%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP125-3.005 : TPTP v3.4.2. Released v1.2.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art04.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 0.0s
% Output : Assurance 0.0s
% 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/GRP125-3.005+noeq.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: nne
% detected subclass: medium
%
% strategies selected:
% (hyper 27 #f 1 13)
% (binary-unit 10 #f 1 13)
% (binary-double 16 #f 1 13)
% (binary 54 #t 1 13)
% (binary-order 27 #f 1 13)
% (binary-posweight-order 125 #f)
% (binary-order-sos 54 #t)
% (binary-unit-uniteq 27 #f)
% (binary-weightorder 54 #f)
% (binary-order 54 #f)
% (hyper-order 43 #f)
% (binary 109 #t)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(58,40,0,116,0,0)
%
%
% START OF PROOF
% 59 [] next(e_0,e_1).
% 60 [] next(e_1,e_2).
% 61 [] next(e_2,e_3).
% 62 [] next(e_3,e_4).
% 63 [] next(e_4,e_5).
% 64 [] greater(e_1,e_0).
% 65 [] greater(e_2,e_0).
% 66 [] greater(e_3,e_0).
% 67 [] greater(e_4,e_0).
% 73 [] greater(e_3,e_2).
% 74 [] greater(e_4,e_2).
% 75 [] greater(e_5,e_2).
% 76 [] greater(e_4,e_3).
% 77 [] greater(e_5,e_3).
% 80 [] cycle(X,e_3) | cycle(X,e_4) | cycle(X,e_2) | cycle(X,e_0) | cycle(X,e_1) | -group_element(X).
% 81 [] cycle(e_5,e_0).
% 82 [] -greater(X,e_0) | -cycle(Y,Z) | -cycle(U,X) | -next(Z,V) | -next(U,Y) | equalish(X,V).
% 83 [] -cycle(X,e_0) | -cycle(Y,Z) | -cycle(U,V) | -greater(X,U) | -greater(V,Z) | -next(X,Y).
% 84 [] -product(X,e_1,Y) | -cycle(X,e_0) | -greater(Y,X).
% 85 [] -product(X,e_1,Y) | -greater(Z,e_0) | -cycle(X,Z) | -next(X,U) | equalish(Y,U).
% 86 [] group_element(e_1).
% 87 [] group_element(e_2).
% 88 [] group_element(e_3).
% 89 [] group_element(e_4).
% 91 [] -equalish(e_1,e_2).
% 92 [] -equalish(e_1,e_3).
% 93 [] -equalish(e_1,e_4).
% 94 [] -equalish(e_1,e_5).
% 95 [] -equalish(e_2,e_1).
% 96 [] -equalish(e_2,e_3).
% 97 [] -equalish(e_2,e_4).
% 98 [] -equalish(e_2,e_5).
% 99 [] -equalish(e_3,e_1).
% 100 [] -equalish(e_3,e_2).
% 101 [] -equalish(e_3,e_4).
% 102 [] -equalish(e_3,e_5).
% 103 [] -equalish(e_4,e_1).
% 104 [] -equalish(e_4,e_2).
% 105 [] -equalish(e_4,e_3).
% 106 [] -equalish(e_4,e_5).
% 107 [] -equalish(e_5,e_1).
% 108 [] -equalish(e_5,e_2).
% 109 [] -equalish(e_5,e_3).
% 110 [] -equalish(e_5,e_4).
% 111 [] product(X,Y,e_4) | product(X,Y,e_5) | product(X,Y,e_2) | product(X,Y,e_3) | product(X,Y,e_1) | -group_element(Y) | -group_element(X).
% 112 [] -product(X,Y,U) | -product(X,Y,Z) | equalish(Z,U).
% 113 [] -product(X,U,Z) | -product(X,Y,Z) | equalish(Y,U).
% 114 [] -product(U,Y,Z) | -product(X,Y,Z) | equalish(X,U).
% 115 [] product(X,X,X).
% 116 [] -product(Y,X,U) | -product(X,Y,Z) | product(Z,U,X).
% 120 [hyper:80,87] cycle(e_2,e_4) | cycle(e_2,e_3) | cycle(e_2,e_2) | cycle(e_2,e_1) | cycle(e_2,e_0).
