TSTP Solution File: GRP024-5 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP024-5 : TPTP v3.4.2. Released v2.2.0.
% 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 89.5s
% Output : Assurance 89.5s
% 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/GRP024-5+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: ueq
%
% strategies selected:
% (binary-posweight-kb-big-order 60 #f 4 1)
% (binary-posweight-lex-big-order 30 #f 4 1)
% (binary 30 #t)
% (binary-posweight-kb-big-order 180 #f)
% (binary-posweight-lex-big-order 120 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-posweight-kb-small-order 60 #f)
% (binary-posweight-lex-small-order 60 #f)
%
%
% **** EMPTY CLAUSE DERIVED ****
%
%
% timer checkpoints: c(7,40,1,14,0,1,2124,3,3005,2457,4,4512,2809,5,6002,2809,1,6002,2809,50,6002,2809,40,6002,2816,0,6002,2829,50,6004,2836,0,6004,2857,50,6009,2864,0,6009,3306,3,7470,3309,4,8215,3311,5,8910,3311,1,8910,3311,50,8910,3311,40,8910,3318,0,8910,3318,50,8910,3318,40,8910,3325,0,8911)
%
%
% START OF PROOF
% 3320 [] equal(multiply(identity,X),X).
% 3321 [] equal(multiply(inverse(X),X),identity).
% 3322 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 3323 [] equal(commutator(X,Y),multiply(inverse(X),multiply(inverse(Y),multiply(X,Y)))).
% 3324 [] equal(commutator(commutator(X,Y),Z),commutator(X,commutator(Y,Z))).
% 3325 [] -equal(multiply(a,commutator(b,c)),multiply(commutator(b,c),a)).
% 3326 [para:3321.1.1,3322.1.1.1,demod:3320] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 3327 [para:3320.1.1,3326.1.2.2] equal(X,multiply(inverse(identity),X)).
% 3328 [para:3321.1.1,3326.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 3329 [para:3322.1.1,3326.1.2.2] equal(X,multiply(inverse(multiply(Y,Z)),multiply(Y,multiply(Z,X)))).
% 3330 [para:3326.1.2,3326.1.2.2] equal(multiply(X,Y),multiply(inverse(inverse(X)),Y)).
% 3331 [para:3330.1.2,3321.1.1] equal(multiply(X,inverse(X)),identity).
% 3332 [para:3330.1.2,3326.1.2] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 3333 [para:3330.1.2,3328.1.2] equal(X,multiply(X,identity)).
% 3334 [para:3333.1.2,3321.1.1] equal(inverse(identity),identity).
% 3335 [para:3333.1.2,3328.1.2] equal(X,inverse(inverse(X))).
% 3336 [para:3320.1.1,3323.1.2.2.2,demod:3320,3321,3334] equal(commutator(identity,X),identity).
% 3337 [para:3321.1.1,3323.1.2.2.2,demod:3331,3333,3335] equal(commutator(inverse(X),X),identity).
% 3338 [para:3323.1.2,3322.1.1.1,demod:3322] equal(multiply(commutator(X,Y),Z),multiply(inverse(X),multiply(inverse(Y),multiply(X,multiply(Y,Z))))).
% 3339 [para:3322.1.1,3323.1.2.2.2] equal(commutator(multiply(X,Y),Z),multiply(inverse(multiply(X,Y)),multiply(inverse(Z),multiply(X,multiply(Y,Z))))).
% 3340 [para:3323.1.2,3326.1.2.2,demod:3335] equal(multiply(inverse(X),multiply(Y,X)),multiply(Y,commutator(Y,X))).
% 3341 [para:3326.1.2,3323.1.2.2,demod:3321] equal(commutator(X,X),identity).
% 3342 [para:3326.1.2,3323.1.2.2.2,demod:3335] equal(commutator(inverse(X),multiply(X,Y)),multiply(X,multiply(inverse(multiply(X,Y)),Y))).
% 3343 [para:3327.1.2,3323.1.2.2,demod:3321,3333] equal(commutator(X,identity),identity).
