TSTP Solution File: GRP111-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP111-1 : TPTP v3.4.2. Bugfixed v2.7.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art08.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/GRP111-1+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 7 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 7 7)
% (binary-posweight-lex-big-order 30 #f 7 7)
% (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))) | -equal(multiply(a4,b4),multiply(b4,a4)).
% 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))).
% -equal(multiply(a4,b4),multiply(b4,a4)).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(4,40,0,8,0,0,1925,4,754)
%
%
% START OF PROOF
% 5 [] equal(X,X).
% 6 [] equal(double_divide(inverse(double_divide(inverse(double_divide(X,inverse(Y))),Z)),double_divide(X,Z)),Y).
% 7 [] equal(multiply(X,Y),inverse(double_divide(Y,X))).
% 8 [] -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)) | -equal(multiply(a4,b4),multiply(b4,a4)).
% 9 [para:6.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,Y),multiply(Y,multiply(inverse(Z),X))),inverse(Z)).
% 10 [para:7.1.2,6.1.1.1,demod:7] equal(double_divide(multiply(X,multiply(inverse(Y),Z)),double_divide(Z,X)),Y).
% 11 [para:7.1.2,6.1.1.1.1.1.1.2,demod:7] equal(double_divide(multiply(X,multiply(multiply(Y,Z),U)),double_divide(U,X)),double_divide(Z,Y)).
% 12 [para:6.1.1,6.1.1.1.1,demod:7] equal(double_divide(inverse(X),double_divide(multiply(inverse(X),Y),double_divide(Y,inverse(Z)))),Z).
% 13 [para:6.1.1,6.1.1.2,demod:7] equal(double_divide(multiply(double_divide(X,Y),multiply(inverse(Z),multiply(Y,multiply(inverse(U),X)))),U),Z).
% 14 [para:7.1.2,9.1.1.2.2.1,demod:7] equal(multiply(double_divide(X,Y),multiply(Y,multiply(multiply(Z,U),X))),multiply(Z,U)).
% 15 [para:6.1.1,9.1.1.1,demod:7] equal(multiply(X,multiply(double_divide(Y,Z),multiply(inverse(U),multiply(Z,multiply(inverse(X),Y))))),inverse(U)).
% 18 [para:7.1.2,12.1.1.1,demod:7] equal(double_divide(multiply(X,Y),double_divide(multiply(multiply(X,Y),Z),double_divide(Z,inverse(U)))),U).
% 22 [para:12.1.1,9.1.1.1] equal(multiply(X,multiply(double_divide(multiply(inverse(Y),Z),double_divide(Z,inverse(X))),multiply(inverse(U),inverse(Y)))),inverse(U)).
% 23 [para:11.1.1,6.1.1.2,demod:7] equal(double_divide(multiply(double_divide(X,Y),multiply(inverse(Z),multiply(Y,multiply(multiply(U,V),X)))),double_divide(V,U)),Z).
% 25 [para:11.1.1,9.1.1.1] equal(multiply(double_divide(X,Y),multiply(double_divide(Z,U),multiply(inverse(V),multiply(U,multiply(multiply(Y,X),Z))))),inverse(V)).
% 29 [para:14.1.1,9.1.1.2] equal(multiply(double_divide(multiply(multiply(X,Y),Z),double_divide(Z,inverse(U))),multiply(X,Y)),inverse(U)).
% 33 [para:11.1.1,14.1.1.1] equal(multiply(double_divide(X,Y),multiply(double_divide(Z,U),multiply(multiply(V,W),multiply(U,multiply(multiply(Y,X),Z))))),multiply(V,W)).
% 38 [para:18.1.1,14.1.1.1] equal(multiply(X,multiply(double_divide(multiply(multiply(Y,Z),U),double_divide(U,inverse(X))),multiply(multiply(V,W),multiply(Y,Z)))),multiply(V,W)).
% 44 [para:29.1.1,9.1.1.2] equal(multiply(double_divide(X,double_divide(multiply(multiply(inverse(Y),X),Z),double_divide(Z,inverse(U)))),inverse(U)),inverse(Y)).
% 47 [para:15.1.1,13.1.1.1.2,demod:10] equal(double_divide(multiply(inverse(X),inverse(Y)),Y),X).
% 48 [para:15.1.1,15.1.1.2.2,demod:10] equal(multiply(X,multiply(inverse(Y),inverse(X))),inverse(Y)).
