%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP181-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 11:52:04 EDT 2024

% Result   : Unsatisfiable 26.56s 4.20s
% Output   : Refutation 26.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  392
% Syntax   : Number of formulae    : 1372 (  47 unt;   0 def)
%            Number of atoms       : 3866 (1001 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 4621 (2127   ~;2125   |;   0   &)
%                                         ( 369 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :  371 ( 369 usr; 370 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   : 1986 (1986   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f75363,plain,
    $false,
    inference(avatar_sat_refutation,[],[f28,f33,f37,f42,f46,f50,f54,f61,f66,f70,f74,f78,f82,f86,f100,f104,f108,f144,f156,f160,f213,f217,f221,f225,f256,f335,f339,f343,f372,f376,f380,f414,f443,f447,f451,f455,f529,f533,f581,f585,f589,f593,f597,f601,f605,f609,f613,f617,f621,f759,f1116,f1120,f1137,f1154,f1158,f1162,f1167,f1171,f1175,f1179,f1184,f1188,f1192,f1196,f1200,f1204,f1719,f1982,f1986,f1990,f1994,f2329,f2333,f2337,f2341,f2345,f2349,f2353,f2357,f2361,f2402,f2406,f2410,f2414,f2418,f2422,f2426,f4045,f4049,f4053,f4407,f4455,f4614,f4619,f4761,f4766,f4925,f4930,f4935,f5077,f5082,f5235,f5240,f5380,f5385,f5539,f5543,f5548,f5688,f5692,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f6994,f6998,f7002,f7394,f7398,f7402,f7407,f7412,f7416,f7420,f7424,f7428,f7432,f7995,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8984,f8988,f8992,f8996,f9000,f9004,f9008,f9012,f10727,f11910,f11915,f11920,f11924,f11928,f11932,f11937,f11941,f11945,f11950,f11954,f11958,f11962,f11967,f11971,f11975,f11980,f11985,f11990,f11995,f11999,f12003,f12007,f12011,f13809,f15504,f15508,f15551,f15555,f15559,f15563,f15567,f15571,f15575,f15579,f15583,f15587,f15633,f15637,f15641,f15645,f15649,f15653,f15657,f15661,f15665,f15669,f15715,f15719,f15723,f15727,f15731,f15735,f15739,f15743,f15747,f15838,f18212,f19633,f21091,f21095,f21099,f21103,f21107,f21111,f21115,f21119,f21123,f21127,f21131,f21135,f21302,f21306,f21310,f21314,f21318,f21322,f21326,f21330,f21334,f21338,f21507,f21511,f21515,f21519,f21523,f21527,f21531,f21535,f21539,f21543,f21714,f21718,f21722,f21726,f21730,f26695,f30393,f34651,f35083,f35087,f35091,f35095,f35099,f35103,f35107,f35111,f35115,f35119,f35123,f35127,f35131,f35135,f35139,f35143,f35147,f35151,f35155,f35159,f35363,f35367,f35371,f35375,f35379,f35383,f35387,f35391,f35395,f35399,f35577,f35582,f35587,f44518,f44863,f44867,f44871,f44875,f44879,f47018,f47605,f47609,f47613,f47617,f47621,f47625,f47629,f47633,f47637,f47641,f47645,f47649,f47653,f47657,f47661,f47665,f47669,f47673,f47677,f47681,f47685,f47689,f47693,f47697,f47701,f47705,f47709,f47713,f47717,f47721,f47725,f47730,f47734,f47738,f47742,f47746,f47750,f47754,f47758,f47762,f47766,f47770,f47775,f47779,f47783,f47787,f47791,f47795,f47799,f47804,f47808,f47812,f47816,f47820,f47825,f47830,f47834,f47838,f47842,f47847,f47851,f47855,f47859,f47863,f47867,f47871,f47875,f47879,f47883,f47887,f50168,f55262,f60392,f66902,f71474,f75362]) ).

fof(f75362,plain,
    ( spl0_1
    | ~ spl0_3
    | ~ spl0_8
    | ~ spl0_10
    | ~ spl0_33
    | ~ spl0_40
    | ~ spl0_80
    | ~ spl0_116
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f73241,f47822,f35369,f5714,f2359,f583,f441,f68,f58,f35,f25]) ).