% 3344 [para:3323.1.2,3330.1.2] equal(multiply(X,multiply(inverse(Y),multiply(inverse(X),Y))),commutator(inverse(X),Y)).
% 3345 [para:3330.1.2,3323.1.2.2] equal(commutator(X,inverse(Y)),multiply(inverse(X),multiply(Y,multiply(X,inverse(Y))))).
% 3346 [para:3323.1.2,3323.1.2.2.2,demod:3335] equal(commutator(inverse(X),multiply(inverse(Y),multiply(X,Y))),multiply(X,multiply(inverse(multiply(inverse(Y),multiply(X,Y))),commutator(X,Y)))).
% 3348 [para:3341.1.1,3324.1.1.1,demod:3336] equal(identity,commutator(X,commutator(X,Y))).
% 3349 [para:3321.1.1,3329.1.2.2,demod:3333] equal(X,inverse(multiply(inverse(multiply(Y,X)),Y))).
% 3350 [para:3321.1.1,3329.1.2.2.2,demod:3333] equal(X,multiply(inverse(multiply(Y,inverse(X))),Y)).
% 3352 [para:3326.1.2,3329.1.2.2.2] equal(multiply(X,Y),multiply(inverse(multiply(Z,inverse(X))),multiply(Z,Y))).
% 3355 [para:3323.1.2,3329.1.2.2] equal(multiply(X,Y),multiply(inverse(multiply(inverse(X),inverse(Y))),commutator(X,Y))).
% 3357 [para:3331.1.1,3323.1.2.2.2,demod:3321,3333,3335] equal(commutator(X,inverse(X)),identity).
% 3358 [para:3331.1.1,3329.1.2.2.2,demod:3333] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 3359 [para:3337.1.1,3324.1.1.1,demod:3336] equal(identity,commutator(inverse(X),commutator(X,Y))).
% 3361 [para:3357.1.1,3324.1.1.1,demod:3336] equal(identity,commutator(X,commutator(inverse(X),Y))).
% 3366 [para:3332.1.2,3322.1.1] equal(X,multiply(Y,multiply(Z,multiply(inverse(multiply(Y,Z)),X)))).
% 3367 [para:3332.1.2,3329.1.2.2.2] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 3370 [para:3326.1.2,3349.1.2.1.1.1] equal(multiply(X,Y),inverse(multiply(inverse(Y),inverse(X)))).
% 3371 [para:3332.1.2,3349.1.2.1.1.1] equal(multiply(inverse(X),Y),inverse(multiply(inverse(Y),X))).
% 3372 [para:3349.1.2,3349.1.2.1.1] equal(X,inverse(multiply(Y,inverse(multiply(X,Y))))).
% 3374 [para:3326.1.2,3358.1.2.1.1] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 3375 [para:3358.1.2,3323.1.2.2.2,demod:3322,3374,3335] equal(commutator(inverse(multiply(X,Y)),X),multiply(X,multiply(Y,inverse(multiply(Y,X))))).
% 3377 [para:3349.1.2,3358.1.2.1] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 3380 [para:3322.1.1,3338.1.2.2.2] equal(multiply(commutator(multiply(X,Y),Z),U),multiply(inverse(multiply(X,Y)),multiply(inverse(Z),multiply(X,multiply(Y,multiply(Z,U)))))).
% 3382 [para:3338.1.2,3326.1.2.2,demod:3335] equal(multiply(inverse(X),multiply(Y,multiply(X,Z))),multiply(Y,multiply(commutator(Y,X),Z))).
% 3383 [para:3326.1.2,3338.1.2.2.2.2,demod:3335] equal(multiply(commutator(X,inverse(Y)),multiply(Y,Z)),multiply(inverse(X),multiply(Y,multiply(X,Z)))).
% 3386 [para:3338.1.2,3323.1.2.2.2,demod:3322,3371,3335] equal(commutator(inverse(X),multiply(inverse(Y),multiply(X,multiply(Y,Z)))),multiply(X,multiply(inverse(multiply(X,multiply(Y,Z))),multiply(Y,multiply(commutator(X,Y),Z))))).