% 49 [para:7.1.2,47.1.1.1.1] equal(double_divide(multiply(multiply(X,Y),inverse(Z)),Z),double_divide(Y,X)).
% 50 [para:7.1.2,47.1.1.1.2] equal(double_divide(multiply(inverse(X),multiply(Y,Z)),double_divide(Z,Y)),X).
% 64 [para:48.1.1,10.1.1.1] equal(double_divide(inverse(X),double_divide(inverse(Y),Y)),X).
% 65 [para:48.1.1,9.1.1.2] equal(multiply(double_divide(inverse(X),X),inverse(Y)),inverse(Y)).
% 80 [para:7.1.2,64.1.1.1] equal(double_divide(multiply(X,Y),double_divide(inverse(Z),Z)),double_divide(Y,X)).
% 105 [para:48.1.1,50.1.1.1] equal(double_divide(inverse(X),double_divide(inverse(inverse(Y)),inverse(X))),Y).
% 131 [para:80.1.1,47.1.1,demod:7] equal(double_divide(multiply(X,inverse(X)),inverse(Y)),Y).
% 137 [para:131.1.1,6.1.1.2,demod:7,131] equal(double_divide(multiply(inverse(X),inverse(Y)),X),Y).
% 160 [para:137.1.1,80.1.1,demod:7] equal(X,double_divide(inverse(X),multiply(Y,inverse(Y)))).
% 161 [para:137.1.1,131.1.1] equal(inverse(inverse(X)),X).
% 162 [para:22.1.1,10.1.1.1.2,demod:161] equal(double_divide(multiply(X,inverse(Y)),double_divide(multiply(double_divide(multiply(inverse(Z),U),double_divide(U,V)),multiply(inverse(Y),inverse(Z))),X)),V).
% 164 [para:22.1.1,11.1.1.1.2,demod:162] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 176 [para:161.1.1,6.1.1.1.1.1.1.2,demod:7] equal(double_divide(multiply(X,multiply(Y,Z)),double_divide(Z,X)),inverse(Y)).
% 177 [para:161.1.1,9.1.1.2.2.1,demod:161] equal(multiply(double_divide(X,Y),multiply(Y,multiply(Z,X))),Z).
% 187 [para:161.1.1,47.1.1.1.1] equal(double_divide(multiply(X,inverse(Y)),Y),inverse(X)).
% 191 [para:161.1.1,48.1.1.2.1,demod:161] equal(multiply(X,multiply(Y,inverse(X))),Y).
% 192 [para:161.1.1,48.1.1.2.2] equal(multiply(inverse(X),multiply(inverse(Y),X)),inverse(Y)).
% 196 [para:161.1.1,65.1.1.2,demod:161] equal(multiply(double_divide(inverse(X),X),Y),Y).
% 202 [para:161.1.1,105.1.1.1,demod:161] equal(double_divide(X,double_divide(Y,X)),Y).
% 206 [para:161.1.1,137.1.1.1.1] equal(double_divide(multiply(X,inverse(Y)),inverse(X)),Y).
% 207 [para:161.1.1,137.1.1.1.2] equal(double_divide(multiply(inverse(X),Y),X),inverse(Y)).
% 211 [para:202.1.1,7.1.2.1] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 214 [para:6.1.1,202.1.1.2,demod:7] equal(double_divide(double_divide(X,Y),Z),multiply(Y,multiply(inverse(Z),X))).
% 215 [para:202.1.1,10.1.1.2,demod:202,214] equal(double_divide(double_divide(X,Y),X),Y).
% 217 [para:11.1.1,202.1.1.2] equal(double_divide(double_divide(X,Y),double_divide(Z,U)),multiply(Y,multiply(multiply(U,Z),X))).
% 218 [para:47.1.1,202.1.1.2] equal(double_divide(X,Y),multiply(inverse(Y),inverse(X))).
% 223 [para:137.1.1,202.1.1.2,demod:218] equal(double_divide(X,Y),double_divide(Y,X)).
% 224 [para:215.1.1,7.1.2.1] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 229 [para:137.1.1,215.1.1.1,demod:218] equal(double_divide(X,double_divide(X,Y)),Y).
% 230 [para:223.1.1,7.1.2.1,demod:7] equal(multiply(X,Y),multiply(Y,X)).
% 235 [para:223.1.1,202.1.1] equal(double_divide(double_divide(X,Y),Y),X).
