%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP179-3 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art02.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 10.0s
% Output : Assurance 10.0s
% 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/GRP179-3+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 3 1)
% (binary-posweight-lex-big-order 30 #f 3 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(20,40,0,40,0,0,146,50,17,166,0,17)
%
%
% START OF PROOF
% 148 [] equal(multiply(identity,X),X).
% 149 [] equal(multiply(inverse(X),X),identity).
% 150 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 151 [] equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)).
% 152 [] equal(least_upper_bound(X,Y),least_upper_bound(Y,X)).
% 153 [] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)).
% 154 [] equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)).
% 157 [] equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X).
% 158 [] equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X).
% 159 [] equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))).
% 160 [] equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))).
% 161 [] equal(multiply(least_upper_bound(X,Y),Z),least_upper_bound(multiply(X,Z),multiply(Y,Z))).
% 162 [] equal(multiply(greatest_lower_bound(X,Y),Z),greatest_lower_bound(multiply(X,Z),multiply(Y,Z))).
% 163 [] equal(inverse(identity),identity).
% 164 [] equal(inverse(inverse(X)),X).
% 165 [] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 166 [] -equal(least_upper_bound(inverse(a),identity),inverse(greatest_lower_bound(a,identity))).
% 167 [para:163.1.1,165.1.2.1,demod:148] equal(inverse(multiply(X,identity)),inverse(X)).
% 168 [?] ?
% 169 [para:164.1.1,165.1.2.1] equal(inverse(multiply(X,inverse(Y))),multiply(Y,inverse(X))).
% 171 [para:164.1.1,149.1.1.1] equal(multiply(X,inverse(X)),identity).
% 172 [para:167.1.1,164.1.1.1,demod:164] equal(X,multiply(X,identity)).
% 175 [para:151.1.1,157.1.1.2] equal(least_upper_bound(X,greatest_lower_bound(Y,X)),X).
% 176 [para:157.1.1,152.1.1] equal(X,least_upper_bound(greatest_lower_bound(X,Y),X)).
% 177 [para:158.1.1,151.1.1] equal(X,greatest_lower_bound(least_upper_bound(X,Y),X)).
% 178 [para:152.1.1,158.1.1.2] equal(greatest_lower_bound(X,least_upper_bound(Y,X)),X).
% 182 [para:149.1.1,150.1.1.1,demod:148] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 185 [para:152.1.1,177.1.2.1] equal(X,greatest_lower_bound(least_upper_bound(Y,X),X)).
% 187 [para:176.1.2,177.1.2.1] equal(greatest_lower_bound(X,Y),greatest_lower_bound(X,greatest_lower_bound(X,Y))).
% 188 [para:153.1.2,151.1.1] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,greatest_lower_bound(X,Y))).
% 196 [para:178.1.1,153.1.2.1] equal(greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(Y,X),Z)),greatest_lower_bound(X,Z)).
% 199 [para:165.1.2,182.1.2.2,demod:164] equal(inverse(X),multiply(Y,inverse(multiply(X,Y)))).
% 215 [para:154.1.2,185.1.2.1] equal(X,greatest_lower_bound(least_upper_bound(Y,least_upper_bound(Z,X)),X)).
% 218 [para:199.1.2,199.1.2.2.1,demod:164] equal(inverse(X),multiply(inverse(multiply(Y,X)),Y)).
% 228 [para:149.1.1,159.1.2.1] equal(multiply(inverse(X),least_upper_bound(X,Y)),least_upper_bound(identity,multiply(inverse(X),Y))).
% 229 [para:149.1.1,159.1.2.2] equal(multiply(inverse(X),least_upper_bound(Y,X)),least_upper_bound(multiply(inverse(X),Y),identity)).
% 232 [para:172.1.2,159.1.2.1] equal(multiply(X,least_upper_bound(identity,Y)),least_upper_bound(X,multiply(X,Y))).
% 233 [para:172.1.2,159.1.2.2] equal(multiply(X,least_upper_bound(Y,identity)),least_upper_bound(multiply(X,Y),X)).
% 236 [para:182.1.2,159.1.2.2] equal(multiply(inverse(X),least_upper_bound(Y,multiply(X,Z))),least_upper_bound(multiply(inverse(X),Y),Z)).
% 237 [para:159.1.2,154.1.2.1] equal(least_upper_bound(multiply(X,Y),least_upper_bound(multiply(X,Z),U)),least_upper_bound(multiply(X,least_upper_bound(Y,Z)),U)).
% 255 [para:172.1.2,160.1.2.1] equal(multiply(X,greatest_lower_bound(identity,Y)),greatest_lower_bound(X,multiply(X,Y))).
% 256 [para:172.1.2,160.1.2.2] equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(multiply(X,Y),X)).
