TSTP Solution File: GRP108-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP108-1 : 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 : 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/GRP108-1+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 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 8 7)
% (binary-posweight-lex-big-order 30 #f 8 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(4,40,0,8,0,0,1789,4,760)
%
%
% START OF PROOF
% 5 [] equal(X,X).
% 6 [] equal(inverse(double_divide(inverse(double_divide(X,inverse(double_divide(Y,double_divide(X,Z))))),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,demod:7] equal(multiply(X,multiply(multiply(double_divide(Y,X),Z),Y)),Z).
% 10 [para:6.1.1,6.1.1.1.1.1.2,demod:7] equal(multiply(X,multiply(Y,Z)),multiply(multiply(double_divide(U,double_divide(Z,X)),Y),U)).
% 11 [para:10.1.2,9.1.1.2] equal(multiply(double_divide(X,Y),multiply(Y,multiply(Z,X))),Z).
% 13 [para:9.1.1,11.1.1.2.2] equal(multiply(double_divide(multiply(multiply(double_divide(X,Y),Z),X),U),multiply(U,Z)),Y).
% 14 [para:10.1.2,11.1.1.2] equal(multiply(double_divide(X,multiply(double_divide(multiply(Y,X),double_divide(Z,U)),V)),multiply(U,multiply(V,Z))),Y).
% 15 [para:10.1.2,11.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Y,multiply(Z,multiply(U,V)))),multiply(double_divide(X,double_divide(V,Z)),U)).
% 16 [para:11.1.1,11.1.1.2] equal(multiply(double_divide(multiply(X,Y),double_divide(Y,Z)),X),Z).
% 17 [para:11.1.1,11.1.1.2.2] equal(multiply(double_divide(multiply(X,multiply(Y,Z)),U),multiply(U,Y)),double_divide(Z,X)).
% 18 [para:9.1.1,16.1.1.1.1] equal(multiply(double_divide(X,double_divide(multiply(multiply(double_divide(Y,Z),X),Y),U)),Z),U).
% 19 [para:10.1.2,16.1.1.1.1] equal(multiply(double_divide(multiply(X,multiply(Y,Z)),double_divide(U,V)),multiply(double_divide(U,double_divide(Z,X)),Y)),V).
% 20 [para:16.1.1,11.1.1.2] equal(multiply(double_divide(X,double_divide(multiply(multiply(Y,X),Z),double_divide(Z,U))),U),Y).
% 21 [para:16.1.1,11.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Y,Z)),double_divide(multiply(X,U),double_divide(U,Z))).
% 26 [para:13.1.1,11.1.1.2.2] equal(multiply(double_divide(multiply(X,Y),Z),multiply(Z,U)),double_divide(multiply(multiply(double_divide(V,U),Y),V),X)).
% 37 [para:17.1.1,16.1.1] equal(double_divide(X,multiply(double_divide(multiply(Y,X),Z),Y)),Z).
% 46 [para:37.1.1,7.1.2.1] equal(multiply(multiply(double_divide(multiply(X,Y),Z),X),Y),inverse(Z)).
% 58 [para:17.1.1,37.1.1.2] equal(double_divide(multiply(X,Y),double_divide(Y,multiply(Z,X))),Z).
% 81 [para:58.1.1,7.1.2.1] equal(multiply(double_divide(X,multiply(Y,Z)),multiply(Z,X)),inverse(Y)).
% 144 [para:81.1.1,14.1.1,demod:7] equal(multiply(double_divide(X,Y),multiply(Z,multiply(Y,X))),Z).
% 157 [para:144.1.1,9.1.1.2.1] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z))).
% 164 [para:11.1.1,144.1.1.2] equal(multiply(double_divide(multiply(X,Y),Z),X),double_divide(Y,Z)).
% 167 [para:16.1.1,144.1.1.2] equal(multiply(double_divide(X,Y),Z),double_divide(multiply(multiply(Y,X),U),double_divide(U,Z))).
% 175 [para:17.1.1,144.1.1.2] equal(multiply(double_divide(X,Y),double_divide(Z,U)),double_divide(multiply(U,multiply(X,Z)),Y)).
% 183 [para:58.1.1,144.1.1.1,demod:81] equal(multiply(X,multiply(Y,inverse(X))),Y).
