TSTP Solution File: GRP501-1 by Gandalf---c-2.6
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%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP501-1 : 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 : 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/GRP501-1+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 7 1)
% (binary-posweight-lex-big-order 30 #f 7 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(4,40,0,8,0,0)
%
%
% START OF PROOF
% 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(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% 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)))).
% 17 [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)))).
% 22 [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))))).
% 23 [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).
% 32 [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).
% 33 [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).
% 53 [para:32.1.1,11.1.1.2.2] 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)).
% 68 [para:32.1.1,33.1.1.2.2.2,demod:53] equal(double_divide(inverse(X),double_divide(Y,inverse(X))),double_divide(Z,double_divide(Y,Z))).
% 82 [para:68.1.1,6.1.1.2.1.1.1.2,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))).
% 119 [para:68.1.1,68.1.1] equal(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(Y,Z))).
% 122 [para:119.1.1,7.1.2.1,demod:7] equal(multiply(double_divide(X,Y),Y),multiply(double_divide(X,Z),Z)).
% 123 [para:119.1.1,6.1.1.2.1.1.1,demod:7] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),multiply(double_divide(Z,U),U))),X).
% 142 [para:119.1.1,32.1.1.2.1] equal(multiply(double_divide(X,double_divide(Y,X)),multiply(double_divide(Z,double_divide(inverse(U),Z)),U)),Y).
% 147 [para:119.1.1,119.1.1.2] equal(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z))),double_divide(U,double_divide(Y,U))).
% 167 [para:119.1.1,122.1.1.1] equal(multiply(double_divide(X,double_divide(Y,X)),double_divide(Y,Z)),multiply(double_divide(Z,U),U)).
% 205 [para:147.1.1,12.1.2.2.1,demod:82] 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))).
% 345 [para:147.1.1,123.1.1.2.2.1,demod:7,205] equal(double_divide(inverse(X),double_divide(Y,multiply(double_divide(Y,Z),Z))),X).
% 361 [para:345.1.1,7.1.2.1] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),inverse(Z)),inverse(Z)).
% 362 [para:7.1.2,345.1.1.1] equal(double_divide(multiply(X,Y),double_divide(Z,multiply(double_divide(Z,U),U))),double_divide(Y,X)).
% 383 [para:119.1.1,345.1.1.2.2.1] equal(double_divide(inverse(X),double_divide(Y,multiply(double_divide(Z,double_divide(U,Z)),double_divide(U,Y)))),X).
% 408 [para:7.1.2,361.1.1.2,demod:7] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),multiply(Z,U)),multiply(Z,U)).
% 478 [para:32.1.1,408.1.1.2,demod:32] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Y)),Z),Z).
% 554 [para:478.1.1,11.1.1.2.2] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),X)),multiply(double_divide(Z,U),U)).
% 564 [para:119.1.1,478.1.1.1.2.1] equal(multiply(double_divide(X,multiply(double_divide(Y,double_divide(Z,Y)),double_divide(Z,X))),U),U).
% 900 [para:122.1.1,554.1.1.2,demod:7] equal(double_divide(multiply(X,Y),multiply(double_divide(X,Z),Z)),multiply(double_divide(Y,U),U)).
% 1165 [para:900.1.2,478.1.1.1.2] equal(multiply(double_divide(X,double_divide(multiply(Y,X),multiply(double_divide(Y,Z),Z))),U),U).
% 1285 [para:119.1.1,1165.1.1.1] equal(multiply(double_divide(X,double_divide(multiply(Y,multiply(double_divide(Y,Z),Z)),X)),U),U).
% 1292 [para:1165.1.1,167.1.1] equal(double_divide(multiply(X,multiply(double_divide(X,Y),Y)),Z),multiply(double_divide(Z,U),U)).
% 1330 [para:1285.1.1,362.1.1.2.2] equal(double_divide(multiply(X,Y),double_divide(Z,double_divide(multiply(U,multiply(double_divide(U,V),V)),Z))),double_divide(Y,X)).
% 1347 [para:1292.1.1,6.1.1.2.1.1.1.2,demod:1330,7] equal(double_divide(inverse(X),multiply(multiply(double_divide(Y,Z),Z),X)),Y).
% 1433 [para:1292.1.1,554.1.2.1,demod:1285] equal(double_divide(inverse(X),X),multiply(multiply(double_divide(Y,Z),Z),Y)).
% 1777 [para:1433.1.2,1347.1.1.2] equal(double_divide(inverse(X),double_divide(inverse(Y),Y)),X).
% 1783 [para:1433.1.2,1433.1.2] equal(double_divide(inverse(X),X),double_divide(inverse(Y),Y)).
% 1858 [para:1777.1.1,142.1.1.2.1] equal(multiply(double_divide(X,double_divide(Y,X)),multiply(Z,inverse(Z))),Y).
% 1964 [para:1783.1.1,6.1.1.2.1,demod:7] equal(double_divide(inverse(X),multiply(Y,inverse(Y))),X).