fof(f25,plain,
    ( spl0_1
  <=> a = b ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f35,plain,
    ( spl0_3
  <=> ! [X0] : inverse(inverse(X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f58,plain,
    ( spl0_8
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f68,plain,
    ( spl0_10
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f441,plain,
    ( spl0_33
  <=> ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f583,plain,
    ( spl0_40
  <=> ! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f2359,plain,
    ( spl0_80
  <=> ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f5714,plain,
    ( spl0_116
  <=> ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f35369,plain,
    ( spl0_277
  <=> ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),least_upper_bound(identity,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f47822,plain,
    ( spl0_349
  <=> least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f73241,plain,
    ( a = b
    | ~ spl0_3
    | ~ spl0_8
    | ~ spl0_10
    | ~ spl0_33
    | ~ spl0_40
    | ~ spl0_80
    | ~ spl0_116
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f73240,f7621]) ).

fof(f7621,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,X1),least_upper_bound(identity,multiply(inverse(X1),X0))) = X0
    | ~ spl0_3
    | ~ spl0_33
    | ~ spl0_40
    | ~ spl0_80
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f7620,f36]) ).

fof(f36,plain,
    ( ! [X0] : inverse(inverse(X0)) = X0
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f7620,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X0,X1),least_upper_bound(identity,multiply(inverse(X1),X0)))
    | ~ spl0_33
    | ~ spl0_40
    | ~ spl0_80
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f7519,f682]) ).

fof(f682,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1))) = least_upper_bound(identity,multiply(inverse(X1),X0))
    | ~ spl0_33
    | ~ spl0_40 ),
    inference(superposition,[],[f442,f584]) ).

fof(f584,plain,
    ( ! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f583]) ).

fof(f442,plain,
    ( ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(X0))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f441]) ).

fof(f7519,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = multiply(greatest_lower_bound(X0,X1),inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1))))
    | ~ spl0_80
    | ~ spl0_116 ),
    inference(superposition,[],[f5715,f2360]) ).

fof(f2360,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f2359]) ).

fof(f5715,plain,
    ( ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0)))
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f5714]) ).

fof(f73240,plain,
    ( b = multiply(greatest_lower_bound(a,c),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_3
    | ~ spl0_8
    | ~ spl0_10
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f73239,f60]) ).

fof(f60,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f73239,plain,
    ( b = multiply(greatest_lower_bound(b,c),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_3
    | ~ spl0_10
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f73238,f36]) ).

fof(f73238,plain,
    ( b = multiply(greatest_lower_bound(b,inverse(inverse(c))),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_10
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(forward_demodulation,[],[f73155,f69]) ).

fof(f69,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f73155,plain,
    ( b = multiply(greatest_lower_bound(inverse(inverse(c)),b),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_277
    | ~ spl0_349 ),
    inference(superposition,[],[f35370,f47824]) ).

fof(f47824,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a))
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f47822]) ).

fof(f35370,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),least_upper_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f35369]) ).

fof(f71474,plain,
    ( spl0_369
    | ~ spl0_130
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9890,f8787,f7430,f71472]) ).

fof(f71472,plain,
    ( spl0_369
  <=> ! [X0] : b = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X0)),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f7430,plain,
    ( spl0_130
  <=> ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f8787,plain,
    ( spl0_139
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f9890,plain,
    ( ! [X0] : b = greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X0)),b)
    | ~ spl0_130
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f7431]) ).

fof(f7431,plain,
    ( ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X0)))
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f7430]) ).

fof(f8788,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f8787]) ).

fof(f66902,plain,
    ( spl0_368
    | ~ spl0_61
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f8738,f7430,f1182,f66900]) ).

fof(f66900,plain,
    ( spl0_368
  <=> ! [X0] : b = greatest_lower_bound(b,least_upper_bound(X0,least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f1182,plain,
    ( spl0_61
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f8738,plain,
    ( ! [X0] : b = greatest_lower_bound(b,least_upper_bound(X0,least_upper_bound(a,c)))
    | ~ spl0_61
    | ~ spl0_130 ),
    inference(superposition,[],[f7431,f1183]) ).

fof(f1183,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1))
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1182]) ).

fof(f60392,plain,
    ( spl0_367
    | ~ spl0_11
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f8729,f7430,f72,f60390]) ).

fof(f60390,plain,
    ( spl0_367
  <=> ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(X0,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f72,plain,
    ( spl0_11
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f8729,plain,
    ( ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(X0,c)))
    | ~ spl0_11
    | ~ spl0_130 ),
    inference(superposition,[],[f7431,f73]) ).

fof(f73,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f55262,plain,
    ( spl0_366
    | ~ spl0_57
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f8708,f7426,f1165,f55260]) ).

