23
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968,679950,50,28968,679950,30,28968,679950,40,28968,679990,0,28968,680129,50,28968,680129,30,28968,680129,40,28968,680169,0,28973,680290,50,28973,680290,30,28973,680290,40,28973,680330,0,28973,680435,50,28974,680475,0,28974)
%
%
% START OF PROOF
% 680369 [?] ?
% 680440 [] -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 680459 [] equal(multiply(sk_c4,sk_c7),sk_c8) | equal(inverse(sk_c1),sk_c7).
% 680460 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c8).
% 680464 [?] ?
% 680465 [?] ?
% 680485 [hyper:680440,680460,binarycut:680465] equal(inverse(sk_c4),sk_c8).
% 680506 [hyper:680440,680459,binarycut:680464] equal(multiply(sk_c4,sk_c7),sk_c8).
% 680510 [hyper:680440,680506,demod:680485,cut:680369] 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 23
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(sk_c8),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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968,679950,50,28968,679950,30,28968,679950,40,28968,679990,0,28968,680129,50,28968,680129,30,28968,680129,40,28968,680169,0,28973,680290,50,28973,680290,30,28973,680290,40,28973,680330,0,28973,680435,50,28974,680475,0,28974,680509,50,28975,680509,30,28975,680509,40,28975,680549,0,28979,680663,50,28980,680703,0,28980,680855,50,28983,680895,0,28987,681055,50,28991,681095,0,28991,681263,50,28997,681303,0,28997,681477,50,29005,681517,0,29010,681699,50,29025,681739,0,29025,681929,50,29054,681969,0,29058,682169,50,29115,682209,0,29115,682419,50,29231,682419,40,29231,682459,0,29231)
%
%
% START OF PROOF
% 682421 [] equal(multiply(identity,X),X).
% 682422 [] equal(multiply(inverse(X),X),identity).
% 682423 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 682424 [] -equal(inverse(sk_c8),sk_c7).
% 682450 [] equal(inverse(sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 682455 [?] ?
% 682456 [?] ?
% 682457 [?] ?
% 682458 [?] ?
% 682459 [?] ?
% 682482 [input:682455,cut:682424] equal(inverse(sk_c5),sk_c8).
% 682483 [para:682482.1.1,682422.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 682484 [input:682459,cut:682424] equal(inverse(sk_c4),sk_c8).
% 682485 [para:682484.1.1,682422.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 682508 [input:682456,cut:682424] equal(multiply(sk_c5,sk_c8),sk_c6).
% 682509 [input:682457,cut:682424] equal(multiply(sk_c8,sk_c6),sk_c7).
% 682510 [input:682458,cut:682424] equal(multiply(sk_c4,sk_c7),sk_c8).
% 682524 [para:682422.1.1,682423.1.1.1,demod:682421] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 682527 [para:682483.1.1,682423.1.1.1,demod:682421] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 682528 [para:682485.1.1,682423.1.1.1,demod:682421] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 682547 [para:682509.1.1,682423.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 682566 [para:682508.1.1,682527.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 682571 [para:682566.1.2,682509.1.1] equal(sk_c8,sk_c7).
% 682572 [para:682566.1.2,682423.1.1.1,demod:682547] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 682573 [para:682571.1.1,682424.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 682599 [para:682450.1.1,682573.1.1,cut:682571] equal(inverse(sk_c5),sk_c8).
% 682608 [para:682510.1.1,682528.1.2.2,demod:682572] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 682626 [para:682608.1.2,682524.1.2.2,demod:682422] equal(sk_c8,identity).
% 682640 [para:682626.1.1,682483.1.1.1,demod:682421] equal(sk_c5,identity).
% 682648 [para:682626.1.1,682571.1.1] equal(identity,sk_c7).
% 682656 [para:682640.1.1,682599.1.1.1] equal(inverse(identity),sk_c8).
% 682659 [para:682648.1.2,682573.1.1.1,demod:682656,cut:682571] 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(inverse(sk_c8),sk_c7) | -equal(inverse(sk_c7),sk_c8) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c8,Y),sk_c7) | -equal(multiply(Z,sk_c8),Y) | -equal(inverse(Z),sk_c8) | -equal(inverse(U),sk_c8) | -equal(multiply(U,sk_c7),sk_c8) | -equal(multiply(sk_c8,V),sk_c7) | -equal(multiply(W,sk_c8),V) | -equal(inverse(W),sk_c8).
