TSTP Solution File: GRP052-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP052-1 : TPTP v3.4.2. Released v1.0.0.
% 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/GRP052-1+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 10 5)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 10 5)
% (binary-posweight-lex-big-order 30 #f 10 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(3,40,1,6,0,1,7,50,1,10,0,1)
%
%
% START OF PROOF
% 8 [] equal(X,X).
% 9 [] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(Y))),Z))),Y))),Z).
% 10 [] -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)).
% 11 [para:9.1.1,9.1.1.2.1.1.2.1] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y))),inverse(multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),inverse(U))),Z))),U))).
% 13 [para:11.1.1,9.1.1] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(Z))),inverse(X))),multiply(inverse(multiply(Y,inverse(Z))),U)))),X)),U).
% 14 [para:11.1.2,9.1.1.2] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y)))),Z).
% 16 [para:9.1.1,14.1.1.2.2.1.1] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,Y)))),multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(U))),Z))),U)).
% 20 [para:9.1.1,13.1.1.1.1.2.1.1.1.1.1,demod:9] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(Y),inverse(X))),multiply(inverse(Y),Z)))),X)),Z).
% 25 [para:14.1.1,13.1.1.1.1.2.1.2] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(Z))),inverse(X))),U))),X)),multiply(Y,inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(U)),Z)))).
% 33 [para:20.1.1,20.1.1.1.1.2.1.1.1.1,demod:20] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),X)),Z).
% 36 [para:33.1.1,11.1.1.2] equal(multiply(X,Y),inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(U))),inverse(Z))),multiply(inverse(multiply(V,inverse(U))),multiply(V,Y))))),Z))).
% 38 [para:33.1.1,14.1.1.1] equal(multiply(X,multiply(multiply(multiply(inverse(inverse(Y)),inverse(Y)),inverse(multiply(inverse(multiply(Z,inverse(inverse(Y)))),multiply(Z,X)))),inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(U)),Y)))),U).
% 39 [para:33.1.1,14.1.1.2.2] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)),multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z))).
% 40 [para:33.1.1,14.1.1.2.2.1.1.2] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y)))),multiply(multiply(multiply(inverse(U),U),inverse(multiply(inverse(multiply(V,inverse(U))),multiply(V,Z)))),U)).
% 48 [para:33.1.1,39.1.1.1.1.2,demod:33] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 50 [para:48.1.1,9.1.1.2.1.1.1] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)),inverse(multiply(inverse(multiply(X,inverse(multiply(U,Z)))),V))),multiply(U,Z)))),V).
% 62 [para:48.1.1,48.1.1.1.1] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)),multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))).
% 63 [para:48.1.1,48.1.1.2] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))),multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))).
% 240 [para:16.1.2,9.1.1.2.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(multiply(Z,X)))))),Z).
% 244 [para:11.1.1,16.1.1.2,demod:9] equal(X,multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),inverse(Y))),multiply(multiply(inverse(Z),Z),inverse(X))))),Y)).
% 247 [para:16.1.2,33.1.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y))))),Z).
% 295 [para:48.1.1,240.1.1.2.1.2.2.1] equal(multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),inverse(multiply(inverse(multiply(Z,inverse(multiply(X,Y)))),multiply(Z,inverse(multiply(inverse(multiply(U,V)),multiply(U,Y))))))),inverse(multiply(X,V))).
% 300 [para:62.1.1,240.1.1.2.1.2.2.1,demod:295] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))).
% 558 [para:48.1.1,244.1.2.1.2.1] equal(X,multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(Z,inverse(Y))),multiply(Z,inverse(X))))),Y)).
% 951 [para:558.1.2,50.1.1.2.1.1.1.1.1,demod:558] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(multiply(Z,U)))),V))),multiply(Z,U)))),V).
% 956 [para:9.1.1,951.1.1.2.1.1.2.1.1.1.2.1,demod:9] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(Z))),U))),Z))),U).
% 986 [para:247.1.1,956.1.1.2.1.1.2] equal(multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),U))),multiply(X,inverse(multiply(multiply(multiply(inverse(U),U),Z),U)))).
% 994 [para:986.1.2,14.1.1.2] equal(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(U)),Y)))),U).