fof(f55260,plain,
    ( spl0_366
  <=> ! [X0] : b = least_upper_bound(b,greatest_lower_bound(X0,greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f1165,plain,
    ( spl0_57
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f7426,plain,
    ( spl0_129
  <=> ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f8708,plain,
    ( ! [X0] : b = least_upper_bound(b,greatest_lower_bound(X0,greatest_lower_bound(a,c)))
    | ~ spl0_57
    | ~ spl0_129 ),
    inference(superposition,[],[f7427,f1166]) ).

fof(f1166,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1))
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1165]) ).

fof(f7427,plain,
    ( ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0)))
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f7426]) ).

fof(f50168,plain,
    ( spl0_365
    | ~ spl0_10
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f8699,f7426,f68,f50166]) ).

fof(f50166,plain,
    ( spl0_365
  <=> ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(X0,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f8699,plain,
    ( ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(X0,c)))
    | ~ spl0_10
    | ~ spl0_129 ),
    inference(superposition,[],[f7427,f69]) ).

fof(f47887,plain,
    ( spl0_364
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_105 ),
    inference(avatar_split_clause,[],[f5469,f5383,f106,f98,f35,f47885]) ).

fof(f47885,plain,
    ( spl0_364
  <=> ! [X2,X0,X1] : inverse(multiply(X2,least_upper_bound(X1,X0))) = inverse(multiply(X2,least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f98,plain,
    ( spl0_15
  <=> ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f106,plain,
    ( spl0_17
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f5383,plain,
    ( spl0_105
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,least_upper_bound(inverse(X2),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f5469,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,least_upper_bound(X1,X0))) = inverse(multiply(X2,least_upper_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_105 ),
    inference(forward_demodulation,[],[f5468,f36]) ).

fof(f5468,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,least_upper_bound(inverse(inverse(X1)),X0))) = inverse(multiply(X2,least_upper_bound(X0,X1)))
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_105 ),
    inference(forward_demodulation,[],[f5396,f99]) ).

fof(f99,plain,
    ( ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f98]) ).

fof(f5396,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,least_upper_bound(inverse(inverse(X1)),X0))) = multiply(inverse(least_upper_bound(X0,X1)),inverse(X2))
    | ~ spl0_17
    | ~ spl0_105 ),
    inference(superposition,[],[f5384,f107]) ).

fof(f107,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f5384,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,least_upper_bound(inverse(X2),X0)))
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f5383]) ).

fof(f47883,plain,
    ( spl0_363
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f5166,f5080,f102,f98,f35,f47881]) ).

fof(f47881,plain,
    ( spl0_363
  <=> ! [X2,X0,X1] : inverse(multiply(X2,greatest_lower_bound(X1,X0))) = inverse(multiply(X2,greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f102,plain,
    ( spl0_16
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f5080,plain,
    ( spl0_101
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,greatest_lower_bound(inverse(X2),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f5166,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,greatest_lower_bound(X1,X0))) = inverse(multiply(X2,greatest_lower_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f5165,f36]) ).

fof(f5165,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,greatest_lower_bound(inverse(inverse(X1)),X0))) = inverse(multiply(X2,greatest_lower_bound(X0,X1)))
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f5093,f99]) ).

fof(f5093,plain,
    ( ! [X2,X0,X1] : inverse(multiply(X2,greatest_lower_bound(inverse(inverse(X1)),X0))) = multiply(inverse(greatest_lower_bound(X0,X1)),inverse(X2))
    | ~ spl0_16
    | ~ spl0_101 ),
    inference(superposition,[],[f5081,f103]) ).

fof(f103,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1))
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f5081,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,greatest_lower_bound(inverse(X2),X0)))
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f5080]) ).

fof(f47879,plain,
    ( spl0_362
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f4860,f4764,f106,f98,f35,f47877]) ).

fof(f47877,plain,
    ( spl0_362
  <=> ! [X2,X0,X1] : inverse(multiply(least_upper_bound(X0,X1),X2)) = inverse(multiply(least_upper_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f4764,plain,
    ( spl0_96
  <=> ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = inverse(multiply(least_upper_bound(inverse(X2),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f4860,plain,
    ( ! [X2,X0,X1] : inverse(multiply(least_upper_bound(X0,X1),X2)) = inverse(multiply(least_upper_bound(X1,X0),X2))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_96 ),
    inference(forward_demodulation,[],[f4859,f36]) ).

fof(f4859,plain,
    ( ! [X2,X0,X1] : inverse(multiply(least_upper_bound(X0,X1),X2)) = inverse(multiply(least_upper_bound(inverse(inverse(X1)),X0),X2))
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_96 ),
    inference(forward_demodulation,[],[f4786,f99]) ).

