%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP099-1 : TPTP v3.4.2. Bugfixed v2.7.0.
% 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 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/GRP099-1+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 6 7)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 6 7)
% (binary-posweight-lex-big-order 30 #f 6 7)
% (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),identity) | -equal(multiply(identity,a2),a2) | -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(a4,b4),multiply(b4,a4)).
% was split for some strategies as:
% -equal(multiply(inverse(a1),a1),identity).
% -equal(multiply(identity,a2),a2).
% -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))).
% -equal(multiply(a4,b4),multiply(b4,a4)).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(6,40,0,12,0,0,2073,4,754)
%
%
% START OF PROOF
% 7 [] equal(X,X).
% 8 [] equal(double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),double_divide(identity,identity)),Y).
% 9 [] equal(multiply(X,Y),double_divide(double_divide(Y,X),identity)).
% 10 [] equal(inverse(X),double_divide(X,identity)).
% 11 [] equal(identity,double_divide(X,inverse(X))).
% 12 [] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity) | -equal(multiply(a4,b4),multiply(b4,a4)) | -equal(multiply(identity,a2),a2).
% 13 [para:9.1.2,10.1.2] equal(inverse(double_divide(X,Y)),multiply(Y,X)).
% 14 [para:10.1.2,9.1.2.1,demod:10] equal(multiply(identity,X),inverse(inverse(X))).
% 15 [para:11.1.2,9.1.2.1,demod:10] equal(multiply(inverse(X),X),inverse(identity)).
% 16 [para:9.1.2,9.1.2.1,demod:10] equal(multiply(identity,double_divide(X,Y)),inverse(multiply(Y,X))).
% 17 [para:14.1.2,11.1.2.2] equal(identity,double_divide(inverse(X),multiply(identity,X))).
% 18 [para:14.1.2,14.1.2.1] equal(multiply(identity,inverse(X)),inverse(multiply(identity,X))).
% 22 [para:13.1.1,15.1.1.1] equal(multiply(multiply(X,Y),double_divide(Y,X)),inverse(identity)).
% 26 [para:10.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(X,double_divide(double_divide(Y,inverse(X)),inverse(identity))),inverse(identity)),Y).
% 28 [para:11.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(X,double_divide(inverse(Y),double_divide(identity,inverse(X)))),inverse(identity)),Y).
% 29 [para:11.1.2,8.1.1.1.2.2,demod:10,9] equal(double_divide(double_divide(X,multiply(double_divide(X,inverse(identity)),Y)),inverse(identity)),Y).
% 31 [para:9.1.2,8.1.1.1.2.1.2,demod:10] equal(double_divide(double_divide(double_divide(X,Y),double_divide(double_divide(Z,multiply(Y,X)),inverse(identity))),inverse(identity)),Z).
% 34 [para:8.1.1,8.1.1.1.2.1,demod:10] equal(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z)))).
% 39 [para:11.1.2,29.1.1.1.2.1] equal(double_divide(double_divide(identity,multiply(identity,X)),inverse(identity)),X).
% 43 [para:16.1.1,39.1.1.1.2] equal(double_divide(double_divide(identity,inverse(multiply(X,Y))),inverse(identity)),double_divide(Y,X)).
% 46 [para:11.1.2,26.1.1.1.2.1,demod:10,11] equal(double_divide(inverse(X),inverse(identity)),X).
% 50 [para:39.1.1,26.1.1.1.2.1] equal(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),double_divide(identity,multiply(identity,X))).
% 53 [para:46.1.1,9.1.2.1,demod:10] equal(multiply(inverse(identity),inverse(X)),inverse(X)).
% 54 [para:14.1.2,46.1.1.1] equal(double_divide(multiply(identity,X),inverse(identity)),inverse(X)).
% 57 [para:46.1.1,26.1.1.1.2.1,demod:50] equal(double_divide(identity,multiply(identity,X)),inverse(X)).
% 62 [para:16.1.1,57.1.1.2,demod:13] equal(double_divide(identity,inverse(multiply(X,Y))),multiply(X,Y)).
% 64 [para:54.1.1,26.1.1.1.2.1,demod:46] equal(double_divide(double_divide(identity,X),inverse(identity)),multiply(identity,X)).
% 71 [para:10.1.2,64.1.1.1,demod:46] equal(identity,multiply(identity,identity)).
% 72 [para:11.1.2,64.1.1.1,demod:11] equal(identity,multiply(identity,inverse(identity))).
% 79 [para:64.1.1,26.1.1.1.2.1,demod:64,54] equal(multiply(identity,inverse(X)),double_divide(identity,X)).
% 88 [para:71.1.2,18.1.2.1,demod:72] equal(identity,inverse(identity)).
% 89 [para:88.1.2,29.1.1.1.2.1.2,demod:9,88,10] equal(multiply(multiply(inverse(X),Y),X),Y).
% 90 [para:88.1.2,39.1.1.2,demod:14,10,57] equal(multiply(identity,X),X).
% 92 [para:88.1.2,43.1.1.2,demod:10,62] equal(inverse(multiply(X,Y)),double_divide(Y,X)).