% 191 [para:183.1.1,9.1.1] equal(multiply(double_divide(inverse(X),X),Y),Y).
% 203 [para:183.1.1,58.1.1.2.2,demod:167] equal(multiply(double_divide(inverse(X),Y),Y),X).
% 205 [para:46.1.1,183.1.1.2,demod:164] equal(multiply(X,inverse(Y)),double_divide(inverse(X),Y)).
% 251 [para:191.1.1,9.1.1,demod:205,10] equal(multiply(X,double_divide(inverse(Y),X)),Y).
% 253 [para:191.1.1,16.1.1.1.1,demod:251,205,175] equal(double_divide(X,double_divide(X,Y)),Y).
% 257 [para:191.1.1,58.1.1.1,demod:253] equal(multiply(X,double_divide(inverse(Y),Y)),X).
% 259 [para:191.1.1,46.1.1.1.1.1,demod:251,205,175] equal(multiply(double_divide(X,Y),X),inverse(Y)).
% 261 [para:191.1.1,183.1.1.2,demod:205] equal(double_divide(inverse(X),X),double_divide(inverse(Y),Y)).
% 264 [para:191.1.1,15.1.1.2.2.2,demod:251,205,175] equal(multiply(double_divide(X,Y),multiply(Y,multiply(Z,U))),double_divide(X,double_divide(U,Z))).
% 265 [para:253.1.1,6.1.1.1.1.1.2.1,demod:7] equal(multiply(X,multiply(inverse(X),Y)),Y).
% 268 [para:253.1.1,10.1.2.1.1] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 272 [para:253.1.1,37.1.1.2.1] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 273 [para:37.1.1,253.1.1.2,demod:272] equal(double_divide(X,Y),multiply(double_divide(X,multiply(Y,Z)),Z)).
% 276 [para:7.1.2,203.1.1.1.1,demod:272] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(X,Z)).
% 279 [para:203.1.1,11.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Y,Z)),double_divide(inverse(Z),X)).
% 289 [para:203.1.1,58.1.1.2.2,demod:272] equal(double_divide(X,multiply(double_divide(X,Y),Z)),double_divide(inverse(Y),Z)).
% 290 [para:203.1.1,81.1.1] equal(X,inverse(inverse(X))).
% 291 [para:203.1.1,81.1.1.1.2,demod:205,7] equal(multiply(double_divide(X,Y),multiply(Z,X)),double_divide(inverse(Z),Y)).
% 293 [para:203.1.1,144.1.1.2] equal(multiply(double_divide(X,Y),Z),double_divide(inverse(Z),multiply(Y,X))).
% 295 [para:203.1.1,183.1.1.2] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 296 [para:203.1.1,15.1.1.2,demod:273,272,293] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(double_divide(X,double_divide(Y,Z)),U)).
% 299 [para:7.1.2,290.1.2.1] equal(double_divide(X,Y),inverse(multiply(Y,X))).
% 301 [para:290.1.2,183.1.1.2.2] equal(multiply(inverse(X),multiply(Y,X)),Y).
% 303 [para:290.1.2,203.1.1.1.1] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 306 [para:251.1.1,9.1.1.2.1] equal(multiply(X,multiply(Y,Z)),double_divide(inverse(Y),double_divide(Z,X))).
% 322 [para:11.1.1,18.1.1.1.2.1.1,demod:276,299,289,268,272] equal(double_divide(double_divide(X,Y),X),Y).
% 323 [para:18.1.1,17.1.1.1.1,demod:253,272,293,291,268,279] equal(double_divide(inverse(X),Y),double_divide(Z,multiply(Y,double_divide(Z,X)))).
% 324 [para:37.1.1,18.1.1.1.2,demod:273,272,291,268] equal(multiply(double_divide(X,Y),Z),double_divide(double_divide(inverse(X),Z),Y)).
% 330 [para:18.1.1,183.1.1.2,demod:253,272,295,291,268] equal(multiply(X,Y),multiply(Y,X)).
% 332 [para:322.1.1,7.1.2.1] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 333 [para:322.1.1,6.1.1.1.1.1.2.1,demod:205,272,7] equal(multiply(double_divide(inverse(X),Y),Z),double_divide(double_divide(Z,X),Y)).
