TSTP Solution File: GRP082-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP082-1 : TPTP v3.4.2. Bugfixed v2.3.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art03.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/GRP082-1+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 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 7 5)
% (binary-posweight-lex-big-order 30 #f 7 5)
% (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))).
% 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))).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(4,40,0,8,0,0)
%
%
% START OF PROOF
% 5 [] equal(X,X).
% 6 [] equal(double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(U,double_divide(Y,U))))),Z).
% 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)).
% 9 [para:6.1.1,7.1.2.1,demod:7] equal(multiply(multiply(double_divide(X,double_divide(Y,X)),multiply(double_divide(Y,Z),U)),inverse(U)),inverse(Z)).
% 10 [para:7.1.2,6.1.1.1,demod:7] equal(double_divide(multiply(X,Y),multiply(double_divide(Z,double_divide(U,Z)),multiply(double_divide(U,V),double_divide(Y,X)))),V).
% 11 [para:7.1.2,6.1.1.2,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),multiply(double_divide(Z,U),X))),U).
% 12 [para:6.1.1,6.1.1.2.1.1.1.2,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(inverse(Z),Y)),multiply(U,X))),multiply(double_divide(V,double_divide(W,V)),multiply(double_divide(W,U),Z))).
% 16 [para:6.1.1,9.1.1.1.2.1,demod:7] equal(multiply(multiply(double_divide(X,double_divide(inverse(Y),X)),multiply(Z,U)),inverse(U)),inverse(multiply(double_divide(V,double_divide(W,V)),multiply(double_divide(W,Z),Y)))).
% 18 [para:10.1.1,6.1.1.2.1.1.1.2,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(multiply(Z,U),Y)),multiply(V,X))),multiply(double_divide(W,double_divide(X1,W)),multiply(double_divide(X1,V),double_divide(U,Z)))).
% 23 [para:10.1.1,9.1.1.1.2.1] equal(multiply(multiply(double_divide(X,double_divide(multiply(Y,Z),X)),multiply(U,V)),inverse(V)),inverse(multiply(double_divide(W,double_divide(X1,W)),multiply(double_divide(X1,U),double_divide(Z,Y))))).
% 24 [para:10.1.1,10.1.1.2.1.2] equal(double_divide(multiply(X,Y),multiply(double_divide(multiply(double_divide(Z,double_divide(U,Z)),multiply(double_divide(U,V),double_divide(W,X1))),V),multiply(double_divide(multiply(X1,W),X2),double_divide(Y,X)))),X2).
% 33 [para:12.1.1,11.1.1] equal(multiply(double_divide(X,double_divide(Y,X)),multiply(double_divide(Y,double_divide(inverse(Z),U)),Z)),U).
% 34 [para:12.1.2,11.1.1.2] equal(double_divide(inverse(X),double_divide(inverse(Y),multiply(double_divide(Z,double_divide(inverse(X),Z)),multiply(U,Y)))),U).
% 54 [para:33.1.1,11.1.1.2.2] equal(double_divide(inverse(multiply(double_divide(X,double_divide(inverse(Y),Z)),Y)),multiply(double_divide(U,double_divide(V,U)),Z)),double_divide(X,V)).
% 69 [para:33.1.1,34.1.1.2.2.2,demod:54] equal(double_divide(inverse(X),double_divide(Y,inverse(X))),double_divide(Z,double_divide(Y,Z))).
% 83 [para:69.1.1,6.1.1.2.1.1.1.2,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(inverse(Z),Y)),multiply(double_divide(U,double_divide(V,U)),X))),double_divide(V,inverse(Z))).
% 120 [para:69.1.1,69.1.1] equal(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(Y,Z))).
% 123 [para:120.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,Y),Y),multiply(double_divide(X,Z),Z)).
% 124 [para:120.1.1,6.1.1.2.1.1.1,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),multiply(double_divide(Z,U),U))),X).
% 143 [para:120.1.1,33.1.1.2.1] equal(multiply(double_divide(X,double_divide(Y,X)),multiply(double_divide(Z,double_divide(inverse(U),Z)),U)),Y).
% 148 [para:120.1.1,120.1.1.2] equal(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z))),double_divide(U,double_divide(Y,U))).
% 168 [para:120.1.1,123.1.1.1] equal(multiply(double_divide(X,double_divide(Y,X)),double_divide(Y,Z)),multiply(double_divide(Z,U),U)).
