TSTP Solution File: GRP101-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP101-1 : 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 : art10.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/GRP101-1+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 6 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 6 7)
% (binary-posweight-lex-big-order 30 #f 6 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),identity) | -equal(multiply(identity,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),identity).
% -equal(multiply(identity,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(6,40,0,12,0,0,1746,4,755)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))),double_divide(identity,identity)),Y).
% 9 [] equal(multiply(X,Y),double_divide(double_divide(Y,X),identity)).
% 10 [] equal(inverse(X),double_divide(X,identity)).
% 11 [] equal(identity,double_divide(X,inverse(X))).
% 12 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(a4,b4),multiply(b4,a4)) | -equal(multiply(identity,a2),a2).
% 13 [para:9.1.2,10.1.2] equal(inverse(double_divide(X,Y)),multiply(Y,X)).
% 14 [para:10.1.2,9.1.2.1,demod:10] equal(multiply(identity,X),inverse(inverse(X))).
% 15 [para:11.1.2,9.1.2.1,demod:10] equal(multiply(inverse(X),X),inverse(identity)).
% 16 [para:9.1.2,9.1.2.1,demod:10] equal(multiply(identity,double_divide(X,Y)),inverse(multiply(Y,X))).
% 17 [para:14.1.2,11.1.2.2] equal(identity,double_divide(inverse(X),multiply(identity,X))).
% 18 [para:14.1.2,14.1.2.1] equal(multiply(identity,inverse(X)),inverse(multiply(identity,X))).
% 21 [para:13.1.1,11.1.2.2] equal(identity,double_divide(double_divide(X,Y),multiply(Y,X))).
% 22 [para:13.1.1,15.1.1.1] equal(multiply(multiply(X,Y),double_divide(Y,X)),inverse(identity)).
% 25 [para:18.1.2,17.1.2.1] equal(identity,double_divide(multiply(identity,inverse(X)),multiply(identity,multiply(identity,X)))).
% 26 [para:10.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(identity,double_divide(double_divide(X,inverse(Y)),inverse(Y))),inverse(identity)),X).
% 27 [para:10.1.2,8.1.1.1.2.2,demod:10] equal(double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),inverse(Z))),inverse(identity)),Y).
% 28 [para:11.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(inverse(X),double_divide(inverse(Y),inverse(X))),inverse(identity)),Y).
% 29 [para:8.1.1,9.1.2.1,demod:10] equal(multiply(inverse(identity),double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),inverse(Z)))),inverse(Y)).
% 30 [para:9.1.2,8.1.1.1.2.1.2,demod:10,9] equal(double_divide(double_divide(identity,double_divide(double_divide(X,multiply(Y,Z)),multiply(Y,Z))),inverse(identity)),X).
% 32 [para:21.1.2,8.1.1.1.2.1.2,demod:9,10] equal(double_divide(double_divide(multiply(X,Y),double_divide(inverse(Z),multiply(X,Y))),inverse(identity)),Z).
% 33 [para:8.1.1,8.1.1.1.2.1,demod:10] equal(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z)))).
% 38 [para:11.1.2,28.1.1.1.2,demod:18,10,14] equal(double_divide(multiply(identity,inverse(X)),inverse(identity)),X).
% 44 [para:13.1.1,38.1.1.1.2] equal(double_divide(multiply(identity,multiply(X,Y)),inverse(identity)),double_divide(Y,X)).
% 48 [para:11.1.2,26.1.1.1.2.1] equal(double_divide(double_divide(identity,double_divide(identity,inverse(X))),inverse(identity)),X).
% 53 [para:11.1.2,48.1.1.1.2,demod:10] equal(double_divide(inverse(identity),inverse(identity)),identity).
% 61 [para:53.1.1,26.1.1.1.2.1,demod:53,10,11] equal(identity,inverse(identity)).
% 62 [para:61.1.2,14.1.2.1,demod:61] equal(multiply(identity,identity),identity).
% 63 [para:61.1.2,28.1.1.1.1,demod:9,14,10,61] equal(multiply(multiply(identity,X),identity),X).
% 65 [?] ?
% 66 [para:61.1.2,38.1.1.2,demod:14,18,10] equal(multiply(identity,multiply(identity,X)),X).
% 67 [para:61.1.2,44.1.1.2,demod:18,10] equal(multiply(identity,inverse(multiply(X,Y))),double_divide(Y,X)).
% 79 [para:8.1.1,27.1.1.1.2.1,demod:9,10,61] equal(multiply(inverse(X),identity),double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z)))).
% 81 [para:27.1.1,16.1.1.2,demod:67,18,79,61] equal(multiply(identity,X),double_divide(identity,inverse(X))).
% 83 [para:25.1.2,27.1.1.1.2.1.2,demod:9,61,14,18,10,66] equal(multiply(double_divide(inverse(X),Y),Y),X).
% 84 [para:28.1.1,27.1.1.1.2.1.2,demod:9,65,13,61] equal(multiply(double_divide(double_divide(X,Y),Y),identity),X).
% 85 [?] ?
% 86 [para:48.1.1,27.1.1.1.2,demod:9,61] equal(multiply(X,inverse(X)),identity).
