TSTP Solution File: GRP354-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP354-1 : 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 : art06.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 79.6s
% Output : Assurance 79.6s
% 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/GRP354-1+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 27)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 27)
% (binary-posweight-lex-big-order 30 #f 3 27)
% (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_c7),sk_c9) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9) | -equal(inverse(sk_c9),sk_c7) | -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7) | -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9) | -equal(multiply(V,W),sk_c8) | -equal(inverse(V),W) | -equal(multiply(W,sk_c7),sk_c8).
% was split for some strategies as:
% -equal(multiply(V,W),sk_c8) | -equal(inverse(V),W) | -equal(multiply(W,sk_c7),sk_c8).
% -equal(inverse(U),sk_c9) | -equal(multiply(U,sk_c8),sk_c9).
% -equal(multiply(Z,sk_c9),sk_c8) | -equal(inverse(Z),sk_c9).
% -equal(multiply(Y,sk_c7),sk_c8) | -equal(inverse(Y),sk_c7).
% -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% -equal(multiply(sk_c8,sk_c7),sk_c9).
% -equal(inverse(sk_c9),sk_c7).
% -equal(multiply(sk_c9,sk_c7),sk_c8).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(53,40,0,112,0,0,1947,50,20,2006,0,20,4950,50,54,5009,0,54,8268,50,87,8327,0,87,12000,50,130,12059,0,130,16045,50,184,16104,0,184,20608,50,259,20667,0,259,25588,50,364,25647,0,364,31190,50,527,31249,0,527,37312,50,765,37312,40,765,37371,0,765,49106,3,1066,49767,4,1216,50368,5,1366,50369,1,1366,50369,50,1366,50369,40,1366,50428,0,1366,50626,3,1674,50636,4,1842,50643,5,1967,50643,1,1967,50643,50,1967,50643,40,1967,50702,0,1967,78200,3,3469,78989,4,4218,79664,5,4968,79665,1,4968,79665,50,4969,79665,40,4969,79724,0,4969,94521,3,5720,95529,4,6095,96330,5,6470,96331,1,6470,96331,50,6470,96331,40,6470,96390,0,6470,104632,3,7235,106118,4,7596,107878,5,7971,107879,1,7971,107879,50,7971,107879,40,7971,107938,0,7971)
%
%
% START OF PROOF
% 107880 [] equal(X,X).
% 107881 [] equal(multiply(identity,X),X).
% 107882 [] equal(multiply(inverse(X),X),identity).
% 107883 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 107886 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 107887 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 107888 [] equal(multiply(sk_c4,sk_c8),sk_c9) | equal(inverse(sk_c2),sk_c7).
% 107889 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c9).
% 107890 [] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(inverse(sk_c2),sk_c7).
% 107894 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(inverse(sk_c5),sk_c6).
% 107895 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 107898 [] equal(multiply(sk_c2,sk_c7),sk_c8) | equal(multiply(sk_c9,sk_c7),sk_c8).
% 107902 [] equal(inverse(sk_c9),sk_c7) | equal(inverse(sk_c5),sk_c6).
% 107903 [] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(inverse(sk_c9),sk_c7).
% 107904 [] equal(multiply(sk_c4,sk_c8),sk_c9) | equal(inverse(sk_c9),sk_c7).
% 107905 [] equal(inverse(sk_c9),sk_c7) | equal(inverse(sk_c4),sk_c9).
% 107906 [] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(inverse(sk_c9),sk_c7).
% 107907 [] equal(inverse(sk_c9),sk_c7) | equal(inverse(sk_c3),sk_c9).
% 107908 [] equal(multiply(sk_c3,sk_c9),sk_c8) | equal(inverse(sk_c9),sk_c7).
% 107910 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 107913 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 107915 [] equal(inverse(sk_c1),sk_c9) | equal(inverse(sk_c3),sk_c9).
% 107916 [] equal(multiply(sk_c3,sk_c9),sk_c8) | equal(inverse(sk_c1),sk_c9).
% 107923 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(inverse(sk_c3),sk_c9).
% 107924 [] equal(multiply(sk_c1,sk_c9),sk_c8) | equal(multiply(sk_c3,sk_c9),sk_c8).
% 107926 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c5),sk_c6).
% 107928 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(multiply(sk_c4,sk_c8),sk_c9).
% 107929 [] equal(multiply(sk_c8,sk_c7),sk_c9) | equal(inverse(sk_c4),sk_c9).
% 107933 [] -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | $spltprd0($spltcnst31) | -equal(multiply(X,sk_c7),sk_c8) | -equal(multiply(Y,X),sk_c8) | -equal(inverse(Y),X).
% 107934 [] $spltprd0($spltcnst32) | -equal(multiply(X,sk_c8),sk_c9) | -equal(inverse(X),sk_c9).