% 122 [hyper:111,87,86] product(e_1,e_2,e_5) | product(e_1,e_2,e_4) | product(e_1,e_2,e_3) | product(e_1,e_2,e_1) | product(e_1,e_2,e_2).
% 124 [hyper:111,87,86] product(e_2,e_1,e_4) | product(e_2,e_1,e_5) | product(e_2,e_1,e_2) | product(e_2,e_1,e_3) | product(e_2,e_1,e_1).
% 125 [hyper:80,88] cycle(e_3,e_4) | cycle(e_3,e_3) | cycle(e_3,e_2) | cycle(e_3,e_1) | cycle(e_3,e_0).
% 127 [hyper:111,88,86] product(e_1,e_3,e_5) | product(e_1,e_3,e_4) | product(e_1,e_3,e_3) | product(e_1,e_3,e_1) | product(e_1,e_3,e_2).
% 128 [hyper:111,88,87] product(e_2,e_3,e_5) | product(e_2,e_3,e_4) | product(e_2,e_3,e_3) | product(e_2,e_3,e_1) | product(e_2,e_3,e_2).
% 130 [hyper:111,88,86] product(e_3,e_1,e_4) | product(e_3,e_1,e_5) | product(e_3,e_1,e_2) | product(e_3,e_1,e_3) | product(e_3,e_1,e_1).
% 131 [hyper:111,88,87] product(e_3,e_2,e_4) | product(e_3,e_2,e_5) | product(e_3,e_2,e_2) | product(e_3,e_2,e_3) | product(e_3,e_2,e_1).
% 132 [hyper:80,89] cycle(e_4,e_4) | cycle(e_4,e_3) | cycle(e_4,e_2) | cycle(e_4,e_1) | cycle(e_4,e_0).
% 134 [hyper:111,89,86] product(e_1,e_4,e_5) | product(e_1,e_4,e_4) | product(e_1,e_4,e_3) | product(e_1,e_4,e_1) | product(e_1,e_4,e_2).
% 138 [hyper:111,89,86] product(e_4,e_1,e_4) | product(e_4,e_1,e_5) | product(e_4,e_1,e_2) | product(e_4,e_1,e_3) | product(e_4,e_1,e_1).
% 1581 [hyper:113,122,115,cut:91] product(e_1,e_2,e_4) | product(e_1,e_2,e_2) | product(e_1,e_2,e_3) | product(e_1,e_2,e_5).
% 2896 [hyper:82,132,63,81,59,cut:67,cut:103] cycle(e_4,e_0) | cycle(e_4,e_1) | cycle(e_4,e_2) | cycle(e_4,e_3).
% 3801 [hyper:82,2896,63,81,59,cut:65,cut:95] cycle(e_4,e_1) | cycle(e_4,e_3) | cycle(e_4,e_0).
% 4502 [hyper:82,3801,63,81,59,cut:66,cut:99] cycle(e_4,e_1) | cycle(e_4,e_0).
% 5233 [hyper:113,124,115,cut:95] product(e_2,e_1,e_4) | product(e_2,e_1,e_1) | product(e_2,e_1,e_5) | product(e_2,e_1,e_3).
% 5320 [hyper:82,4502,62,67,125,60,cut:104] cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_3) | cycle(e_4,e_0) | cycle(e_3,e_2).
% 5560 [hyper:83,4502,63,81,120,cut:74,cut:67] cycle(e_2,e_1) | cycle(e_2,e_0) | cycle(e_2,e_2) | cycle(e_4,e_1) | cycle(e_2,e_3).
% 5962 [hyper:113,127,115,cut:92] product(e_1,e_3,e_4) | product(e_1,e_3,e_2) | product(e_1,e_3,e_3) | product(e_1,e_3,e_5).
% 6027 [hyper:113,128,115,cut:96] product(e_2,e_3,e_3) | product(e_2,e_3,e_5) | product(e_2,e_3,e_1) | product(e_2,e_3,e_4).
% 6227 [hyper:113,130,115,cut:99] product(e_3,e_1,e_5) | product(e_3,e_1,e_1) | product(e_3,e_1,e_2) | product(e_3,e_1,e_4).