% 3390 [para:3338.1.2,3329.1.2.2,demod:3322,3335,3374] equal(multiply(X,multiply(Y,Z)),multiply(Y,multiply(X,multiply(commutator(X,Y),Z)))).
% 3398 [para:3358.1.2,3338.1.2.2.2,demod:3374,3335,3322] equal(multiply(commutator(inverse(multiply(X,multiply(Y,Z))),X),Y),multiply(X,multiply(Y,multiply(Z,inverse(multiply(Z,X)))))).
% 3399 [para:3358.1.2,3338.1.2.2.2.2,demod:3322,3335] equal(multiply(commutator(X,inverse(multiply(Y,Z))),Y),multiply(inverse(X),multiply(Y,multiply(Z,multiply(X,inverse(Z)))))).
% 3410 [para:3377.1.2,3332.1.2.2] equal(inverse(multiply(X,inverse(Y))),multiply(Y,inverse(X))).
% 3419 [para:3370.1.2,3370.1.2.1.1,demod:3322,3374] equal(multiply(X,inverse(multiply(Y,Z))),inverse(multiply(Y,multiply(Z,inverse(X))))).
% 3423 [para:3326.1.2,3339.1.2.2] equal(commutator(multiply(X,Y),X),multiply(inverse(multiply(X,Y)),multiply(Y,X))).
% 3434 [para:3350.1.2,3339.1.2.2.2.2,demod:3344,3322,3419,3410] equal(commutator(multiply(X,multiply(Y,inverse(Z))),Z),commutator(inverse(Z),multiply(X,Y))).
% 3459 [para:3340.1.1,3326.1.2.2,demod:3335] equal(multiply(X,Y),multiply(Y,multiply(X,commutator(X,Y)))).
% 3463 [para:3340.1.1,3323.1.2.2.2,demod:3332,3367,3335] equal(commutator(inverse(X),multiply(Y,X)),commutator(Y,X)).
% 3472 [para:3340.1.2,3349.1.2.1.1.1,demod:3423,3322,3371] equal(commutator(X,Y),inverse(commutator(multiply(X,Y),X))).
% 3473 [para:3340.1.2,3358.1.2.1.1,demod:3423,3322,3371] equal(inverse(commutator(X,Y)),commutator(multiply(X,Y),X)).
% 3487 [para:3340.1.1,3339.1.2.2.2,demod:3326,3332,3322,3371] equal(commutator(multiply(inverse(X),Y),X),commutator(Y,X)).
% 3495 [para:3342.1.2,3322.1.1.1,demod:3322] equal(multiply(commutator(inverse(X),multiply(X,Y)),Z),multiply(X,multiply(inverse(multiply(X,Y)),multiply(Y,Z)))).
% 3498 [para:3349.1.2,3342.1.2.2.1,demod:3473,3423,3358,3335] equal(commutator(multiply(X,Y),inverse(Y)),inverse(commutator(X,Y))).
% 3504 [para:3372.1.2,3342.1.2.2.1,demod:3375,3377] equal(commutator(inverse(X),inverse(Y)),commutator(inverse(multiply(X,Y)),X)).
% 3526 [para:3371.1.2,3342.1.2.2.1,demod:3323,3322,3335] equal(commutator(X,multiply(inverse(X),Y)),commutator(X,Y)).
% 3527 [para:3371.1.2,3371.1.2.1.1,demod:3371,3322] equal(multiply(inverse(X),multiply(inverse(Y),Z)),multiply(inverse(multiply(Y,X)),Z)).
% 3544 [para:3344.1.1,3330.1.2,demod:3342,3527,3335] equal(commutator(inverse(X),multiply(X,Y)),commutator(inverse(X),Y)).
% 3546 [para:3323.1.2,3344.1.1.2.2,demod:3544,3495,3322,3371] equal(multiply(commutator(inverse(X),Y),commutator(X,Y)),commutator(inverse(X),multiply(inverse(Y),multiply(X,Y)))).
% 3574 [para:3463.1.1,3348.1.2.2] equal(identity,commutator(inverse(X),commutator(Y,X))).
% 3575 [para:3463.1.1,3359.1.2.2,demod:3335] equal(identity,commutator(X,commutator(Y,X))).
