TSTP Solution File: GRP186-2 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP186-2 : 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 : 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 555.2s
% Output : Assurance 555.2s
% 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/GRP186-2+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 5 1)
% (binary-posweight-lex-big-order 30 #f 5 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(20,40,0,40,0,0,42712,3,3001,52732,4,4504,61672,5,6029,61672,1,6029,61672,50,6033,61672,40,6033,61692,0,6033,73553,3,7535,75248,4,8286,76136,5,9034,76136,1,9034,76136,50,9035,76136,40,9035,76156,0,9035,136392,3,10538,152070,4,11286,161777,5,12036,161777,1,12036,161777,50,12042,161777,40,12042,161797,0,12042,621430,3,21055,925755,4,25546,1240515,5,30043,1240516,1,30043,1240516,50,30048,1240516,40,30048,1240536,0,30048,1399360,3,36052,1504261,4,39079,1618036,5,42066,1618036,1,42066,1618036,50,42072,1618036,40,42072,1618056,0,42072,1810539,3,45075,1926815,4,46573,2075550,5,48073,2075552,1,48073,2075552,50,48118,2075552,40,48118,2075572,0,48118,2192633,3,51119,2266016,4,52622,2351324,5,54119,2351324,1,54119,2351324,50,54124,2351324,40,54124,2351344,0,54124)
%
%
% START OF PROOF
% 152 [?] ?
% 46278 [?] ?
% 47892 [para:152.1.2,46278.1.1.1.2] equal(least_upper_bound(greatest_lower_bound(inverse(X),multiply(X,greatest_lower_bound(identity,Y))),identity),identity).
% 61675 [?] ?
% 61676 [?] ?
% 61690 [?] ?
% 61691 [?] ?
% 61693 [?] ?
% 61707 [?] ?
% 61711 [?] ?
% 61772 [?] ?
% 61918 [?] ?
% 61967 [?] ?
% 62134 [?] ?
% 62144 [?] ?
% 62195 [?] ?
% 62197 [?] ?
% 63389 [para:62134.1.1,62144.1.1.2,demod:62195,61711] equal(greatest_lower_bound(X,identity),multiply(X,greatest_lower_bound(identity,multiply(inverse(X),greatest_lower_bound(identity,X))))).
% 63497 [?] ?
% 63866 [?] ?
% 64428 [?] ?
% 65324 [?] ?
% 71096 [?] ?
% 73681 [?] ?
% 73712 [para:61918.1.1,73681.1.1] -equal(multiply(inverse(X),least_upper_bound(X,multiply(X,multiply(a,b)))),multiply(inverse(greatest_lower_bound(b,inverse(a))),b)).
% 76136 [para:62197.1.1,63497.1.2.2.2,demod:61707,71096,61967,61693,61675,61676,64428,61691,65324,61690,61772,63866] equal(multiply(inverse(X),greatest_lower_bound(identity,X)),multiply(inverse(least_upper_bound(X,identity)),multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))))).
% 161820 [?] ?
% 162284 [?] ?
% 168260 [?] ?
% 170869 [para:161820.1.1,168260.1.2.1.1] equal(X,least_upper_bound(multiply(greatest_lower_bound(Y,greatest_lower_bound(identity,Z)),greatest_lower_bound(U,X)),X)).
% 459702 [?] ?
% 1178900 [para:162284.1.1,459702.1.2.1] equal(identity,greatest_lower_bound(least_upper_bound(X,multiply(least_upper_bound(inverse(Y),Y),least_upper_bound(identity,Z))),identity)).
% 1618078 [?] ?
% 1618175 [?] ?
% 1618400 [?] ?
% 1619165 [para:1618175.1.1,1618078.1.2.2] equal(least_upper_bound(identity,X),multiply(inverse(Y),least_upper_bound(Y,multiply(Y,X)))).
% 1630819 [?] ?
% 2074355 [para:1618400.1.1,1630819.1.1] equal(greatest_lower_bound(multiply(X,Y),identity),multiply(greatest_lower_bound(inverse(Y),X),Y)).