% 6385 [hyper:82,5320,62,4502,60,cut:64,cut:91] cycle(e_3,e_2) | cycle(e_4,e_0) | cycle(e_3,e_3) | cycle(e_3,e_0).
% 6448 [hyper:82,5320,62,125,59,cut:67,cut:103] cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_3) | cycle(e_3,e_2).
% 7098 [hyper:82,6385,62,4502,60,cut:66,cut:100] cycle(e_3,e_2) | cycle(e_4,e_0) | cycle(e_3,e_0).
% 8471 [hyper:113,131,115,cut:100] product(e_3,e_2,e_5) | product(e_3,e_2,e_1) | product(e_3,e_2,e_2) | product(e_3,e_2,e_4).
% 8601 [hyper:82,6448,62,7098,59,cut:66,cut:99] cycle(e_3,e_0) | cycle(e_3,e_2) | cycle(e_3,e_1).
% 9698 [hyper:83,8601,64,76,63,7098,cut:81] cycle(e_3,e_2) | cycle(e_3,e_0).
% 10017 [hyper:82,9698,61,67,120,61,cut:105] cycle(e_2,e_0) | cycle(e_2,e_1) | cycle(e_2,e_3) | cycle(e_3,e_0) | cycle(e_2,e_2).
% 10040 [hyper:82,9698,62,4502,59,cut:65,cut:95] cycle(e_3,e_0) | cycle(e_4,e_1).
% 11035 [hyper:113,134,115,cut:93] product(e_1,e_4,e_4) | product(e_1,e_4,e_2) | product(e_1,e_4,e_3) | product(e_1,e_4,e_5).
% 11268 [hyper:82,5560,61,10040,59,cut:65,cut:95] cycle(e_2,e_3) | cycle(e_4,e_1) | cycle(e_2,e_1) | cycle(e_2,e_0).
% 11662 [hyper:82,11268,61,10040,59,cut:66,cut:99] cycle(e_2,e_1) | cycle(e_4,e_1) | cycle(e_2,e_0).
% 12331 [hyper:83,11662,64,74,4502,81,cut:63] cycle(e_2,e_0) | cycle(e_4,e_1).
% 13396 [hyper:113,138,115,cut:103] product(e_4,e_1,e_2) | product(e_4,e_1,e_1) | product(e_4,e_1,e_5) | product(e_4,e_1,e_3).
% 13705 [hyper:82,10017,61,9698,61,cut:64,cut:92] cycle(e_2,e_2) | cycle(e_3,e_0) | cycle(e_2,e_3) | cycle(e_2,e_0).
% 13747 [hyper:82,10017,61,120,59,cut:67,cut:103] cycle(e_2,e_0) | cycle(e_2,e_1) | cycle(e_2,e_3) | cycle(e_2,e_2).
% 14078 [hyper:82,13705,61,9698,61,cut:65,cut:96] cycle(e_2,e_3) | cycle(e_3,e_0) | cycle(e_2,e_0).
% 15179 [hyper:82,13747,61,14078,59,cut:65,cut:95] cycle(e_2,e_0) | cycle(e_2,e_3) | cycle(e_2,e_1).
% 17584 [hyper:114,1581,115,cut:95] product(e_1,e_2,e_4) | product(e_1,e_2,e_5) | product(e_1,e_2,e_3).
% 17927 [hyper:114,5233,115,cut:91] product(e_2,e_1,e_4) | product(e_2,e_1,e_3) | product(e_2,e_1,e_5).
% 18000 [hyper:84,17927,12331,cut:74] product(e_2,e_1,e_5) | product(e_2,e_1,e_3) | cycle(e_4,e_1).
% 18001 [hyper:84,17927,14078,cut:74] product(e_2,e_1,e_3) | product(e_2,e_1,e_5) | cycle(e_3,e_0) | cycle(e_2,e_3).
% 18341 [hyper:84,18000,cut:75,binarycut:12331] product(e_2,e_1,e_3) | cycle(e_4,e_1).
% 18767 [hyper:84,18341,cut:73,binarycut:12331] cycle(e_4,e_1).