% 93 [para:88.1.2,26.1.1.1.2.1.2,demod:9,90,14,88,10] equal(multiply(X,identity),X).
% 94 [para:88.1.2,53.1.1.1,demod:79] equal(double_divide(identity,X),inverse(X)).
% 96 [para:88.1.2,28.1.1.2,demod:9,90,14,94] equal(multiply(double_divide(inverse(X),Y),Y),X).
% 99 [para:90.1.1,17.1.2.2] equal(identity,double_divide(inverse(X),X)).
% 110 [para:29.1.1,31.1.1.1.2,demod:9,10,88] equal(multiply(X,double_divide(X,inverse(Y))),Y).
% 112 [para:13.1.1,99.1.2.1] equal(identity,double_divide(multiply(X,Y),double_divide(Y,X))).
% 116 [para:14.1.2,89.1.1.1.1,demod:90] equal(multiply(multiply(X,Y),inverse(X)),Y).
% 119 [para:89.1.1,22.1.1.1,demod:88] equal(multiply(X,double_divide(Y,multiply(inverse(Y),X))),identity).
% 122 [para:92.1.1,28.1.1.1.2.1,demod:9,88,90,14,94] equal(multiply(double_divide(double_divide(X,Y),Z),Z),multiply(Y,X)).
% 123 [para:92.1.1,89.1.1.1.1] equal(multiply(multiply(double_divide(X,Y),Z),multiply(Y,X)),Z).
% 124 [para:14.1.2,96.1.1.1.1,demod:90] equal(multiply(double_divide(X,Y),Y),inverse(X)).
% 128 [para:14.1.2,110.1.1.2.2,demod:90] equal(multiply(X,double_divide(X,Y)),inverse(Y)).
% 131 [para:110.1.1,29.1.1.1.2,demod:10,9,88] equal(multiply(X,Y),double_divide(inverse(Y),inverse(X))).
% 133 [para:96.1.1,116.1.1.1,demod:13] equal(multiply(X,multiply(Y,inverse(X))),Y).
% 134 [para:110.1.1,116.1.1.1] equal(multiply(X,inverse(Y)),double_divide(Y,inverse(X))).
% 137 [para:124.1.1,43.1.1.1.2.1,demod:10,88,94,90,14] equal(X,double_divide(Y,double_divide(X,Y))).
% 138 [para:124.1.1,116.1.1.1,demod:13] equal(multiply(inverse(X),multiply(Y,X)),Y).
% 140 [para:137.1.2,8.1.1.1.2.1.2,demod:9,88,13,94] equal(multiply(double_divide(double_divide(X,Y),multiply(Z,Y)),Z),X).
% 142 [para:137.1.2,137.1.2.2] equal(X,double_divide(double_divide(Y,X),Y)).
% 146 [para:142.1.2,26.1.1.1.2.1,demod:9,10,88] equal(multiply(inverse(X),Y),double_divide(inverse(Y),X)).
% 157 [para:142.1.2,34.1.2.2,demod:90,14,10,88,94] equal(X,double_divide(Y,double_divide(Y,X))).
% 158 [para:142.1.2,34.1.2.2.1,demod:92,94,9,88] equal(multiply(X,double_divide(Y,Z)),double_divide(Y,double_divide(X,inverse(Z)))).
% 161 [para:157.1.2,8.1.1.1.2.1.2,demod:9,88,13,94] equal(multiply(double_divide(double_divide(X,Y),multiply(Y,Z)),Z),X).
% 162 [para:157.1.2,8.1.1.1.2.2,demod:9,88,158,94] equal(multiply(double_divide(multiply(X,double_divide(Y,Z)),Z),X),Y).
% 166 [para:137.1.2,157.1.2.2] equal(double_divide(X,Y),double_divide(Y,X)).
% 167 [para:157.1.2,128.1.1.2,demod:13] equal(multiply(X,Y),multiply(Y,X)).
% 175 [para:166.1.1,31.1.1.1,demod:9,88] equal(multiply(double_divide(X,Y),multiply(multiply(Y,X),Z)),Z).
% 177 [para:166.1.1,31.1.1.1.2.1,demod:9,88] equal(multiply(multiply(X,multiply(Y,Z)),double_divide(Z,Y)),X).
% 181 [para:13.1.1,133.1.1.2.2] equal(multiply(double_divide(X,Y),multiply(Z,multiply(Y,X))),Z).
% 191 [para:13.1.1,131.1.2.2] equal(multiply(double_divide(X,Y),Z),double_divide(inverse(Z),multiply(Y,X))).
% 192 [para:131.1.2,8.1.1.1.2.1.2,demod:13,134,9,88,90,14,94] equal(double_divide(X,multiply(Y,double_divide(Z,multiply(Y,X)))),Z).
% 193 [para:92.1.1,131.1.2.1] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(Z,Y),inverse(X))).
% 194 [para:92.1.1,131.1.2.2] equal(multiply(multiply(X,Y),Z),double_divide(inverse(Z),double_divide(Y,X))).