% 263 [para:148.1.1,161.1.2.1] equal(multiply(least_upper_bound(identity,X),Y),least_upper_bound(Y,multiply(X,Y))).
% 264 [para:148.1.1,161.1.2.2] equal(multiply(least_upper_bound(X,identity),Y),least_upper_bound(multiply(X,Y),Y)).
% 267 [para:171.1.1,161.1.2.1] equal(multiply(least_upper_bound(X,Y),inverse(X)),least_upper_bound(identity,multiply(Y,inverse(X)))).
% 281 [para:148.1.1,162.1.2.1] equal(multiply(greatest_lower_bound(identity,X),Y),greatest_lower_bound(Y,multiply(X,Y))).
% 282 [para:148.1.1,162.1.2.2] equal(multiply(greatest_lower_bound(X,identity),Y),greatest_lower_bound(multiply(X,Y),Y)).
% 314 [para:149.1.1,232.1.2.2] equal(multiply(inverse(X),least_upper_bound(identity,X)),least_upper_bound(inverse(X),identity)).
% 315 [para:232.1.2,152.1.1] equal(multiply(X,least_upper_bound(identity,Y)),least_upper_bound(multiply(X,Y),X)).
% 318 [para:157.1.1,232.1.1.2,demod:172] equal(X,least_upper_bound(X,multiply(X,greatest_lower_bound(identity,Y)))).
% 319 [para:232.1.2,158.1.1.2] equal(greatest_lower_bound(X,multiply(X,least_upper_bound(identity,Y))),X).
% 324 [para:232.1.2,177.1.2.1] equal(X,greatest_lower_bound(multiply(X,least_upper_bound(identity,Y)),X)).
% 329 [para:218.1.2,232.1.2.2] equal(multiply(inverse(multiply(X,Y)),least_upper_bound(identity,X)),least_upper_bound(inverse(multiply(X,Y)),inverse(Y))).
% 340 [para:318.1.2,185.1.2.1] equal(multiply(X,greatest_lower_bound(identity,Y)),greatest_lower_bound(X,multiply(X,greatest_lower_bound(identity,Y)))).
% 344 [para:152.1.1,319.1.1.2.2] equal(greatest_lower_bound(X,multiply(X,least_upper_bound(Y,identity))),X).
% 415 [para:196.1.1,175.1.1.2] equal(least_upper_bound(greatest_lower_bound(least_upper_bound(X,Y),Z),greatest_lower_bound(Y,Z)),greatest_lower_bound(least_upper_bound(X,Y),Z)).
% 574 [para:149.1.1,256.1.2.1] equal(multiply(inverse(X),greatest_lower_bound(X,identity)),greatest_lower_bound(identity,inverse(X))).
% 688 [para:315.1.2,215.1.2.1] equal(X,greatest_lower_bound(multiply(least_upper_bound(Y,X),least_upper_bound(identity,Z)),X)).
% 1126 [para:171.1.1,263.1.2.2] equal(multiply(least_upper_bound(identity,X),inverse(X)),least_upper_bound(inverse(X),identity)).
% 1132 [para:175.1.1,263.1.1.1,demod:148] equal(X,least_upper_bound(X,multiply(greatest_lower_bound(Y,identity),X))).
% 1232 [para:1132.1.2,152.1.1] equal(X,least_upper_bound(multiply(greatest_lower_bound(Y,identity),X),X)).
% 1379 [para:281.1.2,255.1.2] equal(multiply(X,greatest_lower_bound(identity,X)),multiply(greatest_lower_bound(identity,X),X)).
% 1412 [para:171.1.1,282.1.2.1] equal(multiply(greatest_lower_bound(X,identity),inverse(X)),greatest_lower_bound(identity,inverse(X))).
% 1508 [para:157.1.1,228.1.1.2,demod:149] equal(identity,least_upper_bound(identity,multiply(inverse(X),greatest_lower_bound(X,Y)))).
% 1540 [para:324.1.2,1508.1.2.2.2,demod:218] equal(identity,least_upper_bound(identity,inverse(least_upper_bound(identity,X)))).
% 1743 [para:1232.1.2,237.1.1.2] equal(least_upper_bound(multiply(greatest_lower_bound(X,identity),Y),Z),least_upper_bound(multiply(greatest_lower_bound(X,identity),least_upper_bound(Y,Z)),Z)).
% 1846 [para:1540.1.2,688.1.2.1.1,demod:148] equal(inverse(least_upper_bound(identity,X)),greatest_lower_bound(least_upper_bound(identity,Y),inverse(least_upper_bound(identity,X)))).
% 2297 [para:314.1.1,281.1.2.2] equal(multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X)),greatest_lower_bound(least_upper_bound(identity,X),least_upper_bound(inverse(X),identity))).
