TSTP Solution File: GRP050-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP050-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.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/GRP050-1+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 8 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 8 5)
% (binary-posweight-lex-big-order 30 #f 8 5)
% (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(inverse(a1),a1),multiply(inverse(b1),b1)) | -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% -equal(multiply(multiply(inverse(b2),b2),a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,0,6,0,0,7,50,0,10,0,0)
%
%
% START OF PROOF
% 8 [] equal(X,X).
% 9 [] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),multiply(inverse(Y),Y))))),Z).
% 10 [] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)).
% 11 [para:9.1.1,9.1.1.2.1.1.1] equal(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),multiply(inverse(U),multiply(inverse(U),U))))).
% 13 [para:11.1.1,9.1.1] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(X,Y)),U))),multiply(inverse(Z),multiply(inverse(Z),Z)))),U).
% 14 [para:11.1.2,9.1.1.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),multiply(inverse(Y),multiply(inverse(Y),Y)))))),Z).
% 18 [para:9.1.1,13.1.1.1.1.1.1.1.1.1,demod:9] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(X),Z))),multiply(inverse(Y),multiply(inverse(Y),Y)))),Z).
% 22 [para:14.1.1,13.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),U)),multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(X,inverse(multiply(inverse(U),multiply(inverse(Y),multiply(inverse(Y),Y)))))).
% 28 [para:18.1.1,14.1.1.2.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(inverse(U),Y)),multiply(inverse(U),Z))).
% 30 [para:18.1.1,18.1.1.1.1.1.1.1.1,demod:18] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Y),multiply(inverse(Y),Y)))),Z).
% 34 [para:28.1.2,11.1.1.2.1] equal(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(inverse(U),U))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,U)),V)),multiply(inverse(U),Z))),multiply(inverse(V),multiply(inverse(V),V))))).
% 39 [para:11.1.2,28.1.2.1] equal(multiply(inverse(multiply(X,multiply(inverse(Y),multiply(inverse(Y),Y)))),multiply(X,Z)),multiply(multiply(U,inverse(multiply(inverse(V),multiply(inverse(W),multiply(inverse(W),W))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(U,W)),Y)),V)),Z))).
% 42 [para:28.1.2,14.1.1.2.2.1] equal(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(multiply(Z,U)),multiply(Z,multiply(inverse(Y),Y)))))),multiply(inverse(Y),U)).
% 48 [para:28.1.2,28.1.2] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 54 [para:9.1.1,48.1.1.2] equal(multiply(inverse(multiply(X,Y)),Z),multiply(inverse(multiply(U,Y)),multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(X,V)),Z)),multiply(inverse(V),multiply(inverse(V),V))))))).
% 60 [para:48.1.1,48.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
% 70 [para:30.1.1,48.1.1.1] equal(multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)),multiply(inverse(multiply(V,multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(V,U))).
% 81 [para:48.1.1,42.1.1.2.2.1.2.2] equal(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,inverse(multiply(inverse(multiply(U,V)),multiply(U,multiply(inverse(multiply(W,Z)),multiply(W,Z))))))),multiply(inverse(multiply(Y,Z)),V)).
% 86 [para:9.1.1,60.1.1.2,demod:54] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U),multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),U)).
% 563 [para:70.1.1,14.1.1.2.2.1,demod:81] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),multiply(inverse(Y),multiply(inverse(Y),Y))),Z).
% 664 [para:563.1.1,70.1.1.2] equal(multiply(inverse(X),X),multiply(inverse(multiply(Y,multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(Y,multiply(inverse(Z),multiply(inverse(Z),Z))))).
% 772 [para:563.1.1,664.1.2.1.1,demod:563] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 776 [para:772.1.1,9.1.1.2.1.2.2] equal(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),multiply(inverse(U),U))))),Z).
% 780 [para:772.1.1,11.1.2.1.1.1,demod:776] equal(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(X),multiply(inverse(X),X))))).
