TSTP Solution File: GRP423-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP423-1 : TPTP v3.4.2. Released v2.6.0.
% 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/GRP423-1+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 11 1)
% (binary-posweight-lex-big-order 30 #f 11 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(3,40,0,6,0,0)
%
%
% START OF PROOF
% 4 [] equal(X,X).
% 5 [] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))),Y).
% 6 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 7 [para:5.1.1,5.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Z),inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))))).
% 8 [para:5.1.1,5.1.1.1.1.1.2.1.1] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(inverse(Y),multiply(inverse(V),inverse(multiply(inverse(V),V))))))),multiply(U,V))).
% 9 [para:7.1.1,5.1.1] equal(multiply(inverse(X),inverse(multiply(inverse(inverse(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(X),X)))))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))),Y).
% 10 [para:7.1.2,5.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),Y).
% 11 [para:7.1.2,7.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))).
% 12 [para:11.1.1,5.1.1.1.1.1.2] equal(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),U))))))),multiply(X,U))),multiply(inverse(U),Z)).
% 13 [para:11.1.1,5.1.1.1.1.1.2.1.1,demod:5] equal(multiply(inverse(multiply(X,Y)),multiply(X,Z)),multiply(inverse(multiply(U,Y)),multiply(U,Z))).
% 15 [para:11.1.1,7.1.2.2] equal(inverse(multiply(inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(Y),Y))),Z))),multiply(X,Y))),multiply(inverse(Y),inverse(multiply(inverse(multiply(U,Z)),multiply(U,inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Y),Y))))))))).
% 16 [para:11.1.1,7.1.2.2.1.1] equal(inverse(multiply(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),multiply(X,V))),multiply(inverse(V),inverse(multiply(inverse(multiply(inverse(multiply(W,Z)),multiply(W,U))),multiply(inverse(inverse(multiply(inverse(V),V))),inverse(multiply(inverse(inverse(multiply(inverse(V),V))),inverse(multiply(inverse(V),V))))))))).
% 17 [para:7.1.1,11.1.1] equal(multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X)))).
% 18 [para:11.1.1,11.1.1.1.1] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V))),inverse(multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V)))).
% 20 [para:8.1.1,5.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)),Y).
% 21 [para:8.1.1,7.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)),multiply(inverse(U),inverse(multiply(inverse(inverse(multiply(Y,multiply(inverse(U),inverse(multiply(inverse(U),U)))))),multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(U),U))))))))).
% 24 [para:8.1.1,11.1.1] equal(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)),inverse(multiply(inverse(multiply(U,inverse(multiply(Y,multiply(inverse(V),inverse(multiply(inverse(V),V))))))),multiply(U,V)))).
% 30 [para:5.1.1,13.1.1.1] equal(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(inverse(X),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),U)),multiply(inverse(multiply(V,multiply(Y,Z))),multiply(V,U))).
% 32 [para:13.1.1,11.1.1.1.2] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V)))),inverse(multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V))))).
% 33 [para:13.1.1,11.1.2.1.2] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U)))),inverse(multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(W,V)),multiply(W,U))))).
% 34 [para:11.1.1,13.1.1.1] 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))).
% 39 [para:13.1.1,13.1.1.2] 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)))).
% 53 [para:7.1.2,20.1.1.1.1] equal(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z)))),Y).
% 895 [para:20.1.1,30.1.1.2] equal(multiply(inverse(X),X),multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,multiply(Z,U)))).
% 972 [para:20.1.1,895.1.2.1.1,demod:20] equal(multiply(inverse(X),X),multiply(inverse(Y),Y)).
% 1258 [para:972.1.1,10.1.1.1.1.1.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Y),Y))))),Y).
% 1267 [para:972.1.1,53.1.1.1.1.1.1.1] equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(Y)),Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z)))),Y).
% 2388 [para:972.1.1,1258.1.1.1.2.2.1] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))),Y).
% 2491 [para:972.1.1,2388.1.1.1.2] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))).
% 2560 [para:2491.1.1,10.1.1.1.1.1.1.1,demod:1267] equal(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)).
% 2864 [para:2560.1.2,12.1.1.1.1.1.2.1.1.1,demod:2388] equal(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Z),Y)).
