TSTP Solution File: GRP317-1 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP317-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art05.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 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/GRP317-1+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 29)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 29)
% (binary-posweight-lex-big-order 30 #f 3 29)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% was split for some strategies as:
% -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8).
% -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U).
% -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8).
% -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% -equal(multiply(sk_c8,sk_c9),sk_c7).
% -equal(multiply(sk_c9,sk_c7),sk_c8).
% -equal(multiply(sk_c8,sk_c7),sk_c9).
% -equal(inverse(sk_c8),sk_c7).
%
% Starting a split proof attempt with 9 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504)
%
%
% START OF PROOF
% 379656 [] equal(multiply(identity,X),X).
% 379657 [] equal(multiply(inverse(X),X),identity).
% 379658 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 379659 [] -equal(multiply(X,sk_c9),sk_c7) | -equal(inverse(X),sk_c9).
% 379660 [] equal(multiply(sk_c4,sk_c9),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 379661 [] equal(multiply(sk_c4,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 379666 [] equal(inverse(sk_c3),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 379667 [?] ?
% 379672 [] equal(inverse(sk_c4),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 379673 [?] ?
% 379678 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 379679 [?] ?
% 379684 [] equal(multiply(sk_c2,sk_c8),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 379685 [] equal(multiply(sk_c2,sk_c8),sk_c9) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 379696 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 379697 [?] ?
% 379702 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c6),sk_c9).
% 379703 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 379708 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c6),sk_c9).
% 379709 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 379717 [hyper:379659,379666,binarycut:379667] equal(inverse(sk_c3),sk_c9).
% 379719 [para:379717.1.1,379657.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 379723 [hyper:379659,379672,binarycut:379673] equal(inverse(sk_c4),sk_c3).
% 379724 [para:379723.1.1,379657.1.1.1] equal(multiply(sk_c3,sk_c4),identity).
% 379727 [hyper:379659,379678,binarycut:379679] equal(inverse(sk_c2),sk_c8).
% 379731 [para:379727.1.1,379657.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 379735 [hyper:379659,379696,binarycut:379697] equal(inverse(sk_c1),sk_c9).
% 379738 [para:379735.1.1,379657.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 379742 [hyper:379659,379661,379660] equal(multiply(sk_c4,sk_c9),sk_c3).
% 379748 [hyper:379659,379685,379684] equal(multiply(sk_c2,sk_c8),sk_c9).
% 379762 [hyper:379659,379703,379702] equal(multiply(sk_c1,sk_c9),sk_c8).
% 379771 [hyper:379659,379709,379708] equal(multiply(sk_c8,sk_c9),sk_c7).
% 379775 [para:379657.1.1,379658.1.1.1,demod:379656] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 379776 [para:379719.1.1,379658.1.1.1,demod:379656] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 379777 [para:379724.1.1,379658.1.1.1,demod:379656] equal(X,multiply(sk_c3,multiply(sk_c4,X))).
% 379778 [para:379731.1.1,379658.1.1.1,demod:379656] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 379779 [para:379738.1.1,379658.1.1.1,demod:379656] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 379787 [para:379742.1.1,379777.1.2.2] equal(sk_c9,multiply(sk_c3,sk_c3)).
% 379789 [para:379748.1.1,379778.1.2.2,demod:379771] equal(sk_c8,sk_c7).
% 379797 [para:379776.1.2,379775.1.2.2] equal(multiply(sk_c3,X),multiply(inverse(sk_c9),X)).
% 379801 [para:379789.1.1,379771.1.1.1] equal(multiply(sk_c7,sk_c9),sk_c7).
% 379803 [para:379779.1.2,379775.1.2.2,demod:379797] equal(multiply(sk_c1,X),multiply(sk_c3,X)).
% 379819 [para:379801.1.1,379775.1.2.2,demod:379657] equal(sk_c9,identity).
% 379820 [para:379819.1.1,379719.1.1.1,demod:379656] equal(sk_c3,identity).
