TSTP Solution File: GRP062-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP062-1 : 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 : art07.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/GRP062-1+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(3,40,0,6,0,0,5606,4,765)
%
%
% START OF PROOF
% 4 [] equal(X,X).
% 5 [] equal(inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(X,Y))))))),U).
% 6 [] -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)).
% 7 [para:5.1.1,5.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(U,X)))),multiply(multiply(V,inverse(V)),Z)))),U).
% 8 [para:7.1.1,5.1.1.1.2.2.2] equal(inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,U)))),multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(W,inverse(W)),Z)))),U).
% 9 [para:7.1.1,7.1.1.1.2.1.2] equal(inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),U),multiply(multiply(V,inverse(V)),W)))),multiply(multiply(X1,inverse(X1)),inverse(multiply(Y,multiply(U,W))))).
% 11 [para:9.1.1,8.1.1] equal(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,Z)))),U).
% 12 [para:9.1.1,8.1.1.1.1.2] equal(inverse(multiply(multiply(multiply(X,inverse(X)),multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(U,V))))),multiply(multiply(multiply(W,inverse(W)),multiply(multiply(X1,inverse(X1)),Z)),multiply(multiply(X2,inverse(X2)),multiply(multiply(X3,inverse(X3)),U))))),multiply(multiply(X4,inverse(X4)),V)).
% 19 [para:7.1.1,11.1.1.2.1.1,demod:5] equal(multiply(multiply(X,inverse(X)),Y),multiply(multiply(Z,inverse(Z)),Y)).
% 20 [para:11.1.1,8.1.1.1.1.2.1.2] equal(inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,Z))),multiply(multiply(multiply(U,inverse(U)),Y),multiply(multiply(V,inverse(V)),multiply(W,inverse(W)))))),inverse(multiply(inverse(multiply(X1,multiply(X2,Z))),multiply(X1,X2)))).
% 25 [para:19.1.1,5.1.1.1.2.2.2.1,demod:5] equal(multiply(X,inverse(X)),multiply(Y,inverse(Y))).
% 28 [para:8.1.1,19.1.1.1.2] equal(multiply(multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,U)))),multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(W,inverse(W)),Z))),U),X1),multiply(multiply(X2,inverse(X2)),X1)).
% 37 [para:9.1.2,19.1.2] equal(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,U)))),inverse(multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(multiply(W,inverse(W)),Z),multiply(multiply(X1,inverse(X1)),U))))).
% 47 [para:25.1.1,8.1.1.1.1.2.1.2] equal(inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,inverse(Z))))),multiply(multiply(multiply(U,inverse(U)),Y),multiply(multiply(V,inverse(V)),W)))),inverse(W)).
% 54 [para:25.1.1,11.1.1.2.1.1.1.2] equal(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(Y,U)))),inverse(U)).
% 55 [para:25.1.1,11.1.1.2.1.2] equal(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(inverse(Y),Z))),multiply(U,inverse(U))))),Z).
% 167 [para:54.1.1,5.1.1.1.2.2] equal(inverse(multiply(X,multiply(Y,inverse(Y)))),inverse(multiply(X,multiply(Z,inverse(Z))))).
% 175 [para:25.1.1,54.1.1.2.1.2] equal(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(U,inverse(U))))),inverse(inverse(Y))).
% 218 [para:167.1.1,25.1.1.2] equal(multiply(multiply(X,multiply(Y,inverse(Y))),inverse(multiply(X,multiply(Z,inverse(Z))))),multiply(U,inverse(U))).
% 406 [para:218.1.1,54.1.1.2.1.2,demod:175] equal(inverse(inverse(multiply(X,multiply(Y,inverse(Y))))),inverse(inverse(multiply(X,multiply(Z,inverse(Z)))))).
% 425 [para:406.1.1,25.1.1.2] equal(multiply(inverse(multiply(X,multiply(Y,inverse(Y)))),inverse(inverse(multiply(X,multiply(Z,inverse(Z)))))),multiply(U,inverse(U))).