% 1965 [para:1783.1.1,6.1.1.2.1.1.1,demod:1858,7] equal(double_divide(inverse(multiply(X,Y)),Y),X).
% 2060 [para:9.1.1,1965.1.1.1.1] equal(double_divide(inverse(inverse(X)),inverse(Y)),multiply(double_divide(Z,double_divide(U,Z)),multiply(double_divide(U,X),Y))).
% 2076 [para:1965.1.1,122.1.1.1] equal(multiply(X,Y),multiply(double_divide(inverse(multiply(X,Y)),Z),Z)).
% 2111 [para:1965.1.1,554.1.1.2.1.2,demod:2076] equal(double_divide(inverse(X),multiply(double_divide(Y,Z),X)),multiply(Z,Y)).
% 2134 [para:1965.1.1,1777.1.1] equal(X,multiply(X,double_divide(inverse(Y),Y))).
% 2164 [para:2134.1.2,17.1.1.2.1.2.1,demod:2134,7,2060] equal(double_divide(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),multiply(U,X))),double_divide(inverse(inverse(U)),Z)).
% 2166 [para:2134.1.2,17.1.2.2,demod:1964,2164] equal(inverse(X),multiply(double_divide(Y,double_divide(Z,Y)),double_divide(Z,X))).
% 2177 [para:383.1.1,2134.1.2.2,demod:2166] equal(X,multiply(X,double_divide(Y,inverse(Y)))).
% 2199 [para:2134.1.2,1347.1.1.2.1,demod:2111] equal(multiply(double_divide(inverse(X),X),Y),Y).
% 2212 [para:2177.1.2,32.1.1.2,demod:2166,7] equal(multiply(X,multiply(inverse(Y),Y)),X).
% 2219 [para:2177.1.2,167.1.2,demod:2166] equal(inverse(X),double_divide(X,double_divide(Y,inverse(Y)))).
% 2224 [para:2177.1.2,345.1.1.2.2,demod:2219] equal(inverse(inverse(X)),X).
% 2227 [para:2177.1.2,362.1.1.2.2,demod:2219] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 2247 [para:2177.1.2,554.1.2,demod:2219,2111] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 2253 [para:2177.1.2,1165.1.1.1.2.1,demod:7,2219,2247] equal(multiply(multiply(inverse(X),X),Y),Y).
% 2263 [para:2177.1.2,22.1.1.1.2,demod:2224,2060,2212,7] equal(multiply(double_divide(X,double_divide(multiply(Y,Z),X)),U),multiply(multiply(Y,Z),U)).
% 2264 [para:2177.1.2,22.1.2.1.2,demod:2224,2166,2253,2263] equal(multiply(multiply(X,Y),inverse(Y)),X).
% 2266 [para:2224.1.1,6.1.1.1,demod:2224,2060,7] equal(double_divide(X,double_divide(Y,X)),Y).
% 2291 [para:2224.1.1,1777.1.1.1] equal(double_divide(X,double_divide(inverse(Y),Y)),inverse(X)).
% 2366 [para:478.1.1,23.1.1.2.2,demod:2227,2247,2266] 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)).
% 2369 [para:564.1.1,23.1.1.2.2,demod:2366,2266] equal(double_divide(X,Y),multiply(Z,double_divide(Z,multiply(Y,X)))).
% 2422 [para:2266.1.1,6.1.1.2.1.1.1.2,demod:2266,7] equal(double_divide(inverse(X),multiply(Y,multiply(Z,X))),double_divide(Z,Y)).
% 2424 [para:2266.1.1,9.1.1.1.2.1,demod:7,2266] equal(multiply(multiply(X,multiply(Y,Z)),inverse(Z)),multiply(X,Y)).
% 2429 [para:2266.1.1,12.1.2.2.1,demod:2422,2266] equal(double_divide(double_divide(X,Y),inverse(Z)),multiply(Y,multiply(X,Z))).
% 2432 [para:2266.1.1,122.1.1.1,demod:2247] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 2434 [para:2266.1.1,16.1.2.1.2.1,demod:2227,2424,2266] equal(multiply(inverse(X),double_divide(Y,Z)),double_divide(multiply(Y,X),Z)).
% 2463 [para:2199.1.1,17.1.2.2,demod:2434,2422,2266] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Z,X),Y)).
% 2467 [para:2199.1.1,22.1.1.1.2,demod:7,2369,2434,2291,2266,2264,2463] equal(double_divide(X,double_divide(Y,multiply(X,Z))),multiply(Z,Y)).
% 2478 [para:17.1.2,2227.1.1.1,demod:2429,2432,2266,7,2422,2467,2463,slowcut:8] 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 7
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 62
% derived clauses: 7907
% kept clauses: 2468
% kept size sum: 59533
% kept mid-nuclei: 0
% kept new demods: 970
% forw unit-subs: 3788
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 4
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 0.21
% process. runtime: 0.19
% 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/GRP501-1+eq_r.in")
%
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