% 379824 [para:379819.1.1,379762.1.1.2] equal(multiply(sk_c1,identity),sk_c8).
% 379830 [para:379820.1.1,379717.1.1.1] equal(inverse(identity),sk_c9).
% 379831 [para:379820.1.1,379787.1.2.2,demod:379824,379803] equal(sk_c9,sk_c8).
% 379843 [para:379831.1.2,379789.1.1] equal(sk_c9,sk_c7).
% 379884 [hyper:379659,379830,demod:379656,cut:379843] 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),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 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504)
%
%
% START OF PROOF
% 379884 [] equal(X,X).
% 379888 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 379909 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 379910 [?] ?
% 379915 [?] ?
% 379916 [] equal(multiply(sk_c2,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 379961 [hyper:379888,379909,binarycut:379915] equal(inverse(sk_c5),sk_c8).
% 379963 [hyper:379888,379909,binarycut:379910] equal(inverse(sk_c2),sk_c8).
% 379976 [hyper:379888,379916,demod:379963,cut:379884] equal(multiply(sk_c5,sk_c8),sk_c9).
% 379978 [hyper:379888,379976,demod:379961,cut:379884] 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U).
% 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510)
%
%
% START OF PROOF
% 379979 [] equal(multiply(identity,X),X).
% 379980 [] equal(multiply(inverse(X),X),identity).
% 379981 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 379982 [] -equal(multiply(X,sk_c9),Y) | -equal(inverse(Y),sk_c9) | -equal(inverse(X),Y).
% 379983 [?] ?
% 379984 [] equal(multiply(sk_c4,sk_c9),sk_c3) | equal(multiply(sk_c6,sk_c9),sk_c7).
% 379985 [?] ?
% 379986 [] equal(multiply(sk_c4,sk_c9),sk_c3) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 379987 [?] ?
% 379988 [] equal(multiply(sk_c4,sk_c9),sk_c3) | equal(multiply(sk_c8,sk_c7),sk_c9).
% 379989 [] equal(inverse(sk_c3),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 379990 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c9).
% 379991 [] equal(inverse(sk_c3),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 379992 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 379993 [] equal(inverse(sk_c3),sk_c9) | equal(inverse(sk_c8),sk_c7).
% 379994 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 379995 [] equal(inverse(sk_c4),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 379996 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c4),sk_c3).
% 379997 [] equal(inverse(sk_c4),sk_c3) | equal(inverse(sk_c5),sk_c8).
% 379998 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c4),sk_c3).
% 379999 [] equal(inverse(sk_c4),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 380000 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c4),sk_c3).
% 380069 [hyper:379982,379995,binarycut:379983,binarycut:379989] equal(inverse(sk_c6),sk_c9).
% 380076 [para:380069.1.1,379980.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 380090 [hyper:379982,379997,binarycut:379985,binarycut:379991] equal(inverse(sk_c5),sk_c8).
% 380094 [para:380090.1.1,379980.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 380098 [hyper:379982,379999,binarycut:379987,binarycut:379993] equal(inverse(sk_c8),sk_c7).
% 380105 [para:380098.1.1,379980.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 380149 [hyper:379982,379996,379990,binarycut:379984] equal(multiply(sk_c6,sk_c9),sk_c7).
% 380156 [hyper:379982,379998,379992,binarycut:379986] equal(multiply(sk_c5,sk_c8),sk_c9).
% 380160 [hyper:379982,380000,379994,binarycut:379988] equal(multiply(sk_c8,sk_c7),sk_c9).
% 380161 [para:379980.1.1,379981.1.1.1,demod:379979] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 380162 [para:380076.1.1,379981.1.1.1,demod:379979] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 380166 [para:380156.1.1,379981.1.1.1] equal(multiply(sk_c9,X),multiply(sk_c5,multiply(sk_c8,X))).