% 19823 [hyper:84,18001,14078,cut:73] product(e_2,e_1,e_5) | cycle(e_3,e_0) | cycle(e_2,e_3).
% 19831 [hyper:85,18001,17927,61,cut:66,cut:105] product(e_2,e_1,e_5) | product(e_2,e_1,e_3) | cycle(e_3,e_0).
% 20265 [hyper:84,19823,14078,cut:75] cycle(e_3,e_0) | cycle(e_2,e_3).
% 21208 [hyper:85,19831,20265,61,cut:66,cut:109] product(e_2,e_1,e_3) | cycle(e_3,e_0).
% 21345 [hyper:82,21208,61,66,15179,59,cut:99] product(e_2,e_1,e_3) | cycle(e_2,e_0) | cycle(e_2,e_1).
% 22150 [hyper:84,21345,17927,cut:74] product(e_2,e_1,e_3) | product(e_2,e_1,e_5) | cycle(e_2,e_1).
% 22802 [hyper:84,22150,21345,cut:75] product(e_2,e_1,e_3) | cycle(e_2,e_1).
% 22813 [hyper:85,22150,17927,61,cut:64,cut:105] product(e_2,e_1,e_5) | product(e_2,e_1,e_3).
% 24536 [hyper:85,22813,64,22802,61,cut:109] product(e_2,e_1,e_3).
% 24581 [hyper:116,24536,17584] product(e_1,e_2,e_5) | product(e_1,e_2,e_4) | product(e_3,e_3,e_1).
% 24750 [hyper:112,24581,115,cut:99] product(e_1,e_2,e_5) | product(e_1,e_2,e_4).
% 24777 [hyper:116,24750,24536] product(e_1,e_2,e_4) | product(e_3,e_5,e_2).
% 24779 [hyper:116,24750,24536] product(e_1,e_2,e_4) | product(e_5,e_3,e_1).
% 24781 [hyper:116,24750,24536] product(e_1,e_2,e_5) | product(e_3,e_4,e_2).
% 24783 [hyper:116,24750,24536] product(e_1,e_2,e_5) | product(e_4,e_3,e_1).
% 25116 [hyper:114,5962,115,cut:99] product(e_1,e_3,e_2) | product(e_1,e_3,e_5) | product(e_1,e_3,e_4).
% 25510 [hyper:113,6027,24536,cut:92] product(e_2,e_3,e_5) | product(e_2,e_3,e_4) | product(e_2,e_3,e_1).
% 25595 [hyper:114,25510,24779,cut:108] product(e_2,e_3,e_4) | product(e_1,e_2,e_4) | product(e_2,e_3,e_5).
% 25596 [hyper:114,25510,24783,cut:104] product(e_2,e_3,e_4) | product(e_1,e_2,e_5) | product(e_2,e_3,e_5).
% 25689 [hyper:112,25596,25595,cut:106] product(e_2,e_3,e_4) | product(e_2,e_3,e_5).
% 25737 [hyper:114,25689,25116,cut:91] product(e_1,e_3,e_2) | product(e_1,e_3,e_4) | product(e_2,e_3,e_4).
% 26461 [hyper:114,6227,115,cut:92] product(e_3,e_1,e_5) | product(e_3,e_1,e_4) | product(e_3,e_1,e_2).
% 26671 [hyper:84,26461,9698,cut:77] product(e_3,e_1,e_2) | product(e_3,e_1,e_4) | cycle(e_3,e_2).
% 26951 [hyper:84,26671,9698,cut:76] product(e_3,e_1,e_2) | cycle(e_3,e_2).
% 26965 [hyper:85,26671,26461,62,cut:65,cut:110] product(e_3,e_1,e_2) | product(e_3,e_1,e_4).
% 27159 [hyper:113,26951,24777,cut:107] product(e_1,e_2,e_4) | cycle(e_3,e_2).
% 27160 [hyper:113,26951,24781,cut:103] product(e_1,e_2,e_5) | cycle(e_3,e_2).
% 27829 [hyper:112,27160,27159,cut:106] cycle(e_3,e_2).
% 28263 [hyper:85,26965,27829,62,cut:65,cut:97] product(e_3,e_1,e_4).