% 2351325 [] equal(X,X).
% 2351326 [] equal(multiply(identity,X),X).
% 2351327 [] equal(multiply(inverse(X),X),identity).
% 2351328 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 2351329 [] equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)).
% 2351330 [] equal(least_upper_bound(X,Y),least_upper_bound(Y,X)).
% 2351331 [] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)).
% 2351332 [] equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)).
% 2351333 [] equal(least_upper_bound(X,X),X).
% 2351334 [] equal(greatest_lower_bound(X,X),X).
% 2351335 [] equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X).
% 2351336 [] equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X).
% 2351337 [] equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))).
% 2351338 [] equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z))).
% 2351339 [] equal(multiply(least_upper_bound(X,Y),Z),least_upper_bound(multiply(X,Z),multiply(Y,Z))).
% 2351340 [] equal(multiply(greatest_lower_bound(X,Y),Z),greatest_lower_bound(multiply(X,Z),multiply(Y,Z))).
% 2351341 [] equal(inverse(identity),identity).
% 2351342 [] equal(inverse(inverse(X)),X).
% 2351343 [] equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))).
% 2351345 [para:2351326.1.1,2351343.1.1.1,demod:2351341] equal(inverse(X),multiply(inverse(X),identity)).
% 2351346 [para:2351342.1.1,2351327.1.1.1] equal(multiply(X,inverse(X)),identity).
% 2351349 [para:2351342.1.1,2351345.1.2.1,demod:2351342] equal(X,multiply(X,identity)).
% 2351352 [para:2351329.1.1,2351335.1.1.2] equal(least_upper_bound(X,greatest_lower_bound(Y,X)),X).
% 2351353 [para:2351335.1.1,2351330.1.1] equal(X,least_upper_bound(greatest_lower_bound(X,Y),X)).
% 2351354 [para:2351336.1.1,2351329.1.1] equal(X,greatest_lower_bound(least_upper_bound(X,Y),X)).
% 2351355 [para:2351330.1.1,2351336.1.1.2] equal(greatest_lower_bound(X,least_upper_bound(Y,X)),X).
% 2351357 [para:2351336.1.1,2351352.1.1.2,demod:2351332] equal(least_upper_bound(X,least_upper_bound(Y,X)),least_upper_bound(X,Y)).
% 2351370 [para:2351353.1.2,2351336.1.1.2,demod:2351331] equal(greatest_lower_bound(X,greatest_lower_bound(Y,X)),greatest_lower_bound(X,Y)).
% 2351372 [para:2351330.1.1,2351354.1.2.1] equal(X,greatest_lower_bound(least_upper_bound(Y,X),X)).
% 2351374 [para:2351353.1.2,2351354.1.2.1] equal(greatest_lower_bound(X,Y),greatest_lower_bound(X,greatest_lower_bound(X,Y))).
% 2351380 [para:2351334.1.1,47892.1.1.1.2.2,demod:2351349] equal(least_upper_bound(greatest_lower_bound(inverse(X),X),identity),identity).
% 2351386 [para:2351342.1.1,2351380.1.1.1.1] equal(least_upper_bound(greatest_lower_bound(X,inverse(X)),identity),identity).
% 2351389 [para:2351380.1.1,2351336.1.1.2,demod:2351331] equal(greatest_lower_bound(inverse(X),greatest_lower_bound(X,identity)),greatest_lower_bound(inverse(X),X)).
% 2351394 [para:2351386.1.1,2351354.1.2.1] equal(greatest_lower_bound(X,inverse(X)),greatest_lower_bound(identity,greatest_lower_bound(X,inverse(X)))).
% 2351400 [para:2351357.1.1,2351355.1.1.2] equal(greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(Y,X)),least_upper_bound(X,Y)).
% 2351406 [para:2351327.1.1,2351328.1.1.1,demod:2351326] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 2351407 [para:2351346.1.1,2351328.1.1.1,demod:2351326] equal(X,multiply(Y,multiply(inverse(Y),X))).