% 3589 [para:3324.1.1,3575.1.2.2] equal(identity,commutator(X,commutator(Y,commutator(Z,X)))).
% 3594 [para:3335.1.2,3574.1.2.1] equal(identity,commutator(X,commutator(Y,inverse(X)))).
% 3605 [para:3358.1.2,3345.1.2.2.2,demod:3345,3322,3498,3371] equal(inverse(commutator(inverse(X),Y)),commutator(Y,inverse(X))).
% 3636 [para:3323.1.2,3472.1.2.1.1,demod:3334,3594,3324,3546] equal(multiply(commutator(inverse(X),Y),commutator(X,Y)),identity).
% 3637 [para:3332.1.2,3472.1.2.1.1,demod:3526] equal(commutator(X,Y),inverse(commutator(Y,X))).
% 3649 [para:3472.1.2,3371.1.2.1.1,demod:3637,3473] equal(multiply(inverse(X),commutator(Y,Z)),inverse(multiply(commutator(Z,Y),X))).
% 3655 [para:3472.1.2,3345.1.2.2.2.2,demod:3637,3473] equal(commutator(X,commutator(Y,Z)),multiply(inverse(X),multiply(commutator(Z,Y),multiply(X,commutator(Y,Z))))).
% 3658 [para:3324.1.1,3637.1.2.1,demod:3324,3637] equal(commutator(X,commutator(Y,Z)),commutator(Z,commutator(X,Y))).
% 3663 [para:3637.1.2,3472.1.2] equal(commutator(X,Y),commutator(X,multiply(X,Y))).
% 3667 [para:3346.1.2,3329.1.2.2,demod:3333,3636,3546,3605,3544,3342,3371] equal(commutator(X,Y),commutator(Y,inverse(X))).
% 3694 [para:3335.1.2,3667.1.2.2] equal(commutator(inverse(X),Y),commutator(Y,X)).
% 3702 [para:3694.1.1,3463.1.1] equal(commutator(multiply(X,Y),Y),commutator(X,Y)).
% 3708 [para:3702.1.1,3324.1.1.1,demod:3324] equal(commutator(X,commutator(Y,Z)),commutator(multiply(X,Y),commutator(Y,Z))).
% 3710 [para:3326.1.2,3702.1.1.1,demod:3694,3544] equal(commutator(X,multiply(Y,X)),commutator(X,Y)).
% 3746 [para:3710.1.1,3589.1.2.2.2] equal(identity,commutator(multiply(X,Y),commutator(Z,commutator(Y,X)))).
% 3875 [para:3348.1.2,3355.1.2.2,demod:3333,3322,3371,3637] equal(multiply(X,commutator(X,Y)),multiply(commutator(X,Y),X)).
% 3877 [para:3361.1.2,3355.1.2.2,demod:3333,3322,3371,3637,3694] equal(multiply(X,commutator(Y,X)),multiply(commutator(Y,X),X)).
% 3882 [para:3355.1.2,3340.1.1.2,demod:3333,3322,3575,3708,3335,3374,3637] equal(multiply(commutator(X,Y),multiply(Y,X)),multiply(X,Y)).
% 3995 [para:3366.1.2,3338.1.2.2.2,demod:3527] equal(multiply(commutator(X,Y),multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(Y,X)),Z)).
% 4099 [para:3663.1.2,3658.1.1.2] equal(commutator(X,commutator(Y,Z)),commutator(multiply(Y,Z),commutator(X,Y))).
% 4262 [para:3875.1.2,3322.1.1.1,demod:3322] equal(multiply(X,multiply(commutator(X,Y),Z)),multiply(commutator(X,Y),multiply(X,Z))).
% 4280 [para:3877.1.2,3322.1.1.1,demod:3322] equal(multiply(X,multiply(commutator(Y,X),Z)),multiply(commutator(Y,X),multiply(X,Z))).
% 4651 [para:3746.1.2,3459.1.2.2.2,demod:3333,3322] equal(multiply(X,multiply(Y,commutator(Z,commutator(Y,X)))),multiply(commutator(Z,commutator(Y,X)),multiply(X,Y))).