% 2866 [para:2560.1.1,12.1.1.1.1.1.2.1.2.2,demod:2864] equal(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Y)),Z)),multiply(inverse(X),Z)).
% 2983 [para:2560.1.1,18.1.1.1.1,demod:2864] equal(inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(Y,Z)),U))),multiply(inverse(U),multiply(Y,Z))).
% 2989 [para:2560.1.2,18.1.1.1.2.1.1,demod:2864] equal(inverse(multiply(multiply(inverse(X),Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),U))),multiply(inverse(U),multiply(inverse(Y),X))).
% 2996 [para:2560.1.1,15.1.1.1.1,demod:2864,2983] equal(multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(X),X))),Y)),multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))),Y))).
% 2997 [para:2560.1.1,15.1.1.1.1.1.2.1.1,demod:2996,2866,2864] equal(multiply(inverse(X),Y),multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(X),X))),Y))).
% 2998 [para:2560.1.2,15.1.1.1.2,demod:2996,2864,2997] equal(inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(multiply(inverse(Z),Z)))),multiply(inverse(X),Y)).
% 3014 [para:2560.1.2,32.1.2.1.2,demod:2998] equal(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V)))),multiply(inverse(multiply(X,V)),Z)).
% 3019 [para:2560.1.2,33.1.1.1.1.1,demod:3014] equal(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),multiply(Z,U)))),multiply(inverse(multiply(Z,U)),Y)).
% 3049 [para:2560.1.2,16.1.1.1.1.1.2.1.1,demod:2997,2996,2989,2864] equal(multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),U))),multiply(inverse(X),multiply(inverse(Z),U))).
% 3050 [para:2560.1.2,16.1.1.1.1.1.2.2,demod:3049,2996,2989,2864] equal(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Z)),inverse(multiply(inverse(U),U)))),multiply(inverse(X),multiply(inverse(Z),Y))).
% 3080 [para:2560.1.1,17.1.1.2.1.2.1.1,demod:2864,3050] equal(multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))),multiply(inverse(X),Y)).
% 3162 [para:2560.1.1,1258.1.1.1.2.2,demod:3019] equal(multiply(inverse(multiply(inverse(X),X)),Y),Y).
% 3167 [para:2560.1.1,2388.1.1.1.1.1,demod:3162] equal(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),X).
% 3178 [para:3162.1.1,7.1.1.1,demod:3080,3167] equal(inverse(multiply(inverse(X),Y)),multiply(inverse(Y),X)).
% 3188 [para:11.1.1,3162.1.1.1,demod:2864] equal(multiply(multiply(inverse(X),X),Y),Y).
% 3193 [para:3162.1.1,13.1.1] equal(multiply(inverse(X),Y),multiply(inverse(multiply(Z,X)),multiply(Z,Y))).
% 3200 [para:3162.1.1,34.1.1.1.1,demod:3193,3178] equal(multiply(multiply(inverse(X),Y),multiply(inverse(multiply(Z,Y)),U)),multiply(inverse(multiply(Z,X)),U)).
% 3201 [para:3162.1.1,34.1.1.2.1.1,demod:3188,3178,3193] equal(multiply(multiply(inverse(X),Y),multiply(inverse(Y),Z)),multiply(inverse(X),Z)).
% 3205 [para:3162.1.1,30.1.1.2,demod:3193,3188,3178] equal(multiply(X,Y),multiply(multiply(inverse(Z),multiply(Z,X)),Y)).
% 3206 [para:3162.1.1,30.1.1.2.1.1,demod:3193,3188,3178] equal(multiply(X,multiply(inverse(multiply(Y,X)),Z)),multiply(inverse(Y),Z)).
% 3207 [para:3162.1.1,30.1.1.2.1.1.2.1.2,demod:3193,3206,3188,3201,3178] equal(multiply(inverse(X),Y),multiply(inverse(multiply(X,multiply(inverse(Z),Z))),Y)).
% 3209 [para:3162.1.1,16.1.2.2.1,demod:3201,3188,3178,3193] equal(inverse(X),multiply(inverse(X),multiply(inverse(X),X))).