% 2351412 [para:2351329.1.1,73712.1.2.1.1] -equal(multiply(inverse(X),least_upper_bound(X,multiply(X,multiply(a,b)))),multiply(inverse(greatest_lower_bound(inverse(a),b)),b)).
% 2351415 [para:2351331.1.2,2351329.1.1] equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(Z,greatest_lower_bound(X,Y))).
% 2351421 [para:2351331.1.2,2351352.1.1.2] equal(least_upper_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Z,X))),X).
% 2351425 [para:2351354.1.2,2351331.1.2.1] equal(greatest_lower_bound(least_upper_bound(X,Y),greatest_lower_bound(X,Z)),greatest_lower_bound(X,Z)).
% 2351434 [para:2351370.1.1,2351331.1.2.1,demod:2351331] equal(greatest_lower_bound(X,greatest_lower_bound(Y,greatest_lower_bound(X,Z))),greatest_lower_bound(X,greatest_lower_bound(Y,Z))).
% 2351445 [para:2351331.1.2,2351421.1.1.2] equal(least_upper_bound(X,greatest_lower_bound(Y,greatest_lower_bound(Z,greatest_lower_bound(U,X)))),X).
% 2351536 [para:2351354.1.2,2351415.1.1.2] equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,greatest_lower_bound(X,least_upper_bound(Y,Z)))).
% 2351610 [para:2351342.1.1,63389.1.2.2.2.1] equal(greatest_lower_bound(inverse(X),identity),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(identity,inverse(X)))))).
% 2351612 [para:2351343.1.1,63389.1.2.2.2.1,demod:2351328] equal(greatest_lower_bound(multiply(X,Y),identity),multiply(X,multiply(Y,greatest_lower_bound(identity,multiply(inverse(Y),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,Y)))))))).
% 2351615 [para:2351336.1.1,63389.1.2.2.2.2,demod:2351345,2351354] equal(identity,multiply(least_upper_bound(identity,X),greatest_lower_bound(identity,inverse(least_upper_bound(identity,X))))).
% 2351756 [para:2351333.1.1,1178900.1.2.1.2.2,demod:2351349] equal(identity,greatest_lower_bound(least_upper_bound(X,least_upper_bound(inverse(Y),Y)),identity)).
% 2351772 [para:2351333.1.1,2351756.1.2.1] equal(identity,greatest_lower_bound(least_upper_bound(inverse(X),X),identity)).
% 2351788 [para:2351772.1.2,2351329.1.1] equal(identity,greatest_lower_bound(identity,least_upper_bound(inverse(X),X))).
% 2351810 [para:2351334.1.1,170869.1.2.1.1] equal(X,least_upper_bound(multiply(greatest_lower_bound(identity,Y),greatest_lower_bound(Z,X)),X)).
% 2352137 [para:2351389.1.1,2351329.1.1,demod:2351331] equal(greatest_lower_bound(inverse(X),X),greatest_lower_bound(X,greatest_lower_bound(identity,inverse(X)))).
% 2352138 [para:2351354.1.2,2351389.1.1.2,demod:2351425,2352137,2351345,2351334,2351615,2351610] equal(inverse(least_upper_bound(identity,X)),greatest_lower_bound(identity,inverse(least_upper_bound(identity,X)))).
% 2352140 [para:2351389.1.1,2351370.1.1.2,demod:2351374,2351394,2351434,2351331,2352137] equal(greatest_lower_bound(X,inverse(X)),greatest_lower_bound(X,greatest_lower_bound(identity,inverse(X)))).
% 2352220 [para:2351389.1.1,2351445.1.1.2.2,demod:2352140,2352137] equal(least_upper_bound(identity,greatest_lower_bound(X,greatest_lower_bound(Y,inverse(Y)))),identity).
% 2352231 [para:2351415.1.1,2352220.1.1.2] equal(least_upper_bound(identity,greatest_lower_bound(inverse(X),greatest_lower_bound(Y,X))),identity).
% 2352264 [para:2351336.1.1,2352231.1.1.2.2] equal(least_upper_bound(identity,greatest_lower_bound(inverse(least_upper_bound(X,Y)),X)),identity).