% 533 [para:55.1.1,5.1.1.1.2.2] equal(inverse(multiply(X,multiply(inverse(X),Y))),inverse(multiply(Z,multiply(inverse(Z),Y)))).
% 613 [para:533.1.1,218.1.1.2] equal(multiply(multiply(X,multiply(Y,inverse(Y))),inverse(multiply(Z,multiply(inverse(Z),inverse(inverse(X)))))),multiply(U,inverse(U))).
% 1034 [para:167.1.1,20.1.1.1.1.2,demod:47] equal(inverse(multiply(X,inverse(X))),inverse(multiply(inverse(multiply(Y,multiply(Z,multiply(U,inverse(U))))),multiply(Y,Z)))).
% 2592 [para:613.1.1,28.1.1,demod:8] equal(multiply(X,inverse(X)),multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(inverse(Z),inverse(multiply(U,inverse(U)))))))).
% 3009 [para:2592.1.2,5.1.1.1.2.2] equal(inverse(multiply(inverse(X),multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z))))),X).
% 3014 [para:2592.1.2,8.1.1.1.1.2.1.2,demod:47] equal(inverse(multiply(X,inverse(X))),inverse(multiply(Y,multiply(inverse(Y),inverse(multiply(Z,inverse(Z))))))).
% 3126 [para:3009.1.1,11.1.1.2] equal(multiply(multiply(X,inverse(X)),multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),U))),U).
% 3161 [para:533.1.1,3009.1.1.1.1,demod:3009] equal(multiply(X,multiply(inverse(X),Y)),multiply(Z,multiply(inverse(Z),Y))).
% 3182 [para:1034.1.1,3009.1.1.1.1,demod:3009] equal(multiply(inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z))))),multiply(X,Y)),multiply(U,inverse(U))).
% 3892 [para:3014.1.1,3009.1.1.1.1,demod:3009] equal(multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Y))))),multiply(Z,inverse(Z))).
% 3915 [para:3892.1.1,8.1.1.1.1.2.1.2,demod:47] equal(inverse(X),multiply(inverse(X),inverse(multiply(Y,inverse(Y))))).
% 3928 [para:5.1.1,3915.1.2.1,demod:5] equal(X,multiply(X,inverse(multiply(Y,inverse(Y))))).
% 4065 [para:3182.1.1,8.1.1.1.1.2.1.2,demod:47] equal(inverse(inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z)))))),multiply(X,Y)).
% 4209 [para:3161.1.1,4065.1.1.1.1.2] equal(inverse(inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(inverse(Z))))))),multiply(X,Z)).
% 4231 [para:533.1.1,4209.1.1.1] equal(inverse(inverse(multiply(X,multiply(inverse(X),multiply(inverse(inverse(Y)),inverse(inverse(Z))))))),multiply(Y,Z)).
% 4663 [para:167.1.1,4231.1.1.1.1.2.2.1.1,demod:4231] equal(multiply(multiply(X,multiply(Y,inverse(Y))),Z),multiply(multiply(X,multiply(U,inverse(U))),Z)).
% 4911 [para:3126.1.1,5.1.1.1,demod:3928] equal(inverse(inverse(multiply(X,multiply(Y,inverse(Y))))),X).
% 4971 [para:3126.1.1,3161.1.1] equal(X,multiply(Y,multiply(inverse(Y),multiply(multiply(Z,inverse(Z)),X)))).
% 4977 [para:3126.1.1,4065.1.1.1.1,demod:3928] equal(inverse(inverse(inverse(multiply(X,inverse(X))))),multiply(Y,inverse(Y))).
% 5014 [para:533.1.1,4911.1.1.1] equal(inverse(inverse(multiply(X,multiply(inverse(X),inverse(inverse(Y)))))),Y).