% 107935 [] $spltprd0($spltcnst33) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 107936 [] $spltprd0($spltcnst34) | -equal(multiply(X,sk_c7),sk_c8) | -equal(inverse(X),sk_c7).
% 107937 [] $spltprd0($spltcnst35) | -equal(multiply(X,sk_c9),sk_c8) | -equal(inverse(X),sk_c9).
% 107938 [] -$spltprd0($spltcnst32) | -$spltprd0($spltcnst31) | -$spltprd0($spltcnst33) | -$spltprd0($spltcnst35) | -$spltprd0($spltcnst34).
% 107944 [input:107933,factor:factor] -equal(multiply(sk_c7,sk_c7),sk_c8) | -equal(multiply(sk_c9,sk_c7),sk_c8) | -equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c9),sk_c7) | $spltprd0($spltcnst31).
% 107968 [para:107910.1.1,107882.1.1.1] equal(multiply(sk_c9,sk_c1),identity) | equal(inverse(sk_c5),sk_c6).
% 107971 [para:107913.1.1,107882.1.1.1] equal(multiply(sk_c9,sk_c1),identity) | equal(inverse(sk_c4),sk_c9).
% 107991 [para:107903.2.1,107882.1.1.1] equal(multiply(sk_c7,sk_c9),identity) | equal(multiply(sk_c5,sk_c6),sk_c8).
% 108077 [para:107888.1.1,107934.2.1,cut:107880] -equal(inverse(sk_c4),sk_c9) | equal(inverse(sk_c2),sk_c7) | $spltprd0($spltcnst32).
% 108078 [para:107904.1.1,107934.2.1,cut:107880] -equal(inverse(sk_c4),sk_c9) | equal(inverse(sk_c9),sk_c7) | $spltprd0($spltcnst32).
% 108082 [para:107928.2.1,107934.2.1,cut:107880] equal(multiply(sk_c8,sk_c7),sk_c9) | -equal(inverse(sk_c4),sk_c9) | $spltprd0($spltcnst32).
% 108096 [para:107923.1.1,107935.2.1,cut:107880,binarycut:107915] equal(inverse(sk_c3),sk_c9) | $spltprd0($spltcnst33).
% 108105 [para:107924.2.1,107935.2.1,cut:107880,binarycut:108096] equal(multiply(sk_c1,sk_c9),sk_c8) | $spltprd0($spltcnst33).
% 108118 [para:107882.1.1,107936.2.1] -equal(inverse(inverse(sk_c7)),sk_c7) | -equal(identity,sk_c8) | $spltprd0($spltcnst34).
% 108122 [para:107894.1.1,107936.2.1,cut:107880,binarycut:107886] equal(inverse(sk_c5),sk_c6) | $spltprd0($spltcnst34).
% 108131 [para:107895.1.1,107936.2.1,cut:107880] equal(multiply(sk_c5,sk_c6),sk_c8) | -equal(inverse(sk_c2),sk_c7) | $spltprd0($spltcnst34).
% 108157 [para:108105.1.1,107935.2.1,cut:107880] -equal(inverse(sk_c1),sk_c9) | $spltprd0($spltcnst33).
% 108169 [para:107923.1.1,107937.2.1,cut:107880,binarycut:107915] equal(inverse(sk_c3),sk_c9) | $spltprd0($spltcnst35).
% 108178 [para:107924.2.1,107937.2.1,cut:107880,binarycut:108169] equal(multiply(sk_c1,sk_c9),sk_c8) | $spltprd0($spltcnst35).
% 108188 [para:107916.2.1,108157.1.1,cut:107880] equal(multiply(sk_c3,sk_c9),sk_c8) | $spltprd0($spltcnst33).
% 108197 [para:107882.1.1,107883.1.1.1,demod:107881] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 108316 [para:108178.1.1,107937.2.1,cut:107880] -equal(inverse(sk_c1),sk_c9) | $spltprd0($spltcnst35).
% 108323 [para:107916.2.1,108316.1.1,cut:107880] equal(multiply(sk_c3,sk_c9),sk_c8) | $spltprd0($spltcnst35).
% 108358 [para:108188.1.1,107935.2.1,cut:107880,binarycut:108096] $spltprd0($spltcnst33).
% 108394 [para:108323.1.1,107937.2.1,cut:107880,binarycut:108169] $spltprd0($spltcnst35).
% 108396 [para:107882.1.1,108197.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 108520 [para:108197.1.2,108197.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 108606 [para:108520.1.2,107882.1.1] equal(multiply(X,inverse(X)),identity).
% 108670 [para:108520.1.2,108396.1.2] equal(X,multiply(X,identity)).
% 108672 [para:108670.1.2,108396.1.2] equal(X,inverse(inverse(X))).