% 28288 [hyper:116,28263,25116] product(e_1,e_3,e_5) | product(e_1,e_3,e_2) | product(e_4,e_4,e_1).
% 28481 [hyper:112,28288,115,cut:103] product(e_1,e_3,e_5) | product(e_1,e_3,e_2).
% 28508 [hyper:116,28481,28263] product(e_1,e_3,e_2) | product(e_4,e_5,e_3).
% 28519 [hyper:112,28481,25737,cut:106] product(e_1,e_3,e_2) | product(e_2,e_3,e_4).
% 29292 [hyper:113,8471,28263,cut:91] product(e_3,e_2,e_2) | product(e_3,e_2,e_5) | product(e_3,e_2,e_1).
% 29377 [hyper:114,29292,115,cut:96] product(e_3,e_2,e_1) | product(e_3,e_2,e_5).
% 29403 [hyper:116,29377,25689] product(e_4,e_1,e_2) | product(e_2,e_3,e_5) | product(e_3,e_2,e_5).
% 29416 [hyper:116,29377,25689] product(e_5,e_5,e_2) | product(e_2,e_3,e_4) | product(e_3,e_2,e_1).
% 29584 [hyper:85,29403,18767,63,cut:64,cut:98] product(e_3,e_2,e_5) | product(e_2,e_3,e_5).
% 29615 [hyper:116,29584,25689] product(e_4,e_5,e_2) | product(e_2,e_3,e_5).
% 29619 [hyper:116,29584,29377] product(e_1,e_5,e_3) | product(e_3,e_2,e_5).
% 29676 [hyper:112,29615,28508,cut:100] product(e_2,e_3,e_5) | product(e_1,e_3,e_2).
% 30057 [hyper:112,29676,28519,cut:106] product(e_1,e_3,e_2).
% 30355 [hyper:112,29416,115,cut:108] product(e_3,e_2,e_1) | product(e_2,e_3,e_4).
% 30388 [hyper:116,30355,25689] product(e_1,e_5,e_3) | product(e_2,e_3,e_4).
% 30470 [hyper:116,30388,29619] product(e_5,e_4,e_3) | product(e_1,e_5,e_3).
% 30742 [hyper:113,11035,30057,cut:101] product(e_1,e_4,e_4) | product(e_1,e_4,e_5) | product(e_1,e_4,e_3).
% 30820 [hyper:114,30742,115,cut:103] product(e_1,e_4,e_3) | product(e_1,e_4,e_5).
% 30860 [hyper:113,30820,30470,cut:110] product(e_1,e_4,e_5) | product(e_5,e_4,e_3).
% 31050 [hyper:114,30860,30820,cut:94] product(e_1,e_4,e_5).
% 31100 [hyper:85,13396,18767,63,cut:64,cut:98] product(e_4,e_1,e_1) | product(e_4,e_1,e_5) | product(e_4,e_1,e_3).
% 31152 [hyper:85,31100,18767,63,cut:64,cut:94] product(e_4,e_1,e_3) | product(e_4,e_1,e_5).
% 31194 [hyper:85,31152,18767,63,cut:64,cut:102] product(e_4,e_1,e_5).
% 31217 [hyper:116,31194,31050] product(e_5,e_5,e_1).
% 31248 [hyper:112,31217,115,cut:107] 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 13
% clause depth limited to 1
% seconds given: 27
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 249
% derived clauses: 63067
% kept clauses: 1906
% kept size sum: 33447
% kept mid-nuclei: 28955
% kept new demods: 0
% forw unit-subs: 13060
% forw double-subs: 7168
% forw overdouble-subs: 11432
% backward subs: 786
% fast unit cutoff: 13826
% full unit cutoff: 0
% dbl unit cutoff: 85
% real runtime : 1.61
% process. runtime: 1.60
% specific non-discr-tree subsumption statistics:
% tried: 416056
% length fails: 39345
% strength fails: 185037
% predlist fails: 40909
% aux str. fails: 16551
% by-lit fails: 109302
% full subs tried: 1291
% full subs fail: 1291
%
% ; 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/GRP125-3.005+noeq.in")
%
%------------------------------------------------------------------------------