% 339 [para:37.1.1,322.1.1.1,demod:273,272] equal(double_divide(X,Y),double_divide(Y,X)).
% 343 [para:322.1.1,322.1.1.1] equal(double_divide(X,double_divide(Y,X)),Y).
% 366 [para:339.1.1,10.1.2.1.1.2,demod:268,296] equal(multiply(X,multiply(Y,Z)),double_divide(U,double_divide(X,multiply(Z,multiply(Y,U))))).
% 380 [para:343.1.1,18.1.1.1.2,demod:291,268] equal(multiply(double_divide(X,Y),Z),double_divide(Y,double_divide(inverse(X),Z))).
% 383 [para:19.1.1,11.1.1.2,demod:205,303,366,268,272] equal(multiply(X,double_divide(inverse(Y),Z)),double_divide(Z,double_divide(X,Y))).
% 384 [para:19.1.1,11.1.1.2.2,demod:268,272,306,279,296] equal(multiply(double_divide(X,multiply(Y,Z)),multiply(U,V)),double_divide(X,multiply(double_divide(V,U),multiply(Y,Z)))).
% 425 [para:257.1.1,15.1.1.2.2.2,demod:259,324,264] equal(double_divide(X,double_divide(Y,Z)),multiply(double_divide(X,inverse(Z)),Y)).
% 426 [para:259.1.1,17.1.1.1.1,demod:253,272,333] equal(double_divide(double_divide(X,multiply(Y,Z)),Z),multiply(Y,X)).
% 428 [para:259.1.1,15.1.1.2.2.2,demod:380,323,296,332,272,175,383,205] equal(double_divide(X,multiply(inverse(Y),Z)),multiply(double_divide(X,Z),Y)).
% 430 [para:265.1.1,15.1.1.2,demod:428,296] equal(multiply(double_divide(X,Y),multiply(Z,U)),double_divide(X,multiply(double_divide(U,Z),Y))).
% 437 [para:20.1.1,13.1.1.1.1.1,demod:253,268,303,430,384,272] equal(double_divide(X,double_divide(Y,inverse(Z))),multiply(double_divide(X,Z),Y)).
% 448 [para:16.1.1,301.1.1.2,demod:289,272] equal(multiply(inverse(X),Y),double_divide(inverse(Y),X)).
% 451 [para:14.1.1,301.1.1.2,demod:289,272,299] equal(multiply(double_divide(X,multiply(Y,Z)),U),double_divide(double_divide(U,double_divide(X,Y)),Z)).
% 461 [para:21.1.2,10.1.2.1.1.2,demod:253,268,437,303,451,272,430] equal(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),U)),double_divide(double_divide(Z,U),Y)).
% 465 [para:13.1.1,21.1.1.2,demod:461,272,322,451,324,289,430,268] equal(double_divide(X,double_divide(Y,Z)),double_divide(double_divide(Z,Y),X)).
% 481 [para:322.1.1,21.1.2.2,demod:272,303,430] equal(double_divide(X,inverse(Y)),double_divide(double_divide(Y,Z),multiply(Z,X))).
% 597 [para:157.1.1,26.1.1.1.1,demod:253,343,451,430,384,268,272] equal(double_divide(X,double_divide(Y,double_divide(Z,U))),double_divide(double_divide(double_divide(X,U),Y),Z)).
% 899 [para:465.1.1,426.1.1] equal(double_divide(double_divide(X,Y),double_divide(Z,multiply(U,double_divide(Y,X)))),multiply(U,Z)).
% 1172 [para:481.1.2,21.1.2.2,demod:425,343,451,272,430] equal(double_divide(X,double_divide(Y,Z)),double_divide(double_divide(U,Z),double_divide(Y,double_divide(X,U)))).
% 1790 [input:8,cut:330] -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)).
% 1791 [para:899.1.2,1790.1.1,demod:268,343,1172,253,597,333,448,cut:5,cut:5,cut:261] 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 8
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 281
% derived clauses: 139919
% kept clauses: 1778
% kept size sum: 34796
% kept mid-nuclei: 2
% kept new demods: 620
% forw unit-subs: 138098
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 4
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.63
% process. runtime: 7.60
% 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/GRP108-1+eq_r.in")
%
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