% 91 [para:86.1.1,44.1.1.1.2,demod:10,61,62] equal(identity,double_divide(inverse(X),X)).
% 93 [para:13.1.1,91.1.2.1] equal(identity,double_divide(multiply(X,Y),double_divide(Y,X))).
% 95 [para:91.1.2,8.1.1.1.2.1,demod:13,9,61,81,10] equal(multiply(multiply(identity,X),Y),multiply(Y,X)).
% 97 [para:91.1.2,28.1.1.1.2,demod:18,61,14,10] equal(multiply(identity,inverse(X)),inverse(X)).
% 98 [para:14.1.2,97.1.1.2,demod:14,66] equal(X,multiply(identity,X)).
% 99 [para:98.1.2,16.1.1] equal(double_divide(X,Y),inverse(multiply(Y,X))).
% 100 [para:98.1.2,63.1.1.1] equal(multiply(X,identity),X).
% 103 [para:100.1.1,44.1.1.1.2,demod:10,61,98] equal(inverse(X),double_divide(identity,X)).
% 106 [para:8.1.1,29.1.1.2.2.1.2,demod:13,98,14,97,85,79,10,103,61] equal(multiply(X,double_divide(Y,X)),inverse(Y)).
% 108 [para:91.1.2,29.1.1.2.2.1,demod:13,99,16,98,81,61] equal(double_divide(X,Y),double_divide(Y,X)).
% 110 [para:108.1.1,9.1.2.1,demod:9] equal(multiply(X,Y),multiply(Y,X)).
% 119 [para:108.1.1,26.1.1.1.2.1,demod:99,10,61,13,103] equal(double_divide(double_divide(inverse(X),Y),inverse(X)),Y).
% 122 [para:108.1.1,30.1.1.1.2,demod:99,10,61,13,103] equal(double_divide(multiply(X,Y),double_divide(Z,multiply(X,Y))),Z).
% 123 [para:108.1.1,30.1.1.1.2.1,demod:99,10,61,13,103] equal(double_divide(double_divide(multiply(X,Y),Z),multiply(X,Y)),Z).
% 124 [para:110.1.1,30.1.1.1.2.1.2,demod:99,10,61,13,103] equal(double_divide(double_divide(X,multiply(Y,Z)),multiply(Z,Y)),X).
% 125 [para:14.1.2,83.1.1.1.1,demod:98] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 133 [para:106.1.1,44.1.1.1.2,demod:98,14,10,61,97] equal(X,double_divide(double_divide(X,Y),Y)).
% 137 [para:133.1.2,8.1.1.1.2.1.2,demod:61,103,9] equal(multiply(double_divide(double_divide(X,Y),multiply(Z,Y)),Z),X).
% 139 [para:108.1.1,133.1.2.1] equal(X,double_divide(double_divide(Y,X),Y)).
% 142 [para:139.1.2,8.1.1.1.2.1.2,demod:61,103,9] equal(multiply(double_divide(double_divide(X,Y),multiply(Y,Z)),Z),X).
% 154 [para:133.1.2,33.1.2.2.1,demod:99,103,9,61] equal(multiply(double_divide(X,Y),Z),double_divide(Y,double_divide(Z,inverse(X)))).
% 160 [para:81.1.2,8.1.1.1.2.1.2,demod:9,61,103,98] equal(multiply(multiply(X,Y),inverse(X)),Y).
% 162 [para:14.1.2,160.1.1.2,demod:98] equal(multiply(multiply(inverse(X),Y),X),Y).
% 165 [para:110.1.1,160.1.1.1] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 166 [para:83.1.1,160.1.1.1,demod:13] equal(multiply(X,multiply(Y,inverse(X))),Y).
% 168 [para:106.1.1,160.1.1.1] equal(multiply(inverse(X),inverse(Y)),double_divide(X,Y)).
% 172 [para:106.1.1,162.1.1.1] equal(multiply(inverse(X),Y),double_divide(X,inverse(Y))).
% 182 [para:83.1.1,165.1.1.1] equal(multiply(X,inverse(Y)),double_divide(inverse(X),Y)).
% 185 [para:83.1.1,166.1.1.2] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 199 [para:168.1.1,22.1.1.1,demod:61,185] equal(multiply(double_divide(X,Y),multiply(X,Y)),identity).
% 200 [para:13.1.1,172.1.1.1] equal(multiply(multiply(X,Y),Z),double_divide(double_divide(Y,X),inverse(Z))).
% 202 [para:172.1.1,30.1.1.1.2.1.2,demod:9,61,99,103,172,154] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Z)),Z),Y).
% 213 [para:13.1.1,182.1.1.2] equal(multiply(X,multiply(Y,Z)),double_divide(inverse(X),double_divide(Z,Y))).
% 216 [para:99.1.2,182.1.1.2] equal(multiply(X,double_divide(Y,Z)),double_divide(inverse(X),multiply(Z,Y))).
% 218 [para:185.1.2,8.1.1.1.2.1.2,demod:99,61,103,213,98,14,10] equal(double_divide(multiply(X,double_divide(Y,multiply(Z,X))),Z),Y).