% Split part used next: -equal(inverse(sk_c7),sk_c8).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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 23
% 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(40,40,0,85,0,0,365165,5,1501,365165,1,1501,365165,50,1501,365165,40,1501,365210,0,1501,377248,3,1802,377904,4,1952,378565,1,2102,378565,50,2102,378565,40,2102,378610,0,2102,379005,3,2404,379015,4,2562,379023,5,2703,379023,1,2703,379023,50,2703,379023,40,2703,379068,0,2703,394066,3,4206,396166,4,4954,397163,50,5129,397163,40,5129,397208,0,5129,407112,3,5880,408580,50,6154,408580,40,6154,408625,0,6154,425865,3,6905,425924,4,7280,426013,5,7655,426014,1,7655,426014,50,7655,426014,40,7655,426059,0,7655,524697,3,11558,525564,4,13507,526092,5,15456,526093,1,15456,526093,50,15459,526093,40,15459,526138,0,15459,576415,3,18013,577294,4,19285,577962,5,20560,577963,1,20560,577963,50,20562,577963,40,20562,578008,0,20562,616354,3,22064,617079,4,22813,617806,1,23563,617806,50,23565,617806,40,23565,617851,0,23565,634699,3,24316,635512,4,24691,636230,5,25066,636231,1,25066,636231,50,25066,636231,40,25066,636276,0,25066,659680,3,26268,660320,4,26867,661030,5,27467,661031,1,27467,661031,50,27467,661031,40,27467,661076,0,27467,678646,3,28218,679280,4,28593,679789,1,28968,679789,50,28968,679789,40,28968,679789,40,28968,679829,0,28968,679950,50,28968,679950,30,28968,679950,40,28968,679990,0,28968,680129,50,28968,680129,30,28968,680129,40,28968,680169,0,28973,680290,50,28973,680290,30,28973,680290,40,28973,680330,0,28973,680435,50,28974,680475,0,28974,680509,50,28975,680509,30,28975,680509,40,28975,680549,0,28979,680663,50,28980,680703,0,28980,680855,50,28983,680895,0,28987,681055,50,28991,681095,0,28991,681263,50,28997,681303,0,28997,681477,50,29005,681517,0,29010,681699,50,29025,681739,0,29025,681929,50,29054,681969,0,29058,682169,50,29115,682209,0,29115,682419,50,29231,682419,40,29231,682459,0,29231,682658,50,29231,682658,30,29231,682658,40,29231,682698,0,29231,682812,50,29232,682852,0,29237,683004,50,29239,683044,0,29239,683204,50,29243,683244,0,29243,683412,50,29249,683452,0,29253,683626,50,29262,683666,0,29262,683848,50,29277,683888,0,29282,684078,50,29310,684118,0,29311,684318,50,29372,684358,0,29372,684568,50,29487,684568,40,29487,684608,0,29487)
%
%
% START OF PROOF
% 684455 [?] ?
% 684570 [] equal(multiply(identity,X),X).
% 684571 [] equal(multiply(inverse(X),X),identity).
% 684572 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 684573 [] -equal(inverse(sk_c7),sk_c8).
% 684599 [?] ?
% 684600 [?] ?
% 684601 [?] ?
% 684602 [?] ?
% 684603 [?] ?
% 684623 [input:684599,cut:684573] equal(inverse(sk_c5),sk_c8).
% 684624 [para:684623.1.1,684571.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 684627 [input:684603,cut:684573] equal(inverse(sk_c4),sk_c8).
% 684628 [para:684627.1.1,684571.1.1.1] equal(multiply(sk_c8,sk_c4),identity).
% 684648 [input:684600,cut:684573] equal(multiply(sk_c5,sk_c8),sk_c6).
% 684649 [input:684601,cut:684573] equal(multiply(sk_c8,sk_c6),sk_c7).
% 684651 [input:684602,cut:684573] equal(multiply(sk_c4,sk_c7),sk_c8).
% 684673 [para:684571.1.1,684572.1.1.1,demod:684570] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 684675 [para:684624.1.1,684572.1.1.1,demod:684570] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 684677 [para:684628.1.1,684572.1.1.1,demod:684570] equal(X,multiply(sk_c8,multiply(sk_c4,X))).
% 684691 [para:684649.1.1,684572.1.1.1] equal(multiply(sk_c7,X),multiply(sk_c8,multiply(sk_c6,X))).
% 684712 [para:684648.1.1,684675.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c6)).
% 684715 [para:684712.1.2,684649.1.1] equal(sk_c8,sk_c7).
% 684716 [para:684712.1.2,684572.1.1.1,demod:684691] equal(multiply(sk_c8,X),multiply(sk_c7,X)).
% 684737 [para:684651.1.1,684677.1.2.2,demod:684716] equal(sk_c7,multiply(sk_c7,sk_c8)).
% 684739 [para:684715.1.1,684737.1.2.2] equal(sk_c7,multiply(sk_c7,sk_c7)).
% 684754 [para:684739.1.2,684673.1.2.2,demod:684571] equal(sk_c7,identity).
% 684774 [para:684754.1.1,684573.1.1.1,cut:684455] 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: 38516
% derived clauses: 5225358
% kept clauses: 258860
% kept size sum: 866387
% kept mid-nuclei: 291674
% kept new demods: 3230
% forw unit-subs: 1191645
% forw double-subs: 2975699
% forw overdouble-subs: 254690
% backward subs: 30506
% fast unit cutoff: 24191
% full unit cutoff: 0
% dbl unit cutoff: 78094
% real runtime : 296.1
% process. runtime: 294.87
% specific non-discr-tree subsumption statistics:
% tried: 27325756
% length fails: 2643414
% strength fails: 10966121
% predlist fails: 2456692
% aux str. fails: 3464597
% by-lit fails: 2775527
% full subs tried: 1394279
% full subs fail: 1259560
%
% ; 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/GRP241-1+eq_r.in")
%
%------------------------------------------------------------------------------