% 3224 [para:3162.1.1,1258.1.1.1.1.1.1,demod:3188,3209,3178] equal(inverse(inverse(X)),X).
% 3227 [para:24.1.2,5.1.1,demod:3193,3209,3178,3224] equal(multiply(multiply(X,inverse(Y)),Y),X).
% 3228 [para:24.1.2,5.1.1.1.1.1.2,demod:3201,3205,3193,3224,3209,3178] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(multiply(X,multiply(inverse(Y),Y))))).
% 3229 [para:24.1.2,5.1.1.1.1.1.2.1.1,demod:3227,3193,3224,3209,3178] equal(multiply(inverse(X),multiply(X,Y)),Y).
% 3232 [para:5.1.1,24.1.1.1.1.2.1.2.1,demod:3227,3200,3207,3206,3229,3193,3224,3209,3178] equal(multiply(inverse(multiply(X,Y)),X),inverse(Y)).
% 3249 [para:24.1.2,53.1.1.1.1.1.1.1.2,demod:3227,3232,3193,3224,3209,3178] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 3253 [para:9.1.1,24.1.1.1.1,demod:3227,3193,3224,3209,3178] equal(multiply(inverse(X),inverse(Y)),inverse(multiply(Y,X))).
% 3265 [para:24.1.1,39.1.1.1.1.1.1,demod:3253,3227,3224,3193,3209,3178] equal(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,U)),V)),multiply(inverse(Y),multiply(inverse(multiply(Z,multiply(U,X))),V))).
% 3279 [para:24.1.2,30.1.1.2.1.1.2,demod:3207,3265,3232,3193,3224,3253,3209,3228,3201,3178] equal(multiply(inverse(X),multiply(inverse(Y),Z)),multiply(inverse(multiply(Y,X)),Z)).
% 3295 [para:972.1.1,24.1.2.1.2,demod:3227,3193,3224,3253,3232,3279,3178] equal(inverse(X),inverse(multiply(X,multiply(inverse(Y),Y)))).
% 3308 [para:3224.1.1,16.1.2.2.1.2.1,demod:3279,3295,3201,3178,3193] equal(inverse(multiply(multiply(inverse(X),Y),Z)),multiply(inverse(multiply(Y,Z)),X)).
% 3310 [para:16.1.1,3224.1.1.1,demod:3279,3295,3308,3201,3178,3193] equal(multiply(inverse(X),multiply(Y,Z)),multiply(multiply(inverse(X),Y),Z)).
% 3343 [para:3229.1.1,34.1.1.2,demod:3310,3178,3193] equal(multiply(inverse(X),multiply(Y,Z)),multiply(inverse(multiply(U,X)),multiply(multiply(U,Y),Z))).
% 3346 [para:3229.1.1,30.1.1.2,demod:3343,3193,3224,3253,3232,3279,3178] equal(multiply(X,Y),multiply(inverse(Z),multiply(multiply(Z,X),Y))).
% 3348 [para:972.1.1,3229.1.1.2,demod:3224] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 3349 [para:21.1.2,3229.1.1.2,demod:3348,3201,3193,3253,3232,3279,3178,3224] equal(multiply(X,inverse(Y)),inverse(multiply(Y,inverse(X)))).
% 3352 [para:8.1.2,3249.1.1.1,demod:3224,3253,3227,3193,3349,3232,3279,3178] equal(inverse(multiply(multiply(X,Y),Z)),inverse(multiply(X,multiply(Y,Z)))).
% 3353 [para:3249.1.1,13.1.1.1.1,demod:3349,3346] equal(multiply(X,Y),multiply(multiply(X,inverse(Z)),multiply(Z,Y))).
% 3377 [para:3232.1.1,30.1.1.2.1.1,demod:3353,3349,3352,3253,3232,3279,3178,3224] equal(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)).
% 3385 [para:3377.1.2,6.1.1,cut:4] 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
% clause length limited to 1
% clause depth limited to 11
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 85
% derived clauses: 42491
% kept clauses: 3378
% kept size sum: 125920
% kept mid-nuclei: 0
% kept new demods: 510
% forw unit-subs: 31183
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 10
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 1.45
% process. runtime: 1.44
% 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/GRP423-1+eq_r.in")
%
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