% 206 [para:148.1.1,12.1.2.2.1,demod:83] equal(double_divide(X,inverse(Y)),multiply(double_divide(Z,double_divide(double_divide(X,U),Z)),multiply(double_divide(V,double_divide(U,V)),Y))).
% 346 [para:148.1.1,124.1.1.2.2.1,demod:7,206] equal(double_divide(inverse(X),double_divide(Y,multiply(double_divide(Y,Z),Z))),X).
% 362 [para:346.1.1,7.1.2.1] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),inverse(Z)),inverse(Z)).
% 363 [para:7.1.2,346.1.1.1] equal(double_divide(multiply(X,Y),double_divide(Z,multiply(double_divide(Z,U),U))),double_divide(Y,X)).
% 384 [para:120.1.1,346.1.1.2.2.1] equal(double_divide(inverse(X),double_divide(Y,multiply(double_divide(Z,double_divide(U,Z)),double_divide(U,Y)))),X).
% 409 [para:7.1.2,362.1.1.2,demod:7] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),multiply(Z,U)),multiply(Z,U)).
% 479 [para:33.1.1,409.1.1.2,demod:33] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),Z),Z).
% 553 [para:479.1.1,11.1.1.2.2] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),X)),multiply(double_divide(Z,U),U)).
% 563 [para:120.1.1,479.1.1.1.2.1] equal(multiply(double_divide(X,multiply(double_divide(Y,double_divide(Z,Y)),double_divide(Z,X))),U),U).
% 895 [para:123.1.1,553.1.1.2,demod:7] equal(double_divide(multiply(X,Y),multiply(double_divide(X,Z),Z)),multiply(double_divide(Y,U),U)).
% 1150 [para:895.1.2,479.1.1.1.2] equal(multiply(double_divide(X,double_divide(multiply(Y,X),multiply(double_divide(Y,Z),Z))),U),U).
% 1268 [para:120.1.1,1150.1.1.1] equal(multiply(double_divide(X,double_divide(multiply(Y,multiply(double_divide(Y,Z),Z)),X)),U),U).
% 1275 [para:1150.1.1,168.1.1] equal(double_divide(multiply(X,multiply(double_divide(X,Y),Y)),Z),multiply(double_divide(Z,U),U)).
% 1313 [para:1268.1.1,363.1.1.2.2] equal(double_divide(multiply(X,Y),double_divide(Z,double_divide(multiply(U,multiply(double_divide(U,V),V)),Z))),double_divide(Y,X)).
% 1330 [para:1275.1.1,6.1.1.2.1.1.1.2,demod:1313,7] equal(double_divide(inverse(X),multiply(multiply(double_divide(Y,Z),Z),X)),Y).
% 1349 [para:1275.1.1,33.1.1.2.1,demod:1268] equal(multiply(multiply(double_divide(double_divide(inverse(X),Y),Z),Z),X),Y).
% 1414 [para:1275.1.1,553.1.2.1,demod:1268] equal(double_divide(inverse(X),X),multiply(multiply(double_divide(Y,Z),Z),Y)).
% 1750 [para:1414.1.2,1330.1.1.2] equal(double_divide(inverse(X),double_divide(inverse(Y),Y)),X).
% 1756 [para:1414.1.2,1414.1.2] equal(double_divide(inverse(X),X),double_divide(inverse(Y),Y)).
% 1829 [para:1750.1.1,143.1.1.2.1] equal(multiply(double_divide(X,double_divide(Y,X)),multiply(Z,inverse(Z))),Y).
% 1934 [para:1756.1.1,6.1.1.2.1,demod:7] equal(double_divide(inverse(X),multiply(Y,inverse(Y))),X).
% 1935 [para:1756.1.1,6.1.1.2.1.1.1,demod:1829,7] equal(double_divide(inverse(multiply(X,Y)),Y),X).
% 2028 [para:9.1.1,1935.1.1.1.1] equal(double_divide(inverse(inverse(X)),inverse(Y)),multiply(double_divide(Z,double_divide(U,Z)),multiply(double_divide(U,X),Y))).
% 2044 [para:1935.1.1,123.1.1.1] equal(multiply(X,Y),multiply(double_divide(inverse(multiply(X,Y)),Z),Z)).
% 2078 [para:1935.1.1,553.1.1.2.1.2,demod:2044] equal(double_divide(inverse(X),multiply(double_divide(Y,Z),X)),multiply(Z,Y)).
% 2101 [para:1935.1.1,1750.1.1] equal(X,multiply(X,double_divide(inverse(Y),Y))).
