%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP276-1 : 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 : art03.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 227.9s
% Output : Assurance 227.9s
% 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/GRP276-1+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 21)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 21)
% (binary-posweight-lex-big-order 30 #f 3 21)
% (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(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7) | -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7) | -equal(inverse(sk_c7),sk_c5) | -equal(multiply(U,sk_c5),sk_c6) | -equal(inverse(U),sk_c5).
% was split for some strategies as:
% -equal(multiply(U,sk_c5),sk_c6) | -equal(inverse(U),sk_c5).
% -equal(multiply(Z,sk_c7),sk_c6) | -equal(inverse(Z),sk_c7).
% -equal(inverse(Y),sk_c7) | -equal(multiply(Y,sk_c6),sk_c7).
% -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% -equal(multiply(sk_c7,sk_c5),sk_c6).
% -equal(multiply(sk_c6,sk_c5),sk_c7).
% -equal(inverse(sk_c7),sk_c5).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(35,40,0,75,0,0,863,50,6,903,0,6,1706,50,12,1746,0,12,2560,50,19,2600,0,19,3421,50,29,3461,0,29,4289,50,38,4329,0,38,5165,50,54,5205,0,54,6050,50,83,6090,0,83,6945,50,145,6985,0,145,7851,50,279,7891,0,279,8769,50,499,8809,0,499,9700,50,929,9700,40,929,9740,0,929,21492,3,1230,22136,4,1380,22773,5,1530,22774,1,1530,22774,50,1530,22774,40,1530,22814,0,1530,22969,3,1839,22977,4,1982,22985,5,2131,22985,1,2131,22985,50,2131,22985,40,2131,23025,0,2131,55825,3,3633,56676,4,4382,57425,1,5132,57425,50,5133,57425,40,5133,57465,0,5133,82091,3,5884,82725,4,6259,83343,5,6634,83344,1,6634,83344,50,6635,83344,40,6635,83384,0,6635,93095,3,7387,94188,4,7761,95710,5,8136,95711,1,8136,95711,50,8136,95711,40,8136,95751,0,8136,147749,3,12037,148782,4,13988,149247,1,15937,149247,50,15938,149247,40,15938,149287,0,15939,193767,3,18497,194712,4,19765,195212,1,21040,195212,50,21041,195212,40,21041,195252,0,21041,240267,3,22545,240777,4,23293)
%
%
% START OF PROOF
% 195213 [] equal(X,X).
% 195214 [] equal(multiply(identity,X),X).
% 195215 [] equal(multiply(inverse(X),X),identity).
% 195216 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 195218 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 195220 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(inverse(sk_c7),sk_c5).
% 195223 [] equal(multiply(sk_c2,sk_c6),sk_c7) | equal(multiply(sk_c6,sk_c5),sk_c7).
% 195224 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 195226 [] equal(inverse(sk_c2),sk_c7) | equal(inverse(sk_c7),sk_c5).
% 195229 [] equal(multiply(sk_c6,sk_c5),sk_c7) | equal(inverse(sk_c2),sk_c7).
% 195230 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c4),sk_c5).
% 195231 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 195232 [] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(inverse(sk_c7),sk_c5).
% 195236 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c4),sk_c5).
% 195238 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c7),sk_c5).
% 195239 [] equal(inverse(sk_c1),sk_c7) | equal(inverse(sk_c3),sk_c7).
% 195240 [] equal(multiply(sk_c3,sk_c7),sk_c6) | equal(inverse(sk_c1),sk_c7).
% 195242 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c4),sk_c5).
% 195243 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c4,sk_c5),sk_c6).
% 195245 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(inverse(sk_c3),sk_c7).
% 195246 [] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c3,sk_c7),sk_c6).
% 195248 [] -equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(multiply(sk_c7,sk_c5),sk_c6) | -equal(inverse(sk_c7),sk_c5) | $spltprd0($spltcnst33) | -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c5).
% 195249 [] $spltprd0($spltcnst34) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 195250 [] $spltprd0($spltcnst35) | -equal(multiply(X,sk_c6),sk_c7) | -equal(inverse(X),sk_c7).
% 195251 [] $spltprd0($spltcnst36) | -equal(multiply(X,sk_c7),sk_c6) | -equal(inverse(X),sk_c7).
% 195252 [] -$spltprd0($spltcnst34) | -$spltprd0($spltcnst33) | -$spltprd0($spltcnst36) | -$spltprd0($spltcnst35).
