TSTP Solution File: GRP441-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP441-1 : TPTP v3.4.2. Released v2.6.0.
% 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 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/GRP441-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 8 1)
% (binary-posweight-lex-big-order 30 #f 8 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(3,40,0,6,0,0,6,50,0,9,0,0,9,50,0,12,0,0,17,50,0,20,0,0,35,50,4,38,0,4)
%
%
% START OF PROOF
% 36 [] equal(X,X).
% 37 [] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(U,multiply(X,Z))))))),U).
% 38 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 39 [para:37.1.1,37.1.1.1.2.2.1.1] equal(inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,W),inverse(multiply(X1,multiply(X,W))))))),X1).
% 40 [para:37.1.1,37.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(V,Z))))),U)))),V).
% 42 [para:40.1.1,37.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(W,U))))),V)),W)))),Z).
% 47 [para:37.1.1,42.1.1.1.2.2.1.1] equal(inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,multiply(multiply(inverse(X),multiply(multiply(inverse(W),X1),inverse(multiply(X2,multiply(X3,X1))))),X2)),X3)))),W).
% 49 [para:37.1.1,42.1.1.1.2.2.1.2.1.2.1.1] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(Z,multiply(X1,X3))))))).
% 53 [para:42.1.1,42.1.1.1.2.2.1.2.1.2.1.1] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(Z),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))).
% 56 [para:39.1.1,40.1.1.1.2.2.1.2.1.1] equal(inverse(multiply(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,W),inverse(multiply(X1,multiply(X,W)))))),multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(X1,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)))),X5).
% 137 [para:49.1.1,42.1.1] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(U),multiply(X,Z)))))),U).
% 152 [para:137.1.1,37.1.1.1.2.2.2.1.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(inverse(V),multiply(X,U)))))),inverse(multiply(W,V)))))),W).
% 156 [para:40.1.1,137.1.1.2.2.2] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(inverse(Z)),U),inverse(multiply(V,multiply(W,U))))),V)),W))),Z).
% 268 [para:49.1.2,152.1.1.1.2.2.1,demod:42] equal(inverse(multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y)))))),Z).
% 332 [para:268.1.1,49.1.2.2.2.2,demod:42] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,inverse(multiply(U,Z)))),U)))).
% 349 [para:268.1.1,152.1.1.1.2.2.1.2.2.2,demod:332] equal(inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(Z,X)))))),Z).
% 352 [para:268.1.1,268.1.1.1.2.2.2] equal(inverse(multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(Z,inverse(multiply(U,Z)))),U)))),inverse(Y)).
% 354 [para:349.1.1,37.1.1.1.2.2.2] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,U)))),Z)))),U).
% 414 [para:349.1.1,137.1.1.2.2.2] equal(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,inverse(U))))),Z))),U).
% 434 [para:349.1.1,268.1.1.1.2.2.2] equal(inverse(multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(inverse(Y),inverse(multiply(Z,U)))),Z)))),U).
% 438 [para:349.1.1,349.1.1.1.2.2.2] equal(inverse(multiply(multiply(X,multiply(inverse(X),inverse(multiply(Y,Z)))),multiply(U,multiply(inverse(U),Y)))),Z).
% 451 [para:332.1.2,137.1.1.2.2.1,demod:332] equal(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),X))))),Z).
% 456 [para:268.1.1,332.1.2.2.2.1.2.2] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(Z,multiply(U,inverse(multiply(V,U)))),V)),inverse(Z))))).
% 459 [para:349.1.1,332.1.2.2.2.1.2.2] equal(X,multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(Z,multiply(inverse(Z),inverse(multiply(U,V)))),U)),V)))).
% 503 [para:268.1.1,451.1.1.2.2.2] equal(multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),multiply(U,multiply(inverse(U),Z))),X).
% 506 [para:349.1.1,451.1.1.2.2.2] equal(multiply(multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Z))))),multiply(U,multiply(inverse(U),Y))),Z).
% 628 [para:352.1.1,42.1.1.1.2.2.1.2.1.2.1.1,demod:42] equal(X,multiply(inverse(Y),multiply(Y,multiply(multiply(X,multiply(Z,inverse(multiply(U,Z)))),U)))).
% 1285 [para:332.1.2,459.1.2.2.2,demod:332] equal(X,multiply(X,multiply(Y,multiply(inverse(Y),multiply(multiply(Z,multiply(inverse(Z),inverse(U))),U))))).
% 1370 [para:1285.1.2,503.1.1] equal(multiply(X,multiply(Y,inverse(multiply(multiply(multiply(Z,multiply(inverse(Z),inverse(U))),U),Y)))),X).
% 1440 [para:1370.1.1,37.1.1.1.2] equal(inverse(multiply(inverse(X),X)),multiply(multiply(Y,multiply(inverse(Y),inverse(Z))),Z)).
% 1577 [para:1440.1.1,49.1.2.2.2.2,demod:42] equal(multiply(X,Y),multiply(X,multiply(Z,multiply(multiply(inverse(Z),Y),multiply(multiply(U,multiply(inverse(U),inverse(V))),V))))).
% 1664 [para:1440.1.2,438.1.1.1] equal(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)).