% 1027 [para:986.1.1,240.1.1.2.1.2,demod:247] equal(multiply(multiply(inverse(X),X),Y),multiply(multiply(inverse(Z),Z),Y)).
% 1096 [para:1027.1.1,240.1.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,inverse(multiply(U,Z)))))),U).
% 1098 [para:1027.1.1,240.1.1.2.1.2.2.1,demod:1096] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1134 [para:1098.1.1,48.1.1.1.1] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 1135 [para:1098.1.1,48.1.1.2] equal(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X))).
% 1160 [para:1098.1.1,300.1.1.1] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))).
% 1232 [para:956.1.1,1160.1.2.1.1.1,demod:956] equal(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))).
% 1588 [para:1098.1.1,25.1.1.1.1.2.1,demod:956] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),X)),inverse(X)).
% 1642 [para:1027.1.1,1588.1.1.1.1] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),Z)),inverse(Z)).
% 1693 [para:956.1.1,1642.1.1.1,demod:1642] equal(inverse(X),inverse(inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(inverse(Z)),X))),Z)))).
% 3438 [para:1642.1.1,994.1.1.2.2.1.1.2,demod:994] equal(X,multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))),X)).
% 3443 [para:1693.1.2,994.1.1.2.2.1.1.2,demod:994] equal(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(inverse(Z)),X))),Z))).
% 3456 [para:3438.1.2,48.1.1.1.1,demod:3438] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 3457 [para:3438.1.2,62.1.1.1.1.1.1,demod:3456,3438] equal(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(Z,X)),U)),multiply(inverse(multiply(Z,Y)),U)).
% 3458 [para:3438.1.2,63.1.1.2.1.1,demod:3456,3438] equal(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),U)),multiply(inverse(Z),multiply(X,U))).
% 3465 [para:3438.1.2,1134.1.2.1.1,demod:3438] equal(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)),multiply(inverse(Y),Z)).
% 3466 [para:3438.1.2,1135.1.2.1.1,demod:3438] equal(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)),multiply(inverse(Y),X)).
% 3469 [para:3438.1.2,994.1.1.1.1,demod:3438] equal(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),X))),Z).
% 3477 [para:1027.1.1,3456.1.2.1.1] equal(multiply(inverse(X),Y),multiply(inverse(multiply(multiply(inverse(Z),Z),X)),multiply(multiply(inverse(U),U),Y))).
% 3515 [para:1232.1.1,3443.1.2.1.1.2.1.1.1] equal(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),X))),multiply(inverse(U),U)))).
% 3522 [para:3469.1.1,48.1.1.2,demod:3456] equal(multiply(inverse(multiply(inverse(inverse(X)),Y)),Z),multiply(inverse(Y),inverse(multiply(multiply(multiply(inverse(U),U),inverse(Z)),X)))).
% 3524 [para:1232.1.1,3469.1.1.1.1,demod:3522] equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y)))),Z),Z).
% 3612 [para:3524.1.1,48.1.1,demod:3456] equal(multiply(inverse(inverse(multiply(inverse(X),X))),Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),Y)).
% 3624 [para:3524.1.1,1098.1.1] equal(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)).
% 3653 [para:3612.1.1,48.1.1.1.1,demod:3456] equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),Y)),multiply(inverse(inverse(multiply(inverse(Z),Z))),U)),multiply(inverse(Y),U)).
% 3733 [para:40.1.1,300.1.1.1,demod:3443,3456] equal(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(multiply(multiply(inverse(Y),Y),X),Y))))).
% 3804 [para:956.1.1,3733.1.2.1.2.1.1] equal(inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(Z))),U))),Z)),inverse(multiply(inverse(inverse(Y)),inverse(multiply(U,Y))))).
% 4032 [para:3477.1.2,36.1.2.1.1.2.1.2.2,demod:3443,3458] equal(multiply(X,multiply(multiply(inverse(Y),Y),Z)),multiply(X,multiply(multiply(inverse(U),U),Z))).
% 4040 [para:4032.1.1,1642.1.1.1,demod:3438] equal(inverse(multiply(multiply(inverse(X),X),Y)),inverse(multiply(multiply(inverse(Z),Z),Y))).
% 4063 [para:4040.1.1,956.1.1.2.1.1.2.1.1,demod:3804] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,Y))))),Z).