% 195355 [para:195245.1.1,195249.2.1,cut:195213,binarycut:195239] equal(inverse(sk_c3),sk_c7) | $spltprd0($spltcnst34).
% 195363 [para:195246.2.1,195249.2.1,cut:195213,binarycut:195355] equal(multiply(sk_c1,sk_c7),sk_c6) | $spltprd0($spltcnst34).
% 195381 [para:195363.1.1,195249.2.1,cut:195213] -equal(inverse(sk_c1),sk_c7) | $spltprd0($spltcnst34).
% 195386 [para:195218.1.1,195250.2.1,cut:195213,binarycut:195224] equal(inverse(sk_c4),sk_c5) | $spltprd0($spltcnst35).
% 195388 [para:195220.1.1,195250.2.1,cut:195213,binarycut:195226] equal(inverse(sk_c7),sk_c5) | $spltprd0($spltcnst35).
% 195393 [para:195223.1.1,195250.2.1,cut:195213] equal(multiply(sk_c6,sk_c5),sk_c7) | -equal(inverse(sk_c2),sk_c7) | $spltprd0($spltcnst35).
% 195399 [para:195240.2.1,195381.1.1,cut:195213] equal(multiply(sk_c3,sk_c7),sk_c6) | $spltprd0($spltcnst34).
% 195420 [para:195245.1.1,195251.2.1,cut:195213,binarycut:195239] equal(inverse(sk_c3),sk_c7) | $spltprd0($spltcnst36).
% 195428 [para:195246.2.1,195251.2.1,cut:195213,binarycut:195420] equal(multiply(sk_c1,sk_c7),sk_c6) | $spltprd0($spltcnst36).
% 195444 [para:195215.1.1,195216.1.1.1,demod:195214] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 195485 [para:195243.2.1,195216.1.1.1] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(multiply(sk_c6,X),multiply(sk_c4,multiply(sk_c5,X))).
% 195518 [para:195399.1.1,195249.2.1,cut:195213,binarycut:195355] $spltprd0($spltcnst34).
% 195519 [binary:195252,195518] -$spltprd0($spltcnst36) | -$spltprd0($spltcnst35) | -$spltprd0($spltcnst33).
% 195544 [para:195428.1.1,195251.2.1,cut:195213] -equal(inverse(sk_c1),sk_c7) | $spltprd0($spltcnst36).
% 195549 [para:195240.2.1,195544.1.1,cut:195213] equal(multiply(sk_c3,sk_c7),sk_c6) | $spltprd0($spltcnst36).
% 195572 [para:195549.1.1,195251.2.1,cut:195213,binarycut:195420] $spltprd0($spltcnst36).
% 195574 [binary:195519,195572] -$spltprd0($spltcnst35) | -$spltprd0($spltcnst33).
% 195594 [para:195214.1.1,195444.1.2.2] equal(X,multiply(inverse(identity),X)).
% 195595 [para:195215.1.1,195444.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 195685 [para:195594.1.2,195444.1.2.2] equal(X,multiply(inverse(inverse(identity)),X)).
% 195706 [para:195595.1.2,195444.1.2.2] equal(identity,multiply(inverse(inverse(inverse(X))),X)).
% 195707 [para:195685.1.2,195215.1.1] equal(inverse(identity),identity).
% 195753 [para:195706.1.2,195444.1.2.2,demod:195595] equal(X,inverse(inverse(X))).
% 195759 [para:195753.1.2,195215.1.1.1] equal(multiply(X,inverse(X)),identity).
% 195760 [para:195224.1.1,195753.1.2.1] equal(sk_c2,inverse(sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 195761 [para:195224.2.1,195753.1.2.1] equal(sk_c4,inverse(sk_c5)) | equal(inverse(sk_c2),sk_c7).
% 195762 [para:195226.1.1,195753.1.2.1] equal(sk_c2,inverse(sk_c7)) | equal(inverse(sk_c7),sk_c5).
% 195763 [para:195226.2.1,195753.1.2.1] equal(sk_c7,inverse(sk_c5)) | equal(inverse(sk_c2),sk_c7).
% 195766 [para:195236.1.1,195753.1.2.1] equal(sk_c1,inverse(sk_c7)) | equal(inverse(sk_c4),sk_c5).