% 1688 [para:1440.1.1,456.1.2.2.2.2,demod:1577] equal(X,multiply(X,multiply(multiply(multiply(inverse(Y),Y),multiply(Z,inverse(multiply(U,Z)))),U))).
% 1862 [para:1664.1.1,332.1.2.2.2.1.1,demod:1688] equal(X,multiply(X,inverse(multiply(inverse(Y),Y)))).
% 2031 [para:1862.1.2,49.1.2.2.2,demod:42] equal(multiply(X,Y),multiply(X,multiply(Z,multiply(inverse(Z),Y)))).
% 2033 [para:1862.1.2,137.1.1.2.2.1,demod:2031,1862] equal(multiply(X,inverse(multiply(inverse(Y),X))),Y).
% 2043 [para:1862.1.2,268.1.1.1.2.2] equal(inverse(multiply(inverse(X),multiply(X,Y))),inverse(Y)).
% 2044 [para:1862.1.2,268.1.1.1.2.2.2.1,demod:2043] equal(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),Y).
% 2048 [para:1862.1.2,332.1.2.2.2,demod:2031,2033] equal(X,multiply(X,multiply(inverse(Y),Y))).
% 2058 [para:1862.1.2,503.1.1.1.2,demod:2031] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 2060 [para:1862.1.2,628.1.2.2.2,demod:2048,2033] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 2069 [para:1862.1.2,414.1.1.2.2,demod:2031,2044] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 2104 [para:2048.1.2,37.1.1.1.2.2.1,demod:2069,2048] equal(inverse(multiply(X,inverse(multiply(Y,X)))),Y).
% 2161 [para:2048.1.2,268.1.1.1,demod:2104] equal(inverse(inverse(X)),X).
% 2173 [para:2048.1.2,354.1.1.1.2.2.1,demod:2069] equal(inverse(multiply(inverse(multiply(X,Y)),X)),Y).
% 2217 [para:56.1.1,156.1.1.2.2.1.1,demod:2161] equal(multiply(X,multiply(multiply(multiply(Y,multiply(multiply(Z,multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(W,multiply(Z,V)))))),multiply(multiply(W,X1),inverse(multiply(X2,multiply(Y,X1)))))),multiply(X3,multiply(multiply(inverse(X3),multiply(multiply(X2,X4),inverse(multiply(X5,multiply(X6,X4))))),X5))),multiply(multiply(X6,multiply(multiply(inverse(X),multiply(multiply(X7,X8),inverse(multiply(X9,multiply(X10,X8))))),X9)),X10))),X7).
% 2285 [para:56.1.1,53.1.2.2.2.1.1,demod:2217] equal(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))),inverse(Z)).
% 2286 [para:56.1.1,53.1.2.2.2.1.2.1.2.1.1,demod:56,2285] equal(X,multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),multiply(multiply(X,U),inverse(multiply(V,multiply(W,U))))),V)),W)))).
% 2345 [para:349.1.1,2161.1.1.1,demod:2069] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 2351 [para:434.1.1,2161.1.1.1,demod:2060,2069] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 2442 [para:506.1.1,2058.1.1.1,demod:2069] equal(multiply(X,inverse(Y)),inverse(multiply(Y,inverse(X)))).
% 2490 [para:49.1.2,2060.1.2.2,demod:2286] equal(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(U,Y))))),multiply(inverse(U),inverse(Z))).
% 2506 [para:451.1.1,2060.1.2.2,demod:2069] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),X)).
% 2544 [para:156.1.1,2069.1.1.2,demod:2161] equal(multiply(X,Y),multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(X,multiply(multiply(Y,U),inverse(multiply(V,multiply(W,U))))),V)),W))).
% 2768 [para:37.1.1,2173.1.1.1.1,demod:2490] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 2783 [para:2173.1.1,49.1.2.2.2.2,demod:2161,2345,2768,2544] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(U,multiply(multiply(inverse(U),Y),Z)))).
% 2792 [para:354.1.1,2173.1.1.1.1,demod:2768] equal(inverse(multiply(X,Y)),multiply(Z,multiply(inverse(multiply(multiply(multiply(U,X),Y),Z)),U))).
% 2934 [para:2351.1.2,42.1.1.1.2.2.1.2.1.2.1,demod:2506,2792,2783,2768] equal(multiply(inverse(X),multiply(multiply(X,Y),Z)),multiply(Y,Z)).
% 2936 [para:2351.1.2,39.1.1.1.2.2.2.1,demod:2934,2161,2345,2768,2490] equal(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(multiply(X,Y),Z))).
% 2960 [para:2351.1.2,47.1.1.1.2.2.1.2.1.2.1,demod:2442,2934,2351,2936,2345,2768,2490] equal(multiply(multiply(X,multiply(Y,Z)),inverse(Z)),multiply(X,Y)).
% 2969 [para:2351.1.2,49.1.2.2.2.2.1,demod:2783,2161,2960,2442,2768,2544,2936] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 3004 [para:2969.1.2,38.1.1,cut:36] 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
% clause length limited to 1
% clause depth limited to 12
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 132
% derived clauses: 34464
% kept clauses: 2985
% kept size sum: 116582
% kept mid-nuclei: 0
% kept new demods: 2193
% forw unit-subs: 25160
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 1
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 1.66
% process. runtime: 1.64
% 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/GRP441-1+eq_r.in")
%
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