% 215 [para:166.1.1,112.1.2.2] equal(identity,double_divide(multiply(X,Y),double_divide(X,Y))).
% 222 [para:215.1.2,8.1.1.1.2.1.2,demod:9,88,191,13,94,10] equal(multiply(multiply(double_divide(X,Y),Z),multiply(X,Y)),Z).
% 226 [para:8.1.1,122.1.1.1,demod:193,93,88,94] equal(X,multiply(multiply(Y,multiply(double_divide(Z,Y),X)),Z)).
% 228 [para:167.1.1,123.1.1.1] equal(multiply(multiply(X,double_divide(Y,Z)),multiply(Z,Y)),X).
% 232 [para:142.1.2,140.1.1.1.1] equal(multiply(double_divide(X,multiply(Y,Z)),Y),double_divide(Z,X)).
% 251 [para:116.1.1,161.1.1.1.2,demod:13,134] equal(double_divide(X,multiply(Y,double_divide(Z,multiply(X,Y)))),Z).
% 252 [para:137.1.2,161.1.1.1.1] equal(multiply(double_divide(X,multiply(double_divide(X,Y),Z)),Z),Y).
% 253 [para:142.1.2,161.1.1.1.1] equal(multiply(double_divide(X,multiply(Y,Z)),Z),double_divide(Y,X)).
% 264 [para:89.1.1,162.1.1.1.1,demod:13] equal(multiply(double_divide(X,Y),multiply(multiply(Y,Z),X)),Z).
% 270 [para:162.1.1,133.1.1.2,demod:13,146] equal(multiply(X,Y),double_divide(double_divide(multiply(Z,Y),X),Z)).
% 315 [para:122.1.1,177.1.1.1] equal(multiply(multiply(X,Y),double_divide(Z,U)),double_divide(double_divide(Y,X),multiply(U,Z))).
% 321 [para:122.1.1,181.1.1.2] equal(multiply(double_divide(X,Y),multiply(Z,U)),double_divide(double_divide(U,Z),multiply(Y,X))).
% 330 [para:142.1.2,192.1.1.2.2] equal(double_divide(X,multiply(Y,Z)),double_divide(multiply(Y,X),Z)).
% 343 [para:119.1.1,222.1.1.1,demod:330,13,146,90] equal(multiply(X,Y),double_divide(Z,double_divide(X,multiply(Y,Z)))).
% 349 [para:110.1.1,226.1.2.1.2,demod:193] equal(multiply(X,multiply(Y,Z)),multiply(multiply(Y,X),Z)).
% 353 [para:226.1.2,138.1.1.2,demod:146] equal(double_divide(inverse(X),Y),multiply(Z,multiply(double_divide(Y,Z),X))).
% 359 [para:122.1.1,228.1.1.1,demod:349] equal(multiply(X,multiply(Y,multiply(Z,U))),double_divide(double_divide(X,Y),double_divide(U,Z))).
% 393 [para:232.1.1,133.1.1.2,demod:146] equal(multiply(X,double_divide(Y,Z)),double_divide(Z,double_divide(inverse(Y),X))).
% 429 [para:251.1.1,232.1.1.1] equal(multiply(X,Y),double_divide(double_divide(X,multiply(Z,Y)),Z)).
% 431 [para:34.1.2,252.1.1.1.2.1,demod:353,193,321,349,393,146,90,14,94,10,88] equal(double_divide(double_divide(X,Y),multiply(Z,X)),double_divide(inverse(Y),Z)).
% 441 [para:232.1.1,253.1.1.1.2] equal(multiply(double_divide(X,double_divide(Y,Z)),U),double_divide(double_divide(Z,multiply(U,Y)),X)).
% 453 [para:175.1.1,264.1.1.2.1,demod:429,349,441] equal(multiply(X,multiply(Y,Z)),multiply(Z,multiply(X,Y))).
% 475 [para:175.1.1,270.1.2.1.1,demod:359,349] equal(double_divide(double_divide(X,Y),double_divide(Z,U)),double_divide(double_divide(Z,X),double_divide(Y,U))).
% 783 [para:315.1.1,343.1.2.2.2] equal(multiply(X,multiply(Y,Z)),double_divide(double_divide(U,V),double_divide(X,double_divide(double_divide(Z,Y),multiply(V,U))))).
% 1789 [para:343.1.2,475.1.1.2] equal(double_divide(double_divide(X,Y),multiply(Z,U)),double_divide(double_divide(V,X),double_divide(Y,double_divide(Z,multiply(U,V))))).
% 2074 [input:12,cut:167,cut:90] -equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) | -equal(multiply(inverse(a1),a1),identity).
% 2075 [para:783.1.1,2074.1.2,demod:99,146,194,431,1789,349,cut:453,cut:7] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 7
% clause depth limited to 6
% seconds given: 10
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 466
% derived clauses: 254418
% kept clauses: 2056
% kept size sum: 37617
% kept mid-nuclei: 4
% kept new demods: 616
% forw unit-subs: 252284
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 11
% fast unit cutoff: 6
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 7.57
% process. runtime: 7.56
% 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/GRP099-1+eq_r.in")
%
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