% 108682 [para:107991.1.1,108197.1.2.2,demod:108670] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(sk_c9,inverse(sk_c7)).
% 108684 [para:107886.1.1,108672.1.2.1] equal(sk_c2,inverse(sk_c7)) | equal(inverse(sk_c5),sk_c6).
% 108691 [para:107902.1.1,108672.1.2.1] equal(sk_c9,inverse(sk_c7)) | equal(inverse(sk_c5),sk_c6).
% 108697 [para:107887.2.1,108672.1.2.1] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(sk_c2,inverse(sk_c7)).
% 108702 [para:107915.1.1,108672.1.2.1] equal(sk_c1,inverse(sk_c9)) | equal(inverse(sk_c3),sk_c9).
% 108705 [para:107890.2.1,108672.1.2.1] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(sk_c2,inverse(sk_c7)).
% 108712 [para:107906.2.1,108672.1.2.1] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(sk_c9,inverse(sk_c7)).
% 108713 [para:107908.2.1,108672.1.2.1] equal(multiply(sk_c3,sk_c9),sk_c8) | equal(sk_c9,inverse(sk_c7)).
% 108803 [para:108122.1.1,108606.1.1.2] equal(multiply(sk_c5,sk_c6),identity) | $spltprd0($spltcnst34).
% 109047 [para:108684.1.2,108691.1.2] equal(inverse(sk_c5),sk_c6) | equal(sk_c9,sk_c2).
% 109066 [para:109047.1.1,108606.1.1.2] equal(multiply(sk_c5,sk_c6),identity) | equal(sk_c9,sk_c2).
% 109660 [para:108702.1.2,107907.1.1] equal(inverse(sk_c3),sk_c9) | equal(sk_c1,sk_c7).
% 109694 [para:109660.1.1,108606.1.1.2] equal(multiply(sk_c3,sk_c9),identity) | equal(sk_c1,sk_c7).
% 110282 [para:107889.2.1,108077.1.1,cut:107880] equal(inverse(sk_c2),sk_c7) | $spltprd0($spltcnst32).
% 110284 [para:107905.2.1,108078.1.1,cut:107880] equal(inverse(sk_c9),sk_c7) | $spltprd0($spltcnst32).
% 110289 [para:110282.1.1,108396.1.2.1.1,demod:108670] equal(sk_c2,inverse(sk_c7)) | $spltprd0($spltcnst32).
% 110297 [para:110284.1.1,108396.1.2.1.1,demod:108670] equal(sk_c9,inverse(sk_c7)) | $spltprd0($spltcnst32).
% 110301 [para:110284.1.1,108606.1.1.2] equal(multiply(sk_c9,sk_c7),identity) | $spltprd0($spltcnst32).
% 110331 [para:110297.1.2,110289.1.2] equal(sk_c2,sk_c9) | $spltprd0($spltcnst32).
% 110337 [para:110331.1.1,107898.1.1.1] equal(multiply(sk_c9,sk_c7),sk_c8) | $spltprd0($spltcnst32).
% 110517 [para:107929.2.1,108082.2.1,cut:107880] equal(multiply(sk_c8,sk_c7),sk_c9) | $spltprd0($spltcnst32).
% 110531 [para:110337.1.1,108197.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),sk_c8)) | $spltprd0($spltcnst32).
% 110544 [para:110337.1.1,110301.1.1] equal(sk_c8,identity) | $spltprd0($spltcnst32).
% 110608 [para:110544.1.1,110517.1.1.1,demod:107881] equal(sk_c7,sk_c9) | $spltprd0($spltcnst32).
% 110973 [para:108672.1.2,108118.1.1,cut:107880] -equal(identity,sk_c8) | $spltprd0($spltcnst34).
% 111104 [para:107887.2.1,108131.2.1,cut:107880] equal(multiply(sk_c5,sk_c6),sk_c8) | $spltprd0($spltcnst34).
% 111110 [para:108803.1.1,111104.1.1,binarycut:110973] $spltprd0($spltcnst34).
% 111189 [para:110531.1.2,107934.2.1,demod:108672,cut:107880,binarycut:110608] $spltprd0($spltcnst32).
% 111190 [binary:107938,111189,cut:108358,cut:108394,cut:111110] -$spltprd0($spltcnst31).
% 112075 [para:108682.2.2,108697.2.2] equal(multiply(sk_c5,sk_c6),sk_c8) | equal(sk_c9,sk_c2).
% 112084 [para:112075.1.1,109066.1.1] equal(sk_c8,identity) | equal(sk_c9,sk_c2).
% 112085 [para:109066.1.1,112075.1.1] equal(identity,sk_c8) | equal(sk_c9,sk_c2).
% 112094 [para:112084.2.2,107898.1.1.1] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(sk_c8,identity).