% 380172 [para:380149.1.1,380162.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 380179 [para:380094.1.1,380161.1.2.2,demod:380098] equal(sk_c5,multiply(sk_c7,identity)).
% 380181 [para:380156.1.1,380161.1.2.2,demod:380090] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 380182 [para:380160.1.1,380161.1.2.2,demod:380098] equal(sk_c7,multiply(sk_c7,sk_c9)).
% 380185 [para:380179.1.2,379981.1.1.1,demod:379979] equal(multiply(sk_c5,X),multiply(sk_c7,X)).
% 380188 [para:380181.1.2,380161.1.2.2,demod:380105,380098] equal(sk_c9,identity).
% 380192 [para:380188.1.1,380172.1.2.1,demod:379979] equal(sk_c9,sk_c7).
% 380205 [para:380192.1.1,380181.1.2.2,demod:380160] equal(sk_c8,sk_c9).
% 380210 [para:380205.1.1,380098.1.1.1] equal(inverse(sk_c9),sk_c7).
% 380211 [para:380205.1.1,380156.1.1.2,demod:380182,380185] equal(sk_c7,sk_c9).
% 380220 [hyper:379982,380166,demod:380210,380156,380181,cut:380211,cut:380211] 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),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 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510)
%
%
% START OF PROOF
% 380220 [] equal(X,X).
% 380224 [] -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c8).
% 380245 [] equal(inverse(sk_c2),sk_c8) | equal(inverse(sk_c5),sk_c8).
% 380246 [?] ?
% 380251 [?] ?
% 380252 [] equal(multiply(sk_c2,sk_c8),sk_c9) | equal(multiply(sk_c5,sk_c8),sk_c9).
% 380297 [hyper:380224,380245,binarycut:380251] equal(inverse(sk_c5),sk_c8).
% 380299 [hyper:380224,380245,binarycut:380246] equal(inverse(sk_c2),sk_c8).
% 380312 [hyper:380224,380252,demod:380299,cut:380220] equal(multiply(sk_c5,sk_c8),sk_c9).
% 380314 [hyper:380224,380312,demod:380297,cut:380220] 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510,380313,50,29510,380313,30,29510,380313,40,29510,380372,0,29515)
%
%
% START OF PROOF
% 380315 [] equal(multiply(identity,X),X).
% 380316 [] equal(multiply(inverse(X),X),identity).
% 380317 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 380318 [] -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 380355 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c6),sk_c9).
% 380356 [] equal(multiply(sk_c6,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c9).
% 380357 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c8).
% 380358 [] equal(multiply(sk_c5,sk_c8),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 380359 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c8),sk_c7).
% 380360 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c1),sk_c9).
% 380361 [?] ?
% 380362 [?] ?
% 380363 [?] ?
% 380364 [?] ?
% 380365 [?] ?
% 380366 [?] ?
% 380397 [hyper:380318,380355,binarycut:380361] equal(inverse(sk_c6),sk_c9).
% 380401 [para:380397.1.1,380316.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 380406 [hyper:380318,380357,binarycut:380363] equal(inverse(sk_c5),sk_c8).
% 380407 [para:380406.1.1,380316.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 380410 [hyper:380318,380359,binarycut:380365] equal(inverse(sk_c8),sk_c7).
% 380412 [para:380410.1.1,380316.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 380431 [hyper:380318,380356,binarycut:380362] equal(multiply(sk_c6,sk_c9),sk_c7).
% 380435 [hyper:380318,380358,binarycut:380364] equal(multiply(sk_c5,sk_c8),sk_c9).
% 380438 [hyper:380318,380360,binarycut:380366] equal(multiply(sk_c8,sk_c7),sk_c9).
% 380439 [para:380316.1.1,380317.1.1.1,demod:380315] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 380440 [para:380401.1.1,380317.1.1.1,demod:380315] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 380441 [para:380407.1.1,380317.1.1.1,demod:380315] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 380446 [para:380431.1.1,380440.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 380448 [para:380435.1.1,380441.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 380457 [para:380448.1.2,380439.1.2.2,demod:380412,380410] equal(sk_c9,identity).