% 5434 [para:4977.1.2,3928.1.2.2.1] equal(X,multiply(X,inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))))).
% 5459 [para:4977.1.1,4231.1.1.1.1.2.2.1,demod:4971] equal(inverse(inverse(inverse(inverse(X)))),multiply(inverse(multiply(Y,inverse(Y))),X)).
% 5460 [para:4977.1.1,4231.1.1.1.1.2.2.1.1,demod:5014,5459] equal(inverse(inverse(inverse(inverse(X)))),multiply(inverse(inverse(multiply(Y,inverse(Y)))),X)).
% 5465 [para:4977.1.1,4663.1.1.1.2.2,demod:5434,5460] equal(multiply(X,Y),multiply(multiply(X,multiply(Z,inverse(Z))),Y)).
% 5474 [para:4977.1.1,4911.1.1.1.1.2.2,demod:5434,5460] equal(inverse(inverse(X)),X).
% 5477 [para:4977.1.2,37.1.1.1,demod:5459,5474] equal(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(multiply(multiply(U,inverse(U)),X),multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(W,inverse(W)),Z))))).
% 5478 [para:4977.1.1,37.1.1.1.2,demod:5477,5465,5474] equal(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,U)))),inverse(multiply(Y,multiply(Z,U)))).
% 5481 [para:4977.1.2,37.1.2.1.1.1,demod:5459,5474,5478] equal(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(X,multiply(multiply(multiply(U,inverse(U)),Y),multiply(multiply(V,inverse(V)),Z))))).
% 5495 [para:8.1.1,5474.1.1.1,demod:5478] equal(inverse(X),multiply(inverse(multiply(Y,multiply(Z,X))),multiply(multiply(multiply(U,inverse(U)),Y),multiply(multiply(V,inverse(V)),Z)))).
% 5499 [para:5474.1.1,9.1.2.1.2,demod:5477] equal(inverse(multiply(X,multiply(Y,Z))),multiply(multiply(inverse(U),U),inverse(multiply(X,multiply(Y,Z))))).
% 5500 [para:9.1.1,5474.1.1.1,demod:5474,5478] equal(multiply(X,multiply(Y,Z)),multiply(multiply(multiply(U,inverse(U)),X),multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(W,inverse(W)),Z)))).
% 5501 [para:5474.1.1,11.1.1.1.2,demod:5499] equal(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,Y))),Z).
% 5509 [para:5474.1.1,12.1.1.1.1.1.2,demod:5474,5495,5481,5499,5478] equal(X,multiply(multiply(Y,inverse(Y)),X)).
% 5510 [para:5474.1.1,12.1.2.1.2,demod:5501,5509] equal(X,multiply(multiply(inverse(Y),Y),X)).
% 5511 [para:12.1.1,5474.1.1.1,demod:5509] equal(inverse(X),multiply(inverse(multiply(Y,multiply(Z,X))),multiply(Y,Z))).
% 5521 [para:167.1.1,5474.1.1.1,demod:4911] equal(X,multiply(X,multiply(Y,inverse(Y)))).
% 5531 [para:20.1.1,5474.1.1.1,demod:5521,5509,5474,5511] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 5535 [para:5474.1.1,425.1.2.2,demod:5474,5521] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 5578 [para:20.1.1,5531.1.2.1,demod:5474,5511,5521,5509] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 5592 [para:8.1.1,5578.1.2.2,demod:5474,5509] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 5607 [input:6,cut:5535] -equal(multiply(multiply(inverse(b2),b2),a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 5608 [para:5500.1.1,5607.2.2,demod:5510,5509,5592,cut:4,cut:4] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos 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 8
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 284
% derived clauses: 378867
% kept clauses: 5597
% kept size sum: 202920
% kept mid-nuclei: 2
% kept new demods: 317
% forw unit-subs: 307088
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 6
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.73
% process. runtime: 7.70
% 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/GRP062-1+eq_r.in")
%
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