% 2129 [para:2101.1.2,18.1.1.2.1.2.1,demod:2101,7,2028] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),multiply(U,X))),double_divide(inverse(inverse(U)),Z)).
% 2131 [para:2101.1.2,18.1.2.2,demod:1934,2129] equal(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),double_divide(Z,X))).
% 2142 [para:384.1.1,2101.1.2.2,demod:2131] equal(X,multiply(X,double_divide(Y,inverse(Y)))).
% 2164 [para:2101.1.2,1330.1.1.2.1,demod:2078] equal(multiply(double_divide(inverse(X),X),Y),Y).
% 2177 [para:2142.1.2,33.1.1.2,demod:2131,7] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 2184 [para:2142.1.2,168.1.2,demod:2131] equal(inverse(X),double_divide(X,double_divide(Y,inverse(Y)))).
% 2189 [para:2142.1.2,346.1.1.2.2,demod:2184] equal(inverse(inverse(X)),X).
% 2191 [para:2142.1.2,363.1.1.2.2,demod:2184] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 2196 [para:2142.1.2,563.1.1,demod:2131] equal(double_divide(X,inverse(X)),double_divide(Y,inverse(Y))).
% 2210 [para:2142.1.2,553.1.2,demod:2184,2078] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 2216 [para:2142.1.2,1150.1.1.1.2.1,demod:7,2184,2210] equal(multiply(multiply(inverse(X),X),Y),Y).
% 2226 [para:2142.1.2,23.1.1.1.2,demod:2189,2028,2177,7] equal(multiply(double_divide(X,double_divide(multiply(Y,Z),X)),U),multiply(multiply(Y,Z),U)).
% 2227 [para:2142.1.2,23.1.2.1.2,demod:2189,2131,2216,2226] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 2229 [para:2189.1.1,6.1.1.1,demod:2189,2028,7] equal(double_divide(X,double_divide(Y,X)),Y).
% 2254 [para:2189.1.1,1750.1.1.1] equal(double_divide(X,double_divide(inverse(Y),Y)),inverse(X)).
% 2327 [para:479.1.1,24.1.1.2.2,demod:2191,2210,2229] equal(double_divide(multiply(X,Y),multiply(double_divide(multiply(Z,multiply(double_divide(Z,U),double_divide(V,W))),U),double_divide(Y,X))),double_divide(V,W)).
% 2330 [para:563.1.1,24.1.1.2.2,demod:2327,2229] equal(double_divide(X,Y),multiply(Z,double_divide(Z,multiply(Y,X)))).
% 2383 [para:2229.1.1,6.1.1.2.1.1.1.2,demod:2229,7] equal(double_divide(inverse(X),multiply(Y,multiply(Z,X))),double_divide(Z,Y)).
% 2385 [para:2229.1.1,9.1.1.1.2.1,demod:7,2229] equal(multiply(multiply(X,multiply(Y,Z)),inverse(Z)),multiply(X,Y)).
% 2390 [para:2229.1.1,12.1.2.2.1,demod:2383,2229] equal(double_divide(double_divide(X,Y),inverse(Z)),multiply(Y,multiply(X,Z))).
% 2393 [para:2229.1.1,123.1.1.1,demod:2210] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 2395 [para:2229.1.1,16.1.2.1.2.1,demod:2191,2385,2229] equal(multiply(inverse(X),double_divide(Y,Z)),double_divide(multiply(Y,X),Z)).
% 2405 [para:2229.1.1,1349.1.1.1.1.1,demod:2210] equal(multiply(inverse(X),Y),double_divide(X,inverse(Y))).
% 2424 [para:2164.1.1,18.1.2.2,demod:2395,2383,2229] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 2428 [para:2164.1.1,23.1.1.1.2,demod:7,2330,2395,2254,2229,2227,2424] equal(double_divide(X,double_divide(Y,multiply(X,Z))),multiply(Z,Y)).
% 2438 [para:18.1.2,2191.1.1.1,demod:2390,2393,2229,7,2383,2428,2424] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 2493 [hyper:8,2216,demod:2405,2438,cut:5,cut:2196] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 5
% clause depth limited to 7
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 67
% derived clauses: 8676
% kept clauses: 2483
% kept size sum: 59633
% kept mid-nuclei: 0
% kept new demods: 992
% forw unit-subs: 4564
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 6
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 0.26
% process. runtime: 0.24
% 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/GRP082-1+eq_r.in")
%
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