% 380458 [para:380457.1.1,380401.1.1.1,demod:380315] equal(sk_c6,identity).
% 380461 [para:380457.1.1,380446.1.2.1,demod:380315] equal(sk_c9,sk_c7).
% 380463 [para:380458.1.1,380397.1.1.1] equal(inverse(identity),sk_c9).
% 380465 [para:380458.1.1,380440.1.2.2.1,demod:380315] equal(X,multiply(sk_c9,X)).
% 380468 [para:380461.1.1,380448.1.2.2,demod:380438] equal(sk_c8,sk_c9).
% 380471 [para:380468.1.1,380407.1.1.1,demod:380465] equal(sk_c5,identity).
% 380477 [para:380471.1.1,380406.1.1.1,demod:380463] equal(sk_c9,sk_c8).
% 380484 [hyper:380318,380463,demod:380315,cut:380477] 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c8,sk_c9),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 29
% clause depth limited to 3
% seconds given: 2
%
%
% 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 29
% clause depth limited to 4
% seconds given: 2
%
%
% 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 29
% clause depth limited to 5
% seconds given: 2
%
%
% 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 29
% clause depth limited to 6
% seconds given: 2
%
%
% 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 29
% clause depth limited to 7
% seconds given: 2
%
%
% 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 29
% clause depth limited to 8
% seconds given: 2
%
%
% 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 29
% clause depth limited to 9
% seconds given: 2
%
%
% 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 29
% clause depth limited to 10
% seconds given: 2
%
%
% 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(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510,380313,50,29510,380313,30,29510,380313,40,29510,380372,0,29515,380483,50,29515,380483,30,29515,380483,40,29515,380542,0,29515,380669,50,29516,380728,0,29520,380899,50,29523,380958,0,29523,381137,50,29527,381196,0,29531,381387,50,29537,381446,0,29538,381644,50,29547,381703,0,29552,381909,50,29568,381968,0,29568,382183,50,29600,382242,0,29604,382467,50,29667,382467,40,29667,382526,0,29667)
%
%
% START OF PROOF
% 382348 [?] ?
% 382469 [] equal(multiply(identity,X),X).
% 382470 [] equal(multiply(inverse(X),X),identity).
% 382471 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 382472 [] -equal(multiply(sk_c8,sk_c9),sk_c7).
% 382523 [?] ?
% 382524 [?] ?
% 382620 [input:382523,cut:382472] equal(inverse(sk_c5),sk_c8).
% 382621 [para:382620.1.1,382470.1.1.1] equal(multiply(sk_c8,sk_c5),identity).
% 382642 [input:382524,cut:382472] equal(multiply(sk_c5,sk_c8),sk_c9).
% 382685 [para:382621.1.1,382471.1.1.1,demod:382469] equal(X,multiply(sk_c8,multiply(sk_c5,X))).
% 382737 [para:382642.1.1,382685.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 382738 [para:382737.1.2,382472.1.1,cut:382348] 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_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c9,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 29
% clause depth limited to 3
% seconds given: 2
%
%
% 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 29
% clause depth limited to 4
% seconds given: 2
%
%
% 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 29
% clause depth limited to 5
% seconds given: 2
%
%
% 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 29
% clause depth limited to 6
% seconds given: 2
%
%
% 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 29
% clause depth limited to 7
% seconds given: 2
%
%
% 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 29
% clause depth limited to 8
% seconds given: 2
%
%
% 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 29
% clause depth limited to 9
% seconds given: 2
%
%
% 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 29
% clause depth limited to 10
% seconds given: 2
%
%
% 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(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510,380313,50,29510,380313,30,29510,380313,40,29510,380372,0,29515,380483,50,29515,380483,30,29515,380483,40,29515,380542,0,29515,380669,50,29516,380728,0,29520,380899,50,29523,380958,0,29523,381137,50,29527,381196,0,29531,381387,50,29537,381446,0,29538,381644,50,29547,381703,0,29552,381909,50,29568,381968,0,29568,382183,50,29600,382242,0,29604,382467,50,29667,382467,40,29667,382526,0,29667,382737,50,29668,382737,30,29668,382737,40,29668,382796,0,29673,382923,50,29674,382982,0,29674,383153,50,29676,383212,0,29681,383391,50,29685,383450,0,29685,383641,50,29691,383700,0,29695,383898,50,29704,383957,0,29704,384163,50,29721,384222,0,29726,384437,50,29758,384496,0,29758,384721,50,29824,384721,40,29824,384780,0,29825)
%
%
% START OF PROOF
% 384607 [?] ?