% 2352432 [para:63389.1.1,2352264.1.1.2,demod:2351345,2351334,2351346,2352138,2351342] equal(least_upper_bound(identity,inverse(least_upper_bound(identity,X))),identity).
% 2352438 [para:2351330.1.1,2352432.1.1.2.1] equal(least_upper_bound(identity,inverse(least_upper_bound(X,identity))),identity).
% 2353186 [para:2351788.1.2,2351536.1.2.2,demod:2351610] equal(greatest_lower_bound(identity,inverse(X)),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,greatest_lower_bound(identity,inverse(X)))))).
% 2354024 [para:2351334.1.1,2351810.1.2.1.2] equal(X,least_upper_bound(multiply(greatest_lower_bound(identity,Y),X),X)).
% 2354106 [para:2351329.1.1,2354024.1.2.1.1] equal(X,least_upper_bound(multiply(greatest_lower_bound(Y,identity),X),X)).
% 2356811 [para:2351325.1.1,2074355.1.1,demod:2351612] equal(multiply(X,multiply(Y,greatest_lower_bound(identity,multiply(inverse(Y),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,Y))))))),multiply(greatest_lower_bound(inverse(Y),X),Y)).
% 2356815 [para:2351326.1.1,2074355.1.1.1,demod:2353186,2351610] equal(greatest_lower_bound(X,identity),multiply(greatest_lower_bound(identity,inverse(X)),X)).
% 2356816 [para:2074355.1.1,2351329.1.1,demod:2356811] equal(multiply(X,multiply(Y,greatest_lower_bound(identity,multiply(inverse(Y),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,Y))))))),greatest_lower_bound(identity,multiply(X,Y))).
% 2356818 [para:2351336.1.1,2074355.1.2.1,demod:2351327,2356816,2351612] equal(greatest_lower_bound(identity,multiply(least_upper_bound(inverse(X),Y),X)),identity).
% 2356931 [para:2351342.1.1,2356815.1.2.1.2,demod:2353186,2351610] equal(greatest_lower_bound(identity,inverse(X)),multiply(greatest_lower_bound(identity,X),inverse(X))).
% 2356958 [para:2351342.1.1,2356818.1.1.2.1.1] equal(greatest_lower_bound(identity,multiply(least_upper_bound(X,Y),inverse(X))),identity).
% 2357021 [para:2356958.1.1,2351329.1.1,demod:2351345,2356958,2351342,2351612] equal(identity,multiply(least_upper_bound(X,Y),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,inverse(least_upper_bound(X,Y))))))).
% 2357038 [para:2356958.1.1,2352231.1.1.2.2,demod:2351345,2351334,2357021,2351612,2351342,2351343] equal(least_upper_bound(identity,multiply(X,inverse(least_upper_bound(X,Y)))),identity).
% 2357199 [para:2357038.1.1,2351372.1.2.1] equal(multiply(X,inverse(least_upper_bound(X,Y))),greatest_lower_bound(identity,multiply(X,inverse(least_upper_bound(X,Y))))).
% 2357454 [para:2351327.1.1,1619165.1.2.2.2,demod:2351342] equal(least_upper_bound(identity,X),multiply(X,least_upper_bound(inverse(X),identity))).
% 2357465 [para:1619165.1.1,2351372.1.2.1] equal(X,greatest_lower_bound(multiply(inverse(Y),least_upper_bound(Y,multiply(Y,X))),X)).
% 2357472 [para:1619165.1.2,2351406.1.2.2,demod:2351342] equal(least_upper_bound(X,multiply(X,Y)),multiply(X,least_upper_bound(identity,Y))).
% 2357726 [para:2357454.1.2,2351406.1.2.2] equal(least_upper_bound(inverse(X),identity),multiply(inverse(X),least_upper_bound(identity,X))).
% 2357803 [para:2357472.1.1,2351330.1.1] equal(multiply(X,least_upper_bound(identity,Y)),least_upper_bound(multiply(X,Y),X)).
