TSTP Solution File: GRP100-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP100-1 : 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/GRP100-1+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(6,40,1,12,0,1,2204,4,758)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),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))).
% 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))).
% 26 [para:10.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(X,double_divide(double_divide(Y,inverse(X)),inverse(identity))),inverse(identity)),Y).
% 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(X,Z)),inverse(Z))),inverse(identity)),Y).
% 28 [para:11.1.2,8.1.1.1.2.1.2,demod:14,10] equal(double_divide(double_divide(X,double_divide(inverse(Y),multiply(identity,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(X,Z)),inverse(Z)))),inverse(Y)).
% 30 [para:9.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(double_divide(X,Y),double_divide(double_divide(Z,multiply(Y,X)),inverse(identity))),inverse(identity)),Z).
% 32 [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(Y,Z)),inverse(Z)))).
% 40 [para:17.1.2,28.1.1.1.2,demod:10] equal(double_divide(inverse(X),inverse(identity)),X).
% 42 [para:40.1.1,9.1.2.1,demod:10] equal(multiply(inverse(identity),inverse(X)),inverse(X)).
% 43 [para:14.1.2,40.1.1.1] equal(double_divide(multiply(identity,X),inverse(identity)),inverse(X)).
% 44 [para:13.1.1,40.1.1.1] equal(double_divide(multiply(X,Y),inverse(identity)),double_divide(Y,X)).
% 54 [para:43.1.1,26.1.1.1.2.1,demod:40] equal(double_divide(double_divide(identity,X),inverse(identity)),multiply(identity,X)).
% 56 [para:10.1.2,54.1.1.1,demod:40] equal(identity,multiply(identity,identity)).
% 57 [para:11.1.2,54.1.1.1,demod:11] equal(identity,multiply(identity,inverse(identity))).
% 63 [para:54.1.1,26.1.1.1.2.1,demod:54,43] equal(multiply(identity,inverse(X)),double_divide(identity,X)).
% 64 [para:56.1.2,18.1.2.1,demod:57] equal(identity,inverse(identity)).
% 68 [para:64.1.2,40.1.1.2,demod:14,10] equal(multiply(identity,X),X).
% 69 [para:64.1.2,42.1.1.1,demod:63] equal(double_divide(identity,X),inverse(X)).
% 70 [para:64.1.2,44.1.1.2,demod:10] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 71 [para:64.1.2,26.1.1.1.2.2,demod:64,9] equal(multiply(multiply(inverse(X),Y),X),Y).
% 72 [para:11.1.2,27.1.1.1.2.1.2,demod:9,64,68,14,10] equal(multiply(double_divide(inverse(X),Y),Y),X).
% 73 [para:27.1.1,9.1.2.1,demod:10,70,16,64] equal(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z))),inverse(Y)).
% 77 [para:27.1.1,8.1.1.1.2.1.2,demod:9,69,64,73] equal(multiply(multiply(X,Y),inverse(X)),Y).
% 84 [para:68.1.1,17.1.2.2] equal(identity,double_divide(inverse(X),X)).
% 86 [para:69.1.1,9.1.2.1,demod:68,14,10] equal(multiply(X,identity),X).
% 88 [para:13.1.1,84.1.2.1] equal(identity,double_divide(multiply(X,Y),double_divide(Y,X))).
% 92 [para:70.1.1,28.1.1.1.2.1,demod:9,64,68] equal(multiply(double_divide(double_divide(X,Y),Z),Z),multiply(Y,X)).
% 99 [para:14.1.2,72.1.1.1.1,demod:68] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 106 [para:71.1.1,77.1.1.1,demod:70] equal(multiply(X,double_divide(X,inverse(Y))),Y).
% 107 [para:72.1.1,77.1.1.1,demod:13] equal(multiply(X,multiply(Y,inverse(X))),Y).
% 111 [para:99.1.1,44.1.1.1,demod:68,14,10,64] equal(X,double_divide(Y,double_divide(X,Y))).
% 112 [para:99.1.1,77.1.1.1,demod:13] equal(multiply(inverse(X),multiply(Y,X)),Y).
% 114 [para:111.1.2,8.1.1.1.2.1.2,demod:64,69,9] equal(multiply(double_divide(double_divide(X,Y),multiply(Z,Y)),Z),X).
% 115 [para:111.1.2,111.1.2.2] equal(X,double_divide(double_divide(Y,X),Y)).
% 133 [para:115.1.2,26.1.1.1.2.1,demod:9,10,64] equal(multiply(inverse(X),Y),double_divide(inverse(Y),X)).
% 134 [para:115.1.2,32.1.2.2,demod:69,68,14,10,64] equal(X,double_divide(Y,double_divide(Y,X))).
% 135 [para:115.1.2,32.1.2.2.1,demod:70,69,9,64] equal(multiply(X,double_divide(Y,Z)),double_divide(Y,double_divide(X,inverse(Z)))).
% 140 [para:134.1.2,111.1.2.2] equal(X,double_divide(double_divide(X,Y),Y)).