% 384723 [] equal(multiply(identity,X),X).
% 384724 [] equal(multiply(inverse(X),X),identity).
% 384725 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 384726 [] -equal(multiply(sk_c9,sk_c7),sk_c8).
% 384757 [?] ?
% 384758 [?] ?
% 384850 [input:384757,cut:384726] equal(inverse(sk_c6),sk_c9).
% 384851 [para:384850.1.1,384724.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 384866 [input:384758,cut:384726] equal(multiply(sk_c6,sk_c9),sk_c7).
% 384917 [para:384851.1.1,384725.1.1.1,demod:384723] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 384961 [para:384866.1.1,384917.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c7)).
% 384962 [para:384961.1.2,384726.1.1,cut:384607] 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 8 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% Split part used next: -equal(multiply(sk_c8,sk_c7),sk_c9).
% 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% 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 29
% clause depth limited to 4
% seconds given: 2
%
%
% 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 29
% clause depth limited to 5
% seconds given: 2
%
%
% 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 29
% clause depth limited to 6
% seconds given: 2
%
%
% 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 29
% clause depth limited to 7
% seconds given: 2
%
%
% 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 29
% clause depth limited to 8
% seconds given: 2
%
%
% 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 29
% clause depth limited to 9
% seconds given: 2
%
%
% 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(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510,380313,50,29510,380313,30,29510,380313,40,29510,380372,0,29515,380483,50,29515,380483,30,29515,380483,40,29515,380542,0,29515,380669,50,29516,380728,0,29520,380899,50,29523,380958,0,29523,381137,50,29527,381196,0,29531,381387,50,29537,381446,0,29538,381644,50,29547,381703,0,29552,381909,50,29568,381968,0,29568,382183,50,29600,382242,0,29604,382467,50,29667,382467,40,29667,382526,0,29667,382737,50,29668,382737,30,29668,382737,40,29668,382796,0,29673,382923,50,29674,382982,0,29674,383153,50,29676,383212,0,29681,383391,50,29685,383450,0,29685,383641,50,29691,383700,0,29695,383898,50,29704,383957,0,29704,384163,50,29721,384222,0,29726,384437,50,29758,384496,0,29758,384721,50,29824,384721,40,29824,384780,0,29825,384961,50,29825,384961,30,29825,384961,40,29825,385020,0,29825,385205,50,29827,385264,0,29831,385500,50,29836,385559,0,29836,385803,50,29842,385862,0,29846,386114,50,29855,386173,0,29855,386431,50,29867,386490,0,29871,386756,50,29891,386815,0,29891,387089,50,29925,387089,40,29925,387148,0,29929)
%
%
% START OF PROOF
% 386980 [?] ?
% 387091 [] equal(multiply(identity,X),X).
% 387092 [] equal(multiply(inverse(X),X),identity).
% 387093 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 387094 [] -equal(multiply(sk_c8,sk_c7),sk_c9).
% 387106 [?] ?
% 387112 [?] ?
% 387136 [?] ?
% 387142 [?] ?
% 387196 [input:387106,cut:387094] equal(inverse(sk_c3),sk_c9).
% 387197 [para:387196.1.1,387092.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 387203 [input:387112,cut:387094] equal(inverse(sk_c4),sk_c3).