% 236 [para:229.1.1,7.1.2.1] equal(multiply(double_divide(X,Y),X),inverse(Y)).
% 253 [para:235.1.1,7.1.2.1] equal(multiply(X,double_divide(Y,X)),inverse(Y)).
% 269 [para:7.1.2,191.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Z,multiply(Y,X))),Z).
% 270 [para:191.1.1,10.1.1.1.2,demod:161] equal(double_divide(multiply(X,Y),double_divide(multiply(Y,Z),X)),Z).
% 287 [para:161.1.1,196.1.1.1.1] equal(multiply(double_divide(X,inverse(X)),Y),Y).
% 298 [para:211.1.1,191.1.1.2] equal(multiply(X,inverse(Y)),double_divide(Y,inverse(X))).
% 302 [para:64.1.1,224.1.1.2,demod:298,7] equal(multiply(inverse(X),X),double_divide(Y,inverse(Y))).
% 306 [para:64.1.1,236.1.1.1,demod:7,298] equal(double_divide(X,inverse(X)),double_divide(Y,inverse(Y))).
% 307 [para:105.1.1,236.1.1.1,demod:7,161,298] equal(double_divide(X,inverse(Y)),multiply(inverse(X),Y)).
% 309 [para:131.1.1,236.1.1.1,demod:161,298] equal(multiply(X,double_divide(Y,inverse(Y))),X).
% 317 [para:6.1.1,253.1.1.2,demod:164,307,7] equal(multiply(double_divide(X,Y),Z),double_divide(double_divide(Z,inverse(X)),Y)).
% 318 [para:253.1.1,10.1.1.1.2,demod:317,298] equal(multiply(double_divide(X,multiply(double_divide(Y,X),Z)),Z),Y).
% 383 [para:160.1.2,13.1.1.1.1,demod:7,307,287,218,298] equal(double_divide(multiply(X,double_divide(Y,multiply(Z,X))),Z),Y).
% 387 [para:161.1.1,187.1.1.1.2] equal(double_divide(multiply(X,Y),inverse(Y)),inverse(X)).
% 399 [para:161.1.1,206.1.1.1.2] equal(double_divide(multiply(X,Y),inverse(X)),inverse(Y)).
% 403 [para:218.1.2,11.1.1.1.2.1,demod:7,176] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 419 [para:7.1.2,298.1.1.2] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(Z,Y),inverse(X))).
% 421 [para:164.1.1,298.1.1.2] equal(multiply(X,double_divide(Y,Z)),double_divide(multiply(Z,Y),inverse(X))).
% 432 [para:302.1.1,13.1.1.1.2,demod:307,309] equal(double_divide(double_divide(X,Y),Z),multiply(Y,double_divide(Z,inverse(X)))).
% 459 [para:387.1.1,6.1.1.2,demod:419,164,421] equal(multiply(X,multiply(Y,multiply(Z,double_divide(Y,X)))),Z).
% 482 [para:33.1.1,399.1.1.1,demod:215,217,7] equal(double_divide(multiply(X,Y),multiply(Z,U)),multiply(double_divide(Y,X),double_divide(U,Z))).
% 488 [para:164.1.1,403.1.2.2] equal(multiply(multiply(X,Y),Z),double_divide(inverse(Z),double_divide(Y,X))).
% 540 [para:202.1.1,177.1.1.1] equal(multiply(X,multiply(double_divide(X,Y),multiply(Z,Y))),Z).
% 546 [para:191.1.1,177.1.1.2.2,demod:317,298] equal(multiply(multiply(double_divide(X,Y),Z),multiply(Y,X)),Z).
% 557 [para:298.1.1,177.1.1.2.2,demod:317,298,482,432] equal(multiply(double_divide(X,multiply(Y,double_divide(Z,X))),Y),Z).
% 560 [para:177.1.1,387.1.1.1,demod:7,164] equal(double_divide(X,double_divide(multiply(X,Y),Z)),multiply(Z,Y)).
% 562 [para:177.1.1,399.1.1.1,demod:164,7] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(X,Z),Y)).
% 593 [para:269.1.1,269.1.1.2,demod:562] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(Z,X)).
% 603 [para:191.1.1,270.1.1.2.1,demod:298,562] equal(double_divide(X,multiply(double_divide(Y,X),Z)),double_divide(Z,inverse(Y))).
% 608 [para:270.1.1,236.1.1.1,demod:7,562] equal(multiply(X,multiply(Y,Z)),multiply(multiply(Y,X),Z)).