% 141 [para:111.1.2,134.1.2.2] equal(double_divide(X,Y),double_divide(Y,X)).
% 143 [para:140.1.2,8.1.1.1.2.2,demod:9,64,69,135,10] equal(multiply(double_divide(multiply(X,double_divide(Y,Z)),Z),X),Y).
% 145 [para:140.1.2,99.1.1.1,demod:13] equal(multiply(X,Y),multiply(Y,X)).
% 153 [para:141.1.1,30.1.1.1.1,demod:9,64] equal(multiply(multiply(multiply(X,Y),Z),double_divide(X,Y)),Z).
% 159 [para:106.1.1,71.1.1.1] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 161 [para:13.1.1,107.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Z,multiply(Y,X))),Z).
% 162 [para:70.1.1,107.1.1.2.2] equal(multiply(multiply(X,Y),multiply(Z,double_divide(Y,X))),Z).
% 163 [para:112.1.1,21.1.2.2] equal(identity,double_divide(double_divide(multiply(X,Y),inverse(Y)),X)).
% 175 [para:13.1.1,133.1.1.1] equal(multiply(multiply(X,Y),Z),double_divide(inverse(Z),double_divide(Y,X))).
% 179 [para:70.1.1,133.1.1.1] equal(multiply(double_divide(X,Y),Z),double_divide(inverse(Z),multiply(Y,X))).
% 180 [para:13.1.1,159.1.2.1] equal(multiply(X,double_divide(Y,Z)),double_divide(multiply(Z,Y),inverse(X))).
% 181 [para:159.1.2,8.1.1.1.2.1.2,demod:70,64,69,175,68,14,10] equal(double_divide(X,multiply(Y,double_divide(Z,multiply(Y,X)))),Z).
% 183 [para:70.1.1,159.1.2.1] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(Z,Y),inverse(X))).
% 199 [para:141.1.1,88.1.2.2] equal(identity,double_divide(multiply(X,Y),double_divide(X,Y))).
% 206 [para:199.1.2,8.1.1.1.2.1.2,demod:64,69,179,9,10] equal(multiply(multiply(double_divide(X,Y),Z),multiply(X,Y)),Z).
% 214 [para:8.1.1,92.1.1.1,demod:183,10,86,64,69] equal(X,multiply(multiply(Y,multiply(double_divide(Z,Y),X)),Z)).
% 216 [para:114.1.1,77.1.1.1,demod:13] equal(multiply(X,multiply(multiply(Y,Z),double_divide(X,Z))),Y).
% 219 [para:115.1.2,114.1.1.1.1] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(Z,X)).
% 256 [para:143.1.1,107.1.1.2,demod:13,133] equal(multiply(X,Y),double_divide(double_divide(multiply(Z,Y),X),Z)).
% 310 [para:92.1.1,161.1.1.2] equal(multiply(double_divide(X,Y),multiply(Z,U)),double_divide(double_divide(U,Z),multiply(Y,X))).
% 319 [para:115.1.2,181.1.1.2.2] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Y,X),Z)).
% 336 [para:206.1.1,163.1.2.1.1,demod:70] equal(identity,double_divide(double_divide(X,double_divide(Y,Z)),multiply(double_divide(Z,Y),X))).
% 350 [para:106.1.1,214.1.2.1.2,demod:183] equal(multiply(X,multiply(Y,Z)),multiply(multiply(Y,X),Z)).
% 356 [para:71.1.1,216.1.1.2.1,demod:133] equal(multiply(X,multiply(Y,double_divide(X,Z))),double_divide(inverse(Y),Z)).
% 366 [para:153.1.1,216.1.1.2.1,demod:350,175,356] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,Z))).
% 387 [para:106.1.1,219.1.1.1.2] equal(multiply(double_divide(X,Y),Z),double_divide(double_divide(Z,inverse(Y)),X)).
% 404 [para:219.1.1,162.1.1.2,demod:350] equal(multiply(X,multiply(Y,double_divide(Z,U))),double_divide(U,multiply(double_divide(X,Y),Z))).
% 458 [para:256.1.2,29.1.1.2.2.1,demod:319,404,13,310,350,16,180,64] equal(double_divide(X,multiply(double_divide(Y,Z),U)),multiply(Z,multiply(double_divide(U,X),Y))).
% 767 [para:135.1.2,336.1.2.1.2,demod:458,350,387] equal(identity,double_divide(double_divide(X,multiply(Y,double_divide(Z,U))),double_divide(U,multiply(double_divide(X,Y),Z)))).
% 2205 [input:12,cut:145,cut:68] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity).
% 2206 [para:767.1.1,2205.2.2,demod:350,767,84,133,cut:7,cut:366] 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: 459
% derived clauses: 254635
% kept clauses: 2187
% kept size sum: 40570
% kept mid-nuclei: 4
% kept new demods: 637
% forw unit-subs: 252357
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 8
% fast unit cutoff: 6
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.60
% process. runtime: 7.59
% 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/GRP100-1+eq_r.in")
%
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