% 387204 [para:387203.1.1,387092.1.1.1] equal(multiply(sk_c3,sk_c4),identity).
% 387231 [input:387136,cut:387094] equal(inverse(sk_c1),sk_c9).
% 387232 [para:387231.1.1,387092.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 387259 [input:387142,cut:387094] equal(multiply(sk_c1,sk_c9),sk_c8).
% 387279 [para:387197.1.1,387093.1.1.1,demod:387091] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 387282 [para:387204.1.1,387093.1.1.1,demod:387091] equal(X,multiply(sk_c3,multiply(sk_c4,X))).
% 387300 [para:387232.1.1,387093.1.1.1,demod:387091] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 387337 [para:387204.1.1,387279.1.2.2] equal(sk_c4,multiply(sk_c9,identity)).
% 387338 [para:387337.1.2,387093.1.1.1,demod:387091] equal(multiply(sk_c4,X),multiply(sk_c9,X)).
% 387406 [para:387259.1.1,387300.1.2.2,demod:387338] equal(sk_c9,multiply(sk_c4,sk_c8)).
% 387408 [para:387406.1.2,387282.1.2.2] equal(sk_c8,multiply(sk_c3,sk_c9)).
% 387410 [para:387408.1.2,387093.1.1.1,demod:387282,387338] equal(multiply(sk_c8,X),X).
% 387411 [para:387410.1.1,387094.1.1,cut:386980] 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 9 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(multiply(sk_c8,sk_c9),sk_c7) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(Y,sk_c8),sk_c9) | -equal(inverse(Y),sk_c8) | -equal(inverse(Z),U) | -equal(inverse(U),sk_c9) | -equal(multiply(Z,sk_c9),U) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c8),sk_c7) | -equal(multiply(V,sk_c8),sk_c9) | -equal(inverse(V),sk_c8) | -equal(multiply(W,sk_c9),sk_c7) | -equal(inverse(W),sk_c9).
% 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 29
% clause depth limited to 3
% seconds given: 2
%
%
% 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 29
% clause depth limited to 4
% seconds given: 2
%
%
% 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 29
% clause depth limited to 5
% seconds given: 2
%
%
% 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 29
% clause depth limited to 6
% seconds given: 2
%
%
% 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 29
% clause depth limited to 7
% seconds given: 2
%
%
% 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 29
% clause depth limited to 8
% seconds given: 2
%
%
% 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 29
% clause depth limited to 9
% seconds given: 2
%
%
% 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 *********
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(59,40,0,124,0,1,2078,50,25,2143,0,25,5361,50,68,5426,0,68,8992,50,113,9057,0,113,13017,50,171,13082,0,171,17375,50,243,17440,0,244,22261,50,343,22326,0,343,27613,50,479,27678,0,479,33627,50,687,33692,0,688,40241,50,980,40241,40,980,40306,0,981,52772,3,1282,53445,4,1432,54047,1,1582,54047,50,1582,54047,40,1582,54112,0,1582,54675,3,1893,54694,4,2052,54718,5,2183,54718,1,2183,54718,50,2183,54718,40,2183,54783,0,2183,87007,3,3684,87795,4,4434,88622,1,5184,88622,50,5185,88622,40,5185,88687,0,5185,106416,3,5936,107254,4,6311,107912,1,6686,107912,50,6686,107912,40,6686,107977,0,6686,115298,3,7476,117468,4,7812,119442,5,8187,119443,1,8187,119443,50,8187,119443,40,8187,119508,0,8187