% 225 [para:33.1.2,84.1.1.1.1,demod:100,216,200,98,81,10,61] equal(multiply(X,double_divide(Y,multiply(double_divide(Y,Z),X))),Z).
% 227 [para:95.1.1,32.1.1.1.1,demod:9,61,216,98] equal(multiply(multiply(X,double_divide(Y,Z)),multiply(Y,Z)),X).
% 236 [para:33.1.2,199.1.1.1,demod:99,172,200,98,81,10,61] equal(double_divide(X,double_divide(multiply(multiply(double_divide(Y,Z),X),Y),Z)),identity).
% 237 [para:122.1.1,8.1.1.1.2.1.2,demod:9,61,103,99,10] equal(multiply(double_divide(double_divide(X,Y),double_divide(Z,U)),double_divide(Y,multiply(U,Z))),X).
% 241 [para:110.1.1,123.1.1.1.1] equal(double_divide(double_divide(multiply(X,Y),Z),multiply(Y,X)),Z).
% 245 [para:124.1.1,30.1.1.1.2.1,demod:99,10,61,13,103] equal(double_divide(X,multiply(Y,Z)),double_divide(X,multiply(Z,Y))).
% 263 [para:133.1.2,137.1.1.1.1] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(X,Z)).
% 289 [para:119.1.1,142.1.1.1.1,demod:154,172] equal(multiply(multiply(double_divide(X,Y),Z),X),double_divide(inverse(Z),Y)).
% 315 [para:202.1.1,166.1.1.2,demod:13,182] equal(multiply(X,Y),double_divide(Z,double_divide(multiply(Y,Z),X))).
% 327 [para:218.1.1,133.1.2.1] equal(multiply(X,double_divide(Y,multiply(Z,X))),double_divide(Y,Z)).
% 328 [para:133.1.2,218.1.1.1.2] equal(double_divide(multiply(X,Y),Z),double_divide(Y,multiply(Z,X))).
% 356 [para:93.1.2,225.1.1.2.2.1,demod:328,98] equal(multiply(X,double_divide(Y,multiply(X,Z))),double_divide(Y,Z)).
% 357 [para:122.1.1,225.1.1.2.2.1,demod:328] equal(multiply(X,double_divide(Y,multiply(multiply(Z,X),U))),double_divide(Z,multiply(U,Y))).
% 359 [para:83.1.1,227.1.1.1,demod:213] equal(multiply(X,multiply(Y,Z)),multiply(X,multiply(Z,Y))).
% 360 [para:125.1.1,227.1.1.1,demod:99,172] equal(double_divide(X,double_divide(Y,Z)),double_divide(X,double_divide(Z,Y))).
% 362 [para:227.1.1,165.1.1.1,demod:99] equal(multiply(X,double_divide(Y,Z)),multiply(X,double_divide(Z,Y))).
% 396 [para:241.1.1,125.1.1.1,demod:13,328] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Z),Y)).
% 404 [para:172.1.1,245.1.1.2,demod:182,154] equal(multiply(double_divide(X,Y),Z),double_divide(Y,double_divide(inverse(X),Z))).
% 588 [para:263.1.1,315.1.2.2.1] equal(multiply(X,double_divide(Y,multiply(Z,U))),double_divide(Z,double_divide(double_divide(Y,U),X))).
% 625 [para:263.1.1,327.1.1.2.2] equal(multiply(X,double_divide(Y,double_divide(Z,U))),double_divide(Y,double_divide(Z,multiply(X,U)))).
% 719 [para:360.1.1,362.1.1.2,demod:625] equal(double_divide(X,double_divide(Y,multiply(Z,U))),multiply(Z,double_divide(double_divide(U,Y),X))).
% 810 [para:356.1.1,236.1.1.2.1.1,demod:328] equal(double_divide(double_divide(X,multiply(double_divide(Y,Z),U)),double_divide(Y,multiply(Z,double_divide(X,U)))),identity).
% 811 [para:237.1.1,315.1.2.2.1,demod:719] equal(double_divide(double_divide(X,Y),double_divide(Z,multiply(U,V))),double_divide(double_divide(Z,multiply(Y,X)),double_divide(V,U))).
% 915 [para:263.1.1,357.1.1.2.2.1,demod:588] equal(double_divide(double_divide(X,Y),double_divide(double_divide(Z,U),V)),double_divide(double_divide(X,multiply(V,Y)),multiply(U,Z))).
% 922 [para:357.1.1,328.1.1.1,demod:811,915,396] equal(double_divide(double_divide(X,multiply(Y,Z)),U),double_divide(double_divide(V,Y),double_divide(Z,multiply(X,double_divide(V,U))))).
% 1747 [input:12,cut:110] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(identity,a2),a2).
% 1748 [para:810.1.2,1747.2.2,demod:98,396,91,125,404,289,922,11,172,cut:7,cut:359,cut:7] 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 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 479
% derived clauses: 273360
% kept clauses: 1731
% kept size sum: 30039
% kept mid-nuclei: 2
% kept new demods: 697
% forw unit-subs: 271592
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 12
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.59
% process. runtime: 7.56
% 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/GRP101-1+eq_r.in")
%
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