% 195768 [para:195238.1.1,195753.1.2.1] equal(sk_c1,inverse(sk_c7)) | equal(inverse(sk_c7),sk_c5).
% 195778 [para:195230.2.1,195753.1.2.1] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(sk_c4,inverse(sk_c5)).
% 195779 [para:195232.2.1,195753.1.2.1] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(sk_c7,inverse(sk_c5)).
% 195799 [para:195386.1.1,195753.1.2.1] equal(sk_c4,inverse(sk_c5)) | $spltprd0($spltcnst35).
% 195800 [para:195388.1.1,195753.1.2.1] equal(sk_c7,inverse(sk_c5)) | $spltprd0($spltcnst35).
% 195803 [para:195753.1.2,195595.1.2.1] equal(X,multiply(X,identity)).
% 195843 [para:195386.1.1,195759.1.1.2] equal(multiply(sk_c4,sk_c5),identity) | $spltprd0($spltcnst35).
% 195859 [para:195800.1.2,195799.1.2] equal(sk_c4,sk_c7) | $spltprd0($spltcnst35).
% 195869 [para:195859.1.2,195231.1.1.1] equal(multiply(sk_c4,sk_c5),sk_c6) | $spltprd0($spltcnst35).
% 196015 [para:195869.1.1,195444.1.2.2] equal(sk_c5,multiply(inverse(sk_c4),sk_c6)) | $spltprd0($spltcnst35).
% 196017 [para:195869.1.1,195843.1.1] equal(sk_c6,identity) | $spltprd0($spltcnst35).
% 196256 [para:195761.1.2,195763.1.2] equal(inverse(sk_c2),sk_c7) | equal(sk_c7,sk_c4).
% 196483 [para:195766.1.2,195760.1.2] equal(inverse(sk_c4),sk_c5) | equal(sk_c2,sk_c1).
% 196490 [para:196483.1.1,195595.1.2.1.1,demod:195803] equal(sk_c4,inverse(sk_c5)) | equal(sk_c2,sk_c1).
% 196575 [para:195768.1.2,195762.1.2] equal(inverse(sk_c7),sk_c5) | equal(sk_c2,sk_c1).
% 196585 [para:196575.1.1,195595.1.2.1.1,demod:195803] equal(sk_c7,inverse(sk_c5)) | equal(sk_c2,sk_c1).
% 196587 [para:196575.1.1,195759.1.1.2] equal(multiply(sk_c7,sk_c5),identity) | equal(sk_c2,sk_c1).
% 196627 [para:196490.1.2,196585.1.2] equal(sk_c7,sk_c4) | equal(sk_c2,sk_c1).
% 196705 [para:196627.2.1,196256.1.1.1] equal(inverse(sk_c1),sk_c7) | equal(sk_c7,sk_c4).
% 196846 [para:196705.1.1,195759.1.1.2] equal(multiply(sk_c1,sk_c7),identity) | equal(sk_c7,sk_c4).
% 197171 [para:195229.2.1,195393.2.1,cut:195213] equal(multiply(sk_c6,sk_c5),sk_c7) | $spltprd0($spltcnst35).
% 197224 [para:196017.1.1,197171.1.1.1,demod:195214] equal(sk_c5,sk_c7) | $spltprd0($spltcnst35).
% 197882 [para:196015.1.2,195250.2.1,demod:195753,binarycut:195859,binarycut:197224] $spltprd0($spltcnst35).
% 197884 [binary:195574,197882] -$spltprd0($spltcnst33).
% 202833 [para:195778.2.2,195779.2.2] equal(multiply(sk_c7,sk_c5),sk_c6) | equal(sk_c4,sk_c7).
% 202836 [para:195231.2.1,202833.2.1.1] equal(multiply(sk_c7,sk_c5),sk_c6).
% 202845 [para:202836.1.1,195216.1.1.1] equal(multiply(sk_c6,X),multiply(sk_c7,multiply(sk_c5,X))).
% 202846 [para:202836.1.1,195444.1.2.2] equal(sk_c5,multiply(inverse(sk_c7),sk_c6)).
% 207183 [para:202845.1.1,195759.1.1] equal(multiply(sk_c7,multiply(sk_c5,inverse(sk_c6))),identity).
% 207184 [para:195759.1.1,202845.1.2.2,demod:195803] equal(multiply(sk_c6,inverse(sk_c5)),sk_c7).
% 207337 [para:207184.1.1,195444.1.2.2] equal(inverse(sk_c5),multiply(inverse(sk_c6),sk_c7)).