,193928,3,12089,194767,4,14039,195401,5,15988,195402,1,15989,195402,50,15991,195402,40,15991,195467,0,15991,256216,3,18543,256973,4,19817,257371,1,21092,257371,50,21094,257371,40,21094,257436,0,21094,303648,3,22596,304281,4,23345,304861,1,24095,304861,50,24097,304861,40,24097,304926,0,24097,313873,3,24867,315056,4,25229,315415,5,25599,315415,1,25600,315415,50,25600,315415,40,25600,315480,0,25600,350462,3,26801,350912,4,27401,351336,1,28001,351336,50,28002,351336,40,28002,351401,0,28002,378870,3,28753,379290,4,29128,379654,1,29503,379654,50,29504,379654,40,29504,379654,40,29504,379713,0,29504,379883,50,29504,379883,30,29504,379883,40,29504,379942,0,29504,379977,50,29505,379977,30,29505,379977,40,29505,380036,0,29510,380219,50,29510,380219,30,29510,380219,40,29510,380278,0,29510,380313,50,29510,380313,30,29510,380313,40,29510,380372,0,29515,380483,50,29515,380483,30,29515,380483,40,29515,380542,0,29515,380669,50,29516,380728,0,29520,380899,50,29523,380958,0,29523,381137,50,29527,381196,0,29531,381387,50,29537,381446,0,29538,381644,50,29547,381703,0,29552,381909,50,29568,381968,0,29568,382183,50,29600,382242,0,29604,382467,50,29667,382467,40,29667,382526,0,29667,382737,50,29668,382737,30,29668,382737,40,29668,382796,0,29673,382923,50,29674,382982,0,29674,383153,50,29676,383212,0,29681,383391,50,29685,383450,0,29685,383641,50,29691,383700,0,29695,383898,50,29704,383957,0,29704,384163,50,29721,384222,0,29726,384437,50,29758,384496,0,29758,384721,50,29824,384721,40,29824,384780,0,29825,384961,50,29825,384961,30,29825,384961,40,29825,385020,0,29825,385205,50,29827,385264,0,29831,385500,50,29836,385559,0,29836,385803,50,29842,385862,0,29846,386114,50,29855,386173,0,29855,386431,50,29867,386490,0,29871,386756,50,29891,386815,0,29891,387089,50,29925,387089,40,29925,387148,0,29929,387410,50,29930,387410,30,29930,387410,40,29930,387469,0,29930,387660,50,29932,387719,0,29936,387961,50,29941,388020,0,29941,388270,50,29948,388329,0,29952,388587,50,29961,388646,0,29961,388910,50,29973,388969,0,29978,389241,50,29999,389300,0,29999,389580,50,30035,389580,40,30035,389639,0,30039)
%
%
% START OF PROOF
% 389582 [] equal(multiply(identity,X),X).
% 389583 [] equal(multiply(inverse(X),X),identity).
% 389584 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 389585 [] -equal(inverse(sk_c8),sk_c7).
% 389590 [?] ?
% 389596 [?] ?
% 389602 [?] ?
% 389608 [?] ?
% 389614 [?] ?
% 389626 [?] ?
% 389632 [?] ?
% 389638 [?] ?
% 389648 [input:389596,cut:389585] equal(inverse(sk_c3),sk_c9).
% 389649 [para:389648.1.1,389583.1.1.1] equal(multiply(sk_c9,sk_c3),identity).
% 389657 [input:389602,cut:389585] equal(inverse(sk_c4),sk_c3).
% 389658 [para:389657.1.1,389583.1.1.1] equal(multiply(sk_c3,sk_c4),identity).
% 389665 [input:389608,cut:389585] equal(inverse(sk_c2),sk_c8).
% 389666 [para:389665.1.1,389583.1.1.1] equal(multiply(sk_c8,sk_c2),identity).
% 389675 [input:389626,cut:389585] equal(inverse(sk_c1),sk_c9).
% 389676 [para:389675.1.1,389583.1.1.1] equal(multiply(sk_c9,sk_c1),identity).
% 389678 [input:389590,cut:389585] equal(multiply(sk_c4,sk_c9),sk_c3).
% 389693 [input:389614,cut:389585] equal(multiply(sk_c2,sk_c8),sk_c9).