% 2357804 [para:2351330.1.1,2357472.1.2.2] equal(least_upper_bound(X,multiply(X,Y)),multiply(X,least_upper_bound(Y,identity))).
% 2357812 [para:2351406.1.2,2357472.1.1.2] equal(least_upper_bound(inverse(X),Y),multiply(inverse(X),least_upper_bound(identity,multiply(X,Y)))).
% 2357818 [para:2357472.1.1,2351332.1.2.1] equal(least_upper_bound(X,least_upper_bound(multiply(X,Y),Z)),least_upper_bound(multiply(X,least_upper_bound(identity,Y)),Z)).
% 2357852 [para:2352438.1.1,2357472.1.2.2,demod:2351349] equal(least_upper_bound(X,multiply(X,inverse(least_upper_bound(Y,identity)))),X).
% 2358079 [para:2357852.1.1,2351372.1.2.1] equal(multiply(X,inverse(least_upper_bound(Y,identity))),greatest_lower_bound(X,multiply(X,inverse(least_upper_bound(Y,identity))))).
% 2358393 [para:2357804.1.1,2351400.1.1.1,demod:2351400,2351338,2357803] equal(multiply(X,least_upper_bound(Y,identity)),least_upper_bound(X,multiply(X,Y))).
% 2358555 [para:2351327.1.1,2351337.1.2.2] equal(multiply(inverse(X),least_upper_bound(Y,X)),least_upper_bound(multiply(inverse(X),Y),identity)).
% 2358559 [para:2351406.1.2,2351337.1.2.2] equal(multiply(inverse(X),least_upper_bound(Y,multiply(X,Z))),least_upper_bound(multiply(inverse(X),Y),Z)).
% 2358842 [para:2351349.1.2,2351338.1.2.1] equal(multiply(X,greatest_lower_bound(identity,Y)),greatest_lower_bound(X,multiply(X,Y))).
% 2358843 [para:2351349.1.2,2351338.1.2.2] equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(multiply(X,Y),X)).
% 2358845 [para:2351406.1.2,2351338.1.2.2] equal(multiply(inverse(X),greatest_lower_bound(Y,multiply(X,Z))),greatest_lower_bound(multiply(inverse(X),Y),Z)).
% 2358846 [para:2351407.1.2,2351338.1.2.2] equal(multiply(X,greatest_lower_bound(Y,multiply(inverse(X),Z))),greatest_lower_bound(multiply(X,Y),Z)).
% 2359182 [para:2351326.1.1,2351339.1.2.1] equal(multiply(least_upper_bound(identity,X),Y),least_upper_bound(Y,multiply(X,Y))).
% 2359188 [para:2351339.1.2,2351330.1.1,demod:2351339] equal(multiply(least_upper_bound(X,Y),Z),multiply(least_upper_bound(Y,X),Z)).
% 2359314 [para:2359188.1.1,2351407.1.2] equal(X,multiply(least_upper_bound(Y,Z),multiply(inverse(least_upper_bound(Z,Y)),X))).
% 2359591 [para:2351326.1.1,2351340.1.2.1] equal(multiply(greatest_lower_bound(identity,X),Y),greatest_lower_bound(Y,multiply(X,Y))).
% 2359874 [para:76136.1.2,2358393.1.2.2,demod:2357812,2351345,2351327,2351353,2354106,2357818,2358555] equal(inverse(least_upper_bound(X,identity)),multiply(inverse(least_upper_bound(X,identity)),least_upper_bound(identity,multiply(least_upper_bound(X,identity),multiply(inverse(X),greatest_lower_bound(identity,X)))))).
% 2359916 [para:2351327.1.1,2358842.1.2.2,demod:2356931,2351610] equal(multiply(inverse(X),greatest_lower_bound(identity,X)),multiply(inverse(X),greatest_lower_bound(identity,multiply(X,multiply(greatest_lower_bound(identity,X),inverse(X)))))).
% 2359918 [para:2351329.1.1,2358842.1.1.2] equal(multiply(X,greatest_lower_bound(Y,identity)),greatest_lower_bound(X,multiply(X,Y))).