% 2445 [para:574.1.1,264.1.2.1] equal(multiply(least_upper_bound(inverse(X),identity),greatest_lower_bound(X,identity)),least_upper_bound(greatest_lower_bound(identity,inverse(X)),greatest_lower_bound(X,identity))).
% 2451 [para:1126.1.1,182.1.2.2] equal(inverse(X),multiply(inverse(least_upper_bound(identity,X)),least_upper_bound(inverse(X),identity))).
% 2463 [para:1126.1.1,255.1.2.2,demod:2297] equal(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),multiply(greatest_lower_bound(identity,inverse(X)),least_upper_bound(identity,X))).
% 2549 [para:1379.1.2,182.1.2.2] equal(X,multiply(inverse(greatest_lower_bound(identity,X)),multiply(X,greatest_lower_bound(identity,X)))).
% 2563 [para:1379.1.2,255.1.1,demod:340,153,1379,187] equal(multiply(greatest_lower_bound(identity,X),greatest_lower_bound(identity,X)),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(identity,X)))).
% 2583 [para:1412.1.1,169.1.1.1] equal(inverse(greatest_lower_bound(identity,inverse(X))),multiply(X,inverse(greatest_lower_bound(X,identity)))).
% 2585 [para:1412.1.1,233.1.2.1,demod:2445] equal(multiply(greatest_lower_bound(X,identity),least_upper_bound(inverse(X),identity)),multiply(least_upper_bound(inverse(X),identity),greatest_lower_bound(X,identity))).
% 2724 [para:2451.1.2,344.1.1.2] equal(greatest_lower_bound(inverse(least_upper_bound(identity,X)),inverse(X)),inverse(least_upper_bound(identity,X))).
% 2749 [para:157.1.1,267.1.1.1,demod:171] equal(identity,least_upper_bound(identity,multiply(greatest_lower_bound(X,Y),inverse(X)))).
% 2823 [para:2749.1.2,236.1.1.2,demod:168] equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(greatest_lower_bound(X,Y)),inverse(X))).
% 2865 [para:2823.1.2,178.1.1.2] equal(greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(X,Y))),inverse(X)).
% 2899 [para:151.1.1,2865.1.1.2.1] equal(greatest_lower_bound(inverse(X),inverse(greatest_lower_bound(Y,X))),inverse(X)).
% 2942 [para:2899.1.1,188.1.1.2] equal(greatest_lower_bound(X,inverse(Y)),greatest_lower_bound(inverse(greatest_lower_bound(Z,Y)),greatest_lower_bound(X,inverse(Y)))).
% 3060 [para:2549.1.2,255.1.2.2,demod:182,2563] equal(greatest_lower_bound(identity,X),greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),X)).
% 3063 [para:3060.1.2,153.1.2.1,demod:153] equal(greatest_lower_bound(inverse(greatest_lower_bound(identity,X)),greatest_lower_bound(X,Y)),greatest_lower_bound(identity,greatest_lower_bound(X,Y))).
% 3721 [para:2583.1.2,329.1.1.1.1,demod:2585,2445,1412,169,2463,164] equal(multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(X))),multiply(greatest_lower_bound(X,identity),least_upper_bound(inverse(X),identity))).
% 5332 [para:3063.1.1,2942.1.2] equal(greatest_lower_bound(X,inverse(X)),greatest_lower_bound(identity,greatest_lower_bound(X,inverse(X)))).
% 5335 [para:5332.1.2,157.1.1.2] equal(least_upper_bound(identity,greatest_lower_bound(X,inverse(X))),identity).
% 5379 [para:164.1.1,5335.1.1.2.2] equal(least_upper_bound(identity,greatest_lower_bound(inverse(X),X)),identity).
% 5399 [para:5379.1.1,415.1.1.1.1,demod:5379,153] equal(least_upper_bound(greatest_lower_bound(identity,X),greatest_lower_bound(inverse(Y),greatest_lower_bound(Y,X))),greatest_lower_bound(identity,X)).
% 6167 [para:2724.1.1,5399.1.1.2.2,demod:1846,164] equal(least_upper_bound(greatest_lower_bound(identity,inverse(X)),inverse(least_upper_bound(identity,X))),greatest_lower_bound(identity,inverse(X))).
% 6450 [para:6167.1.1,229.1.1.2,demod:176,1412,1743,3721,164] equal(multiply(greatest_lower_bound(X,identity),least_upper_bound(inverse(X),identity)),identity).
% 6455 [para:6450.1.1,182.1.2.2,demod:168,slowcut:166] 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 4
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 1163
% derived clauses: 697828
% kept clauses: 6393
% kept size sum: 109492
% kept mid-nuclei: 0
% kept new demods: 4544
% forw unit-subs: 289919
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 23
% fast unit cutoff: 0
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 13.23
% process. runtime: 13.20
% 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/GRP179-3+eq_r.in")
%
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