% 4783 [para:3352.1.2,3380.1.2.2.2.2,demod:3527,3322,3419,3694,3434,3410] equal(multiply(commutator(multiply(X,Y),Z),U),multiply(Z,multiply(inverse(multiply(Z,multiply(X,Y))),multiply(X,multiply(Y,U))))).
% 5067 [para:3382.1.2,3339.1.2.2,demod:3323,3367,3995,3322,3527,3649,3694] equal(commutator(multiply(commutator(X,Y),Z),Y),commutator(Z,Y)).
% 5149 [para:3382.1.2,3367.1.2.1.1,demod:3371,3322,3649] equal(multiply(inverse(X),multiply(commutator(Y,Z),U)),multiply(inverse(multiply(Z,multiply(Y,X))),multiply(Y,multiply(Z,U)))).
% 5245 [para:3332.1.2,5067.1.1.1,demod:3637] equal(commutator(X,Y),commutator(multiply(commutator(Y,Z),X),Y)).
% 5253 [para:5067.1.1,3637.1.2.1,demod:3637] equal(commutator(X,multiply(commutator(Y,X),Z)),commutator(X,Z)).
% 5255 [para:5067.1.1,3667.1.2,demod:3667] equal(commutator(X,multiply(commutator(X,Y),Z)),commutator(X,Z)).
% 5335 [para:3342.1.2,5253.1.1.2,demod:3322,3649,3348,5255,3324,3637] equal(identity,commutator(X,multiply(inverse(Y),multiply(commutator(X,Z),Y)))).
% 5404 [para:3345.1.2,3383.1.1.2,demod:3527,3667,3335] equal(multiply(commutator(X,Y),commutator(Z,Y)),multiply(inverse(multiply(Y,X)),multiply(X,multiply(Z,multiply(Y,inverse(Z)))))).
% 5436 [para:3375.1.2,3383.1.1.2,demod:3694,3504,3667] equal(multiply(commutator(X,Y),commutator(X,Z)),multiply(inverse(Y),multiply(X,multiply(Y,multiply(Z,inverse(multiply(Z,X))))))).
% 5469 [para:3383.1.1,5245.1.2.1,demod:3487] equal(commutator(multiply(X,Y),Z),commutator(multiply(X,multiply(Z,Y)),Z)).
% 5881 [para:3882.1.1,3386.1.2.2.1.1.2,demod:4783,3390,4262,4651,5469,3694,3459,3875,4280,3637] equal(commutator(multiply(X,Y),Z),multiply(commutator(multiply(Y,X),Z),commutator(Z,commutator(Y,X)))).
% 6483 [para:3390.1.2,3380.1.2.2.2.2,demod:5149,3527] equal(multiply(commutator(multiply(X,Y),Z),multiply(commutator(Z,Y),U)),multiply(inverse(Y),multiply(commutator(X,Z),multiply(Y,U)))).
% 9004 [para:3398.1.1,3340.1.1.2,demod:3637,3473,3324,3694,3504,5436] equal(multiply(commutator(X,Y),commutator(X,Z)),multiply(commutator(X,multiply(Y,Z)),commutator(X,commutator(Z,Y)))).
% 9494 [para:3399.1.1,3340.1.1.2,demod:5881,4099,3324,3667,5404,3527] equal(multiply(commutator(X,Y),commutator(Z,Y)),commutator(multiply(Z,X),Y)).
% 9504 [para:3399.1.1,3346.1.2.2.1.1.2,demod:3655,6483,9004,4099,9494,5404,3527,3343,5335,3324,3637,3667] equal(identity,commutator(X,commutator(Y,Z))).
% 9692 [para:9504.1.2,3355.1.2.2,demod:3333,3322,3371,3637,slowcut:3325] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 180
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 1727
% derived clauses: 2773876
% kept clauses: 9641
% kept size sum: 205932
% kept mid-nuclei: 0
% kept new demods: 6053
% forw unit-subs: 1030848
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 233
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 91.55
% process. runtime: 90.99
% 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/GRP024-5+eq_r.in")
%
%------------------------------------------------------------------------------