% 112131 [para:112085.2.2,107898.1.1.1] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(identity,sk_c8).
% 112845 [para:108705.2.2,108712.2.2] equal(multiply(sk_c9,sk_c7),sk_c8) | equal(sk_c2,sk_c9).
% 112848 [para:112845.2.1,107898.1.1.1] equal(multiply(sk_c9,sk_c7),sk_c8).
% 112853 [para:112848.1.1,107883.1.1.1] equal(multiply(sk_c8,X),multiply(sk_c9,multiply(sk_c7,X))).
% 112854 [para:112848.1.1,108197.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),sk_c8)).
% 113991 [para:108713.2.2,107882.1.1.1,demod:112848] equal(multiply(sk_c3,sk_c9),sk_c8) | equal(sk_c8,identity).
% 114018 [para:113991.1.1,109694.1.1] equal(sk_c8,identity) | equal(sk_c1,sk_c7).
% 114077 [para:114018.2.2,112094.1.1.2] equal(multiply(sk_c9,sk_c1),sk_c8) | equal(sk_c8,identity).
% 115336 [para:114077.1.1,107968.1.1] equal(inverse(sk_c5),sk_c6) | equal(sk_c8,identity).
% 115337 [para:114077.1.1,107971.1.1] equal(inverse(sk_c4),sk_c9) | equal(sk_c8,identity).
% 115376 [para:115336.2.1,107926.1.1.1,demod:107881] equal(inverse(sk_c5),sk_c6) | equal(sk_c7,sk_c9).
% 115386 [para:115337.2.1,107929.1.1.1,demod:107881] equal(inverse(sk_c4),sk_c9) | equal(sk_c7,sk_c9).
% 115411 [para:115376.2.1,107944.1.1.1,demod:112848,cut:107880,cut:111190,binarycut:107926,binarycut:107902] equal(inverse(sk_c5),sk_c6).
% 115420 [para:115411.1.1,108606.1.1.2] equal(multiply(sk_c5,sk_c6),identity).
% 115613 [para:115386.2.1,107944.1.1.1,demod:112848,cut:107880,cut:111190,binarycut:107929,binarycut:107905] equal(inverse(sk_c4),sk_c9).
% 115619 [para:115613.1.1,107882.1.1.1] equal(multiply(sk_c9,sk_c4),identity).
% 115620 [para:115613.1.1,108197.1.2.1] equal(X,multiply(sk_c9,multiply(sk_c4,X))).
% 115621 [para:115613.1.1,108396.1.2.1.1,demod:108670] equal(sk_c4,inverse(sk_c9)).
% 115635 [para:107903.1.2,115621.2.1,demod:115420] equal(sk_c4,sk_c7) | equal(identity,sk_c8).
% 115656 [para:115621.1.2,112854.1.2.1] equal(sk_c7,multiply(sk_c4,sk_c8)).
% 115749 [para:115635.1.2,112131.1.1.2,demod:115619] equal(identity,sk_c8).
% 115757 [para:115749.1.2,107928.1.1.1,demod:115656,107881] equal(sk_c7,sk_c9).
% 115768 [para:115749.1.2,112854.1.2.2,demod:108670,115621] equal(sk_c7,sk_c4).
% 115866 [para:115757.1.1,112848.1.1.2] equal(multiply(sk_c9,sk_c9),sk_c8).
% 115945 [para:115768.1.1,112853.1.2.2.1,demod:115620] equal(multiply(sk_c8,X),X).
% 115960 [para:115768.1.1,115757.1.1] equal(sk_c4,sk_c9).
% 116040 [para:115866.1.1,108197.1.2.2,demod:115656,115621] equal(sk_c9,sk_c7).
% 116048 [para:116040.1.2,107944.1.1.1,demod:115621,115945,112848,cut:107880,cut:115757,cut:111190] -equal(sk_c4,sk_c7).
% 116082 [para:115757.1.1,116048.1.2,cut:115960] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 78
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 14346
% derived clauses: 1507935
% kept clauses: 63581
% kept size sum: 91494
% kept mid-nuclei: 24108
% kept new demods: 653
% forw unit-subs: 663464
% forw double-subs: 685548
% forw overdouble-subs: 43077
% backward subs: 6988
% fast unit cutoff: 11373
% full unit cutoff: 0
% dbl unit cutoff: 13461
% real runtime : 82.4
% process. runtime: 81.57
% specific non-discr-tree subsumption statistics:
% tried: 15116598
% length fails: 1250194
% strength fails: 3309125
% predlist fails: 1123334
% aux str. fails: 3098708
% by-lit fails: 4356713
% full subs tried: 326456
% full subs fail: 297792
%
% ; 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/GRP354-1+eq_r.in")
%
%------------------------------------------------------------------------------