% 207378 [para:195485.1.1,207184.2.1,demod:195803,195759] equal(multiply(sk_c1,sk_c7),sk_c6) | equal(sk_c7,sk_c4).
% 207475 [para:207183.1.1,195444.1.2.2,demod:195803] equal(multiply(sk_c5,inverse(sk_c6)),inverse(sk_c7)).
% 207608 [para:207475.1.1,195444.1.2.2] equal(inverse(sk_c6),multiply(inverse(sk_c5),inverse(sk_c7))).
% 207864 [para:195226.2.1,207608.1.2.2,demod:195215] equal(inverse(sk_c6),identity) | equal(inverse(sk_c2),sk_c7).
% 208305 [para:207864.1.1,195215.1.1.1,demod:195214] equal(inverse(sk_c2),sk_c7) | equal(sk_c6,identity).
% 208314 [para:208305.1.1,195215.1.1.1] equal(multiply(sk_c7,sk_c2),identity) | equal(sk_c6,identity).
% 208318 [para:208305.1.1,195595.1.2.1.1,demod:195803] equal(sk_c2,inverse(sk_c7)) | equal(sk_c6,identity).
% 208324 [para:196587.2.1,208305.1.1.1,demod:202836] equal(inverse(sk_c1),sk_c7) | equal(sk_c6,identity).
% 208534 [para:208324.1.1,195759.1.1.2] equal(multiply(sk_c1,sk_c7),identity) | equal(sk_c6,identity).
% 222885 [para:207378.1.1,196846.1.1] equal(sk_c6,identity) | equal(sk_c7,sk_c4).
% 223196 [para:222885.2.1,208318.1.2.1] equal(sk_c2,inverse(sk_c4)) | equal(sk_c6,identity).
% 236310 [para:195242.1.1,208534.1.1] equal(inverse(sk_c4),sk_c5) | equal(sk_c6,identity).
% 236391 [para:236310.1.1,223196.1.2] equal(sk_c2,sk_c5) | equal(sk_c6,identity).
% 236537 [para:236391.1.1,208314.1.1.2,demod:202836] equal(sk_c6,identity).
% 236538 [para:236537.1.2,195214.1.1.1] equal(multiply(sk_c6,X),X).
% 236543 [para:236537.1.1,195223.1.1.2,demod:236538,195803] equal(sk_c2,sk_c7) | equal(sk_c5,sk_c7).
% 236552 [para:236537.1.2,195707.1.1.1] equal(inverse(sk_c6),identity).
% 236578 [para:236537.1.1,202846.1.2.2,demod:195803] equal(sk_c5,inverse(sk_c7)).
% 236584 [para:236537.1.1,207184.1.1.1,demod:195214] equal(inverse(sk_c5),sk_c7).
% 236956 [para:195229.1.1,236543.2.1.1,demod:236538,236578] equal(sk_c5,sk_c7).
% 236999 [para:236956.1.1,195248.1.1.2,demod:236578,202836,236538,cut:195213,cut:195213,cut:195213,cut:197884] -equal(multiply(X,sk_c5),sk_c6) | -equal(inverse(X),sk_c5).
% 237070 [para:236956.1.2,202836.1.1.1] equal(multiply(sk_c5,sk_c5),sk_c6).
% 237110 [para:236956.1.2,207337.1.2.2,demod:195214,236552,236584] equal(sk_c7,sk_c5).
% 240778 [binary:237070,236999,demod:236584,cut:237110] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using unit paramodulation strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using first arg depth ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 30
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 22003
% derived clauses: 4702620
% kept clauses: 209463
% kept size sum: 590633
% kept mid-nuclei: 5621
% kept new demods: 1011
% forw unit-subs: 1835957
% forw double-subs: 2460383
% forw overdouble-subs: 163670
% backward subs: 9314
% fast unit cutoff: 14609
% full unit cutoff: 0
% dbl unit cutoff: 3824
% real runtime : 235.92
% process. runtime: 233.63
% specific non-discr-tree subsumption statistics:
% tried: 12260074
% length fails: 1728323
% strength fails: 1846307
% predlist fails: 258628
% aux str. fails: 2777730
% by-lit fails: 2405060
% full subs tried: 274730
% full subs fail: 216429
%
% ; 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/GRP276-1+eq_r.in")
%
%------------------------------------------------------------------------------