% 389709 [input:389632,cut:389585] equal(multiply(sk_c1,sk_c9),sk_c8).
% 389714 [input:389638,cut:389585] equal(multiply(sk_c8,sk_c9),sk_c7).
% 389735 [para:389649.1.1,389584.1.1.1,demod:389582] equal(X,multiply(sk_c9,multiply(sk_c3,X))).
% 389738 [para:389658.1.1,389584.1.1.1,demod:389582] equal(X,multiply(sk_c3,multiply(sk_c4,X))).
% 389740 [para:389666.1.1,389584.1.1.1,demod:389582] equal(X,multiply(sk_c8,multiply(sk_c2,X))).
% 389741 [para:389676.1.1,389584.1.1.1,demod:389582] equal(X,multiply(sk_c9,multiply(sk_c1,X))).
% 389791 [para:389658.1.1,389735.1.2.2] equal(sk_c4,multiply(sk_c9,identity)).
% 389792 [para:389791.1.2,389584.1.1.1,demod:389582] equal(multiply(sk_c4,X),multiply(sk_c9,X)).
% 389797 [para:389678.1.1,389738.1.2.2] equal(sk_c9,multiply(sk_c3,sk_c3)).
% 389802 [para:389797.1.2,389735.1.2.2,demod:389792] equal(sk_c3,multiply(sk_c4,sk_c9)).
% 389806 [para:389693.1.1,389740.1.2.2] equal(sk_c8,multiply(sk_c8,sk_c9)).
% 389809 [para:389806.1.2,389714.1.1] equal(sk_c8,sk_c7).
% 389811 [para:389809.1.1,389585.1.1.1] -equal(inverse(sk_c7),sk_c7).
% 389848 [para:389709.1.1,389741.1.2.2,demod:389792] equal(sk_c9,multiply(sk_c4,sk_c8)).
% 389850 [para:389848.1.2,389738.1.2.2] equal(sk_c8,multiply(sk_c3,sk_c9)).
% 389852 [para:389850.1.2,389584.1.1.1,demod:389738,389792] equal(multiply(sk_c8,X),X).
% 389869 [para:389852.1.1,389714.1.1] equal(sk_c9,sk_c7).
% 389880 [para:389852.1.1,389806.1.2] equal(sk_c8,sk_c9).
% 389881 [para:389809.1.1,389852.1.1.1] equal(multiply(sk_c7,X),X).
% 389889 [para:389869.1.1,389649.1.1.1,demod:389881] equal(sk_c3,identity).
% 389908 [para:389869.1.1,389735.1.2.1,demod:389881] equal(X,multiply(sk_c3,X)).
% 389921 [para:389880.1.1,389714.1.1.1,demod:389802,389792] equal(sk_c3,sk_c7).
% 389929 [para:389889.1.1,389797.1.2.2,demod:389908] equal(sk_c9,identity).
% 389947 [para:389921.1.1,389648.1.1.1] equal(inverse(sk_c7),sk_c9).
% 389948 [para:389921.1.1,389889.1.1] equal(sk_c7,identity).
% 389978 [para:389948.1.1,389811.1.2,demod:389947,cut:389929] 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: 35088
% derived clauses: 4867571
% kept clauses: 310693
% kept size sum: 43428
% kept mid-nuclei: 25234
% kept new demods: 6184
% forw unit-subs: 1742821
% forw double-subs: 2489905
% forw overdouble-subs: 251583
% backward subs: 10094
% fast unit cutoff: 14771
% full unit cutoff: 0
% dbl unit cutoff: 20568
% real runtime : 302.10
% process. runtime: 300.40
% specific non-discr-tree subsumption statistics:
% tried: 52852041
% length fails: 5023919
% strength fails: 12806225
% predlist fails: 3918925
% aux str. fails: 4820361
% by-lit fails: 13758521
% full subs tried: 1585088
% full subs fail: 1492203
%
% ; 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/GRP317-1+eq_r.in")
%
%------------------------------------------------------------------------------