% 609 [para:270.1.1,253.1.1.2,demod:164,562] equal(multiply(double_divide(X,multiply(Y,Z)),Z),double_divide(X,Y)).
% 619 [para:177.1.1,270.1.1.2.1,demod:229,608,482,562] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(Z,X))).
% 643 [para:38.1.1,207.1.1.1,demod:164,161,608,562] equal(double_divide(X,multiply(Y,Z)),double_divide(Z,multiply(double_divide(U,multiply(double_divide(V,Y),multiply(W,V))),multiply(X,multiply(W,U))))).
% 648 [para:38.1.1,399.1.1.1,demod:307,643,164,562,608,421] equal(multiply(X,double_divide(Y,Z)),double_divide(Z,double_divide(X,inverse(Y)))).
% 683 [para:11.1.1,318.1.1.1.2.1,demod:608,609] equal(double_divide(double_divide(X,Y),double_divide(Z,U)),multiply(Y,multiply(Z,multiply(U,X)))).
% 722 [para:49.1.1,383.1.1.1.2,demod:608,164,562] equal(double_divide(X,multiply(Y,double_divide(Z,U))),multiply(Z,multiply(U,double_divide(X,Y)))).
% 756 [para:318.1.1,459.1.1.2.2,demod:229,608,562,482] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z))).
% 831 [para:540.1.1,270.1.1.2.1,demod:603,562] equal(double_divide(X,inverse(Y)),multiply(double_divide(X,Z),multiply(Y,Z))).
% 875 [para:546.1.1,33.1.1.2.2,demod:562,608] equal(multiply(double_divide(X,Y),multiply(double_divide(Z,U),V)),multiply(double_divide(X,multiply(U,multiply(Y,Z))),V)).
% 885 [para:44.1.1,191.1.1.2,demod:317,161,236,562,307,298] equal(double_divide(X,inverse(Y)),double_divide(Z,multiply(double_divide(Z,Y),X))).
% 896 [para:23.1.1,557.1.1.1.2.2,demod:831,875,562,482,7,307,683,608,593] equal(double_divide(X,double_divide(Y,Z)),double_divide(U,multiply(X,double_divide(Y,multiply(U,Z))))).
% 916 [para:33.1.1,560.1.1.2.1,demod:202,609,482,722,683,608,562] equal(double_divide(double_divide(X,Y),double_divide(Z,multiply(U,V))),multiply(U,double_divide(double_divide(Y,X),double_divide(Z,V)))).
% 917 [para:192.1.1,560.1.1.2.1,demod:432,307,298,488] equal(multiply(double_divide(X,inverse(Y)),Z),double_divide(double_divide(Z,Y),X)).
% 1120 [para:25.1.1,593.1.1.1.2,demod:896,831,875,562,7,683,608,317,307,482] equal(multiply(double_divide(X,multiply(Y,Z)),U),double_divide(double_divide(U,double_divide(Z,Y)),X)).
% 1122 [para:33.1.1,593.1.1.1.2,demod:229,1120,916,683,562,608,482] equal(double_divide(X,double_divide(double_divide(Y,Z),double_divide(U,V))),double_divide(double_divide(double_divide(Z,U),double_divide(V,X)),Y)).
% 1285 [para:619.1.1,176.1.1.1.2,demod:1122,562,683] equal(double_divide(X,double_divide(double_divide(double_divide(Y,multiply(Z,X)),U),double_divide(Z,Y))),inverse(U)).
% 1290 [para:214.1.2,562.1.2.1,demod:432,307] equal(double_divide(X,double_divide(double_divide(Y,Z),U)),double_divide(double_divide(double_divide(Y,X),U),Z)).
% 1926 [input:8,cut:230] -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)).
% 1927 [para:1285.1.2,1926.1.1.1.1,demod:608,235,917,307,253,648,885,562,202,1290,cut:5,cut:756,cut:306] 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 7
% clause depth limited to 7
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 452
% derived clauses: 216276
% kept clauses: 1914
% kept size sum: 33524
% kept mid-nuclei: 2
% kept new demods: 1156
% forw unit-subs: 214000
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 36
% fast unit cutoff: 2
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.57
% process. runtime: 7.55
% specific non-discr-tree subsumption statistics:
% tried: 2
% length fails: 0
% strength fails: 2
% 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/GRP111-1+eq_r.in")
%
%------------------------------------------------------------------------------