% 865 [para:48.1.1,780.1.2.1] equal(X,inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(X),X))))).
% 920 [para:772.1.1,865.1.2.1.2.2] equal(X,inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(Z),Z))))).
% 947 [para:772.1.1,920.1.2.1] equal(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))).
% 1026 [para:947.1.2,772.1.1.1] equal(multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)),multiply(inverse(Z),Z)).
% 1028 [para:947.1.1,920.1.2.1] equal(multiply(inverse(X),X),inverse(inverse(multiply(inverse(Y),Y)))).
% 1029 [para:947.1.2,920.1.2.1.1] equal(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(X),multiply(inverse(Z),Z))))).
% 1062 [para:920.1.2,22.1.1.1.1,demod:776] equal(inverse(multiply(X,multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(Y),Y)).
% 1140 [para:1028.1.1,947.1.1] equal(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))).
% 1704 [para:1026.1.1,920.1.2.1.2] equal(X,inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),X)),multiply(inverse(Z),Z)))).
% 2827 [para:1062.1.2,772.1.2] equal(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Y),multiply(inverse(Y),Y))))).
% 3845 [para:947.1.2,34.1.2.1.1.1.1.1.1,demod:920] equal(multiply(inverse(X),Y),inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),U)),multiply(inverse(X),Y))),multiply(inverse(U),multiply(inverse(U),U))))).
% 4684 [para:2827.1.2,34.1.2.1.1.1.1.1.1,demod:3845,920] equal(multiply(X,Y),multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y)).
% 4720 [para:4684.1.2,48.1.1] equal(multiply(X,multiply(inverse(X),Y)),multiply(inverse(multiply(Z,multiply(inverse(X),X))),multiply(Z,Y))).
% 4738 [para:772.1.1,4684.1.2.1.1.2] equal(multiply(X,Y),multiply(inverse(multiply(inverse(X),multiply(inverse(Z),Z))),Y)).
% 4805 [para:1704.1.2,4684.1.2.1] equal(multiply(multiply(multiply(inverse(X),X),Y),Z),multiply(Y,Z)).
% 4809 [para:947.1.1,4805.1.1.1.1] equal(multiply(multiply(inverse(multiply(inverse(X),X)),Y),Z),multiply(Y,Z)).
% 4817 [para:48.1.1,4809.1.1.1] equal(multiply(multiply(inverse(multiply(X,Y)),multiply(X,Z)),U),multiply(multiply(inverse(Y),Z),U)).
% 5081 [para:4738.1.2,48.1.1,demod:4720] equal(multiply(X,multiply(inverse(X),Y)),multiply(Z,multiply(inverse(Z),Y))).
% 5082 [para:48.1.1,4738.1.2.1.1] equal(multiply(multiply(inverse(X),Y),Z),multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,X))),Z)).
% 5089 [para:86.1.1,4738.1.2.1.1,demod:5082,4817] equal(multiply(multiply(inverse(X),Y),Z),multiply(inverse(multiply(multiply(inverse(Y),X),multiply(inverse(U),U))),Z)).
% 5192 [para:4738.1.2,34.1.2.1,demod:920] equal(multiply(X,Y),inverse(multiply(multiply(inverse(multiply(X,Y)),Z),multiply(inverse(Z),multiply(inverse(Z),Z))))).
% 5229 [para:5081.1.1,86.1.1.1.1.2,demod:5082] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Z,multiply(inverse(Z),U)))),V),multiply(multiply(inverse(multiply(inverse(X),U)),Y),V)).
% 5338 [para:5081.1.1,34.1.2.1.1.1.2,demod:5192,5229,920] equal(multiply(X,multiply(inverse(inverse(Y)),Z)),multiply(inverse(inverse(multiply(X,Y))),Z)).
% 5353 [para:5081.1.1,4805.1.1.1,demod:4809] equal(multiply(multiply(X,multiply(inverse(X),Y)),Z),multiply(Y,Z)).