% 4124 [para:3624.1.1,4063.1.1.2.1] equal(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 4145 [para:4124.1.1,956.1.1.2.1.1.2.1.1.1,demod:3515] equal(multiply(multiply(inverse(X),X),Y),Y).
% 4152 [para:4124.1.2,994.1.1.1,demod:3465,4145] equal(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),X))),Y).
% 4156 [para:4124.1.1,36.1.2.1.1.2.1.1.1.1.1,demod:3653,3456,4145] equal(X,inverse(multiply(inverse(multiply(inverse(inverse(Y)),X)),Y))).
% 4161 [para:4124.1.2,3443.1.2.1.1.2.1.1.1,demod:3466,4145] equal(X,inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y))))).
% 4203 [para:4152.1.1,48.1.1.1.1,demod:3456] equal(multiply(inverse(X),multiply(inverse(inverse(Y)),Z)),multiply(inverse(inverse(multiply(inverse(X),Y))),Z)).
% 4204 [para:4152.1.1,48.1.1.2,demod:3456] equal(multiply(inverse(multiply(inverse(inverse(X)),Y)),Z),multiply(inverse(Y),inverse(multiply(inverse(Z),X)))).
% 4229 [para:4156.1.2,48.1.1.1,demod:3456,4204] equal(multiply(X,multiply(inverse(X),inverse(multiply(inverse(Y),Z)))),multiply(inverse(Z),Y)).
% 4232 [para:4156.1.2,63.1.1.1.1.1,demod:4204,3456] equal(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),U)),multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(U),Z))))).
% 4273 [?] ?
% 4280 [para:4161.1.2,38.1.1.2.1.1.1.1,demod:4273,4203,4204,4232,4229,4145,3456,4161] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 4282 [para:4161.1.2,3457.1.1.2.1,demod:4273,4203] equal(multiply(inverse(X),multiply(Y,Z)),multiply(inverse(multiply(inverse(Y),X)),Z)).
% 4290 [para:4161.1.2,3458.1.1.1.1.1,demod:4273,4203] equal(multiply(inverse(multiply(X,Y)),Z),multiply(inverse(Y),multiply(inverse(X),Z))).
% 4296 [para:4280.1.1,62.1.1.2,demod:4282,3456] equal(multiply(inverse(X),multiply(Y,Z)),multiply(inverse(multiply(U,X)),multiply(multiply(U,Y),Z))).
% 4318 [para:4280.1.1,3443.1.2.1.1.2.1,demod:4145] equal(multiply(inverse(X),Y),inverse(multiply(inverse(Y),X))).
% 4327 [para:4280.1.1,3457.1.1.1.1,demod:4290] equal(multiply(inverse(multiply(multiply(X,Y),Z)),U),multiply(inverse(multiply(X,multiply(Y,Z))),U)).
% 4328 [para:4280.1.1,3457.1.1.2,demod:4296,4318] equal(multiply(multiply(inverse(X),Y),Z),multiply(inverse(X),multiply(Y,Z))).
% 4334 [para:4280.1.1,4063.1.1.2.1.2.1,demod:4280,4328,4318] equal(multiply(inverse(inverse(X)),inverse(multiply(Y,X))),inverse(Y)).
% 4335 [para:4063.1.1,4280.1.1.2,demod:4334,4280,4328,4318] equal(X,inverse(inverse(X))).
% 4336 [para:4280.1.1,4152.1.1.2.1,demod:4335] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 4345 [para:4335.1.2,1693.1.2,demod:4280,4328,4335] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 4346 [para:4335.1.2,1135.1.1.1.1.1,demod:3456,4345,4290] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 4357 [para:4336.1.1,36.1.2.1.1.2.1.1.1.1.1,demod:4345,4327,4280,4328,3456,4335,4346] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 4378 [hyper:10,4357,demod:4280,4328,cut:8,cut:1098] 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 11
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 141
% derived clauses: 51070
% kept clauses: 4362
% kept size sum: 146834
% kept mid-nuclei: 4
% kept new demods: 700
% forw unit-subs: 44302
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 73
% fast unit cutoff: 3
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 1.39
% process. runtime: 1.37
% 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/GRP052-1+eq_r.in")
%
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