% 2359925 [para:2358842.1.1,2351406.1.2.2] equal(greatest_lower_bound(identity,X),multiply(inverse(Y),greatest_lower_bound(Y,multiply(Y,X)))).
% 2359926 [para:2351406.1.2,2358842.1.2.2] equal(multiply(inverse(X),greatest_lower_bound(identity,multiply(X,Y))),greatest_lower_bound(inverse(X),Y)).
% 2360077 [para:76136.1.2,2358843.1.2.1,demod:2351406,2357199,2358079,2351331,2358846,2351349,2358845] equal(multiply(inverse(least_upper_bound(X,identity)),multiply(inverse(X),multiply(greatest_lower_bound(X,identity),greatest_lower_bound(least_upper_bound(identity,X),multiply(inverse(greatest_lower_bound(X,identity)),X))))),inverse(least_upper_bound(X,identity))).
% 2360241 [para:76136.1.2,2359918.1.2.2,demod:2359926,2360077,2358846,2351349,2358845] equal(inverse(least_upper_bound(X,identity)),multiply(inverse(least_upper_bound(X,identity)),greatest_lower_bound(identity,multiply(least_upper_bound(X,identity),multiply(inverse(X),greatest_lower_bound(identity,X)))))).
% 2360514 [para:2351346.1.1,2359182.1.2.2,demod:2357726] equal(multiply(least_upper_bound(identity,X),inverse(X)),multiply(inverse(X),least_upper_bound(identity,X))).
% 2361112 [para:2351346.1.1,2359591.1.2.2,demod:2359916,2356931,2351610] equal(multiply(greatest_lower_bound(identity,X),inverse(X)),multiply(inverse(X),greatest_lower_bound(identity,X))).
% 2366088 [para:76136.1.2,2357465.1.2.1.2.2,demod:2351346,2359874,2357812,2351342] equal(multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))),greatest_lower_bound(identity,multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))))).
% 2368053 [para:76136.1.2,2359314.1.2.2] equal(multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))),multiply(least_upper_bound(identity,X),multiply(inverse(X),greatest_lower_bound(identity,X)))).
% 2373703 [para:2360514.1.1,2358842.1.2.2,demod:2368053,2361112,2356931] equal(multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))),greatest_lower_bound(least_upper_bound(identity,X),multiply(inverse(X),least_upper_bound(identity,X)))).
% 2381006 [para:76136.1.2,2359925.1.2.2.2,demod:2351346,2360241,2359926,2351342,2366088] equal(multiply(inverse(X),multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X))),identity).
% 2381243 [para:2360514.1.1,2359925.1.2.2.2,demod:2351345,2381006,2373703,2361112,2356931] equal(multiply(inverse(X),greatest_lower_bound(identity,X)),inverse(least_upper_bound(identity,X))).
% 2381570 [para:2381243.1.2,2351342.1.1.1,demod:2351342,2351343] equal(multiply(inverse(greatest_lower_bound(identity,X)),X),least_upper_bound(identity,X)).
% 2381635 [para:2381243.1.2,1619165.1.2.1,demod:2351407,2358559,2351328,2381570] equal(multiply(inverse(greatest_lower_bound(identity,X)),X),multiply(inverse(Y),least_upper_bound(Y,multiply(Y,X)))).
% 2381694 [para:2381243.1.2,2351412.1.1.1,demod:2351342,2351343,2359926,2381635,2351407,2358559,2351328,2381570,cut:2351325] 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 lex ordering for equality
% preferring smaller arities for lex ordering
% using clause demodulation
% seconds given: 60
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 11995
% derived clauses: 11941700
% kept clauses: 491794
% kept size sum: 699435
% kept mid-nuclei: 0
% kept new demods: 377368
% forw unit-subs: 8528080
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 401
% fast unit cutoff: 1
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 563.27
% process. runtime: 557.88
% 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/GRP186-2+eq_r.in")
%
%------------------------------------------------------------------------------