% 5368 [para:772.1.1,5353.1.1.1.2] equal(multiply(multiply(X,multiply(inverse(Y),Y)),Z),multiply(X,Z)).
% 5369 [para:920.1.2,5353.1.1.1.2.1,demod:5368,4817] equal(multiply(multiply(inverse(X),multiply(X,Y)),Z),multiply(Y,Z)).
% 5385 [para:5081.1.1,5353.1.1.1.2] equal(multiply(multiply(X,multiply(Y,multiply(inverse(Y),Z))),U),multiply(multiply(inverse(inverse(X)),Z),U)).
% 5387 [para:48.1.1,5368.1.1.1,demod:4817] equal(multiply(multiply(inverse(X),Y),Z),multiply(inverse(multiply(inverse(Y),X)),Z)).
% 5395 [para:1140.1.2,5368.1.1.1.2.1,demod:5368,5385,5338] equal(multiply(inverse(inverse(X)),Y),multiply(X,Y)).
% 5410 [para:5395.1.1,772.1.1] equal(multiply(X,inverse(X)),multiply(inverse(Y),Y)).
% 5518 [para:1704.1.2,5395.1.1.1.1,demod:5368] equal(multiply(inverse(X),Y),multiply(inverse(multiply(multiply(inverse(Z),Z),X)),Y)).
% 5549 [para:5410.1.1,86.1.1.1.1.1.1,demod:5082,5518,5387] equal(multiply(inverse(multiply(X,Y)),Z),multiply(multiply(inverse(Y),inverse(X)),Z)).
% 5629 [para:5410.1.1,34.1.2.1.1.1.2,demod:5192,5089,5387,920] equal(multiply(X,inverse(inverse(Y))),multiply(X,Y)).
% 5657 [para:5629.1.1,920.1.2.1.1.1,demod:920] equal(inverse(inverse(X)),X).
% 5662 [para:1704.1.2,5629.1.1.2.1,demod:5518] equal(multiply(X,inverse(Y)),multiply(X,multiply(inverse(Y),multiply(inverse(Z),Z)))).
% 5838 [para:39.1.2,1029.1.2.1,demod:920,5369,5387,5549,5657,5662] equal(multiply(inverse(multiply(X,Y)),X),inverse(Y)).
% 5940 [para:1029.1.2,5657.1.1.1,demod:5662] equal(inverse(X),multiply(multiply(inverse(Y),Y),inverse(X))).
% 5944 [para:1704.1.2,5657.1.1.1,demod:5518] equal(inverse(X),multiply(inverse(X),multiply(inverse(Y),Y))).
% 6034 [para:5838.1.1,1029.1.2.1.2,demod:5657,5940] equal(multiply(multiply(inverse(X),X),Y),Y).
% 6035 [para:1029.1.2,5838.1.1.1,demod:5657,5944] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 6059 [para:6034.1.1,48.1.1.1.1,demod:6034] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 6068 [para:6035.1.1,48.1.1,demod:6059] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),X)).
% 6069 [para:6035.1.1,60.1.1.1.1.1.1,demod:6059,6035,5838,6068] equal(multiply(inverse(X),multiply(inverse(Y),Z)),multiply(inverse(multiply(Y,X)),Z)).
% 6080 [para:6035.1.1,34.1.1.2.1.2.2,demod:6069,6034,5657,5838,6035,6068] equal(multiply(X,Y),multiply(Z,multiply(multiply(inverse(Z),X),Y))).
% 6086 [para:6035.1.1,39.1.2,demod:6080,5657,6059,6068,5838,6069] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 6103 [hyper:10,6086,demod:6034,cut:8,cut:772] 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 5
% clause depth limited to 9
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 138
% derived clauses: 48476
% kept clauses: 6087
% kept size sum: 161625
% kept mid-nuclei: 4
% kept new demods: 624
% forw unit-subs: 36827
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 57
% fast unit cutoff: 3
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 1.7
% process. runtime: 1.4
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; 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/GRP050-1+eq_r.in")
%
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