fof(f4786,plain,
    ( ! [X2,X0,X1] : inverse(multiply(least_upper_bound(inverse(inverse(X1)),X0),X2)) = multiply(inverse(X2),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_17
    | ~ spl0_96 ),
    inference(superposition,[],[f4765,f107]) ).

fof(f4765,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = inverse(multiply(least_upper_bound(inverse(X2),X1),X0))
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f4764]) ).

fof(f47875,plain,
    ( spl0_361
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f4549,f4453,f102,f98,f35,f47873]) ).

fof(f47873,plain,
    ( spl0_361
  <=> ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(X0,X1),X2)) = inverse(multiply(greatest_lower_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f4453,plain,
    ( spl0_92
  <=> ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = inverse(multiply(greatest_lower_bound(inverse(X2),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f4549,plain,
    ( ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(X0,X1),X2)) = inverse(multiply(greatest_lower_bound(X1,X0),X2))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_92 ),
    inference(forward_demodulation,[],[f4548,f36]) ).

fof(f4548,plain,
    ( ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(X0,X1),X2)) = inverse(multiply(greatest_lower_bound(inverse(inverse(X1)),X0),X2))
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_92 ),
    inference(forward_demodulation,[],[f4475,f99]) ).

fof(f4475,plain,
    ( ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(inverse(inverse(X1)),X0),X2)) = multiply(inverse(X2),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_16
    | ~ spl0_92 ),
    inference(superposition,[],[f4454,f103]) ).

fof(f4454,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = inverse(multiply(greatest_lower_bound(inverse(X2),X1),X0))
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f4453]) ).

fof(f47871,plain,
    ( spl0_360
    | ~ spl0_16
    | ~ spl0_34
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f4373,f4051,f445,f102,f47869]) ).

fof(f47869,plain,
    ( spl0_360
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X1,greatest_lower_bound(X0,identity))) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f445,plain,
    ( spl0_34
  <=> ! [X0] : inverse(greatest_lower_bound(X0,identity)) = least_upper_bound(inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f4051,plain,
    ( spl0_90
  <=> ! [X2,X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f4373,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,greatest_lower_bound(X0,identity))) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),identity)
    | ~ spl0_16
    | ~ spl0_34
    | ~ spl0_90 ),
    inference(forward_demodulation,[],[f4307,f103]) ).

fof(f4307,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(X1,X0)),identity) = least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_34
    | ~ spl0_90 ),
    inference(superposition,[],[f4052,f446]) ).

fof(f446,plain,
    ( ! [X0] : inverse(greatest_lower_bound(X0,identity)) = least_upper_bound(inverse(X0),identity)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f445]) ).

fof(f4052,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2)
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f4051]) ).

fof(f47867,plain,
    ( spl0_359
    | ~ spl0_3
    | ~ spl0_17
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f8396,f7418,f106,f35,f47865]) ).

fof(f47865,plain,
    ( spl0_359
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = inverse(inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f7418,plain,
    ( spl0_127
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f8396,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = inverse(inverse(least_upper_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_17
    | ~ spl0_127 ),
    inference(forward_demodulation,[],[f8395,f36]) ).

fof(f8395,plain,
    ( ! [X0,X1] : inverse(inverse(least_upper_bound(X0,X1))) = inverse(inverse(least_upper_bound(X1,X0)))
    | ~ spl0_17
    | ~ spl0_127 ),
    inference(forward_demodulation,[],[f8223,f107]) ).

fof(f8223,plain,
    ( ! [X0,X1] : inverse(inverse(least_upper_bound(X0,X1))) = inverse(greatest_lower_bound(inverse(X1),inverse(X0)))
    | ~ spl0_17
    | ~ spl0_127 ),
    inference(superposition,[],[f7419,f107]) ).

fof(f7419,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0))
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f7418]) ).

fof(f47863,plain,
    ( spl0_358
    | ~ spl0_17
    | ~ spl0_36
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f4255,f4047,f453,f106,f47861]) ).

fof(f47861,plain,
    ( spl0_358
  <=> ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(X1,X0)),identity) = inverse(least_upper_bound(X1,least_upper_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f453,plain,
    ( spl0_36
  <=> ! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f4047,plain,
    ( spl0_89
  <=> ! [X2,X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f4255,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(X1,X0)),identity) = inverse(least_upper_bound(X1,least_upper_bound(X0,identity)))
    | ~ spl0_17
    | ~ spl0_36
    | ~ spl0_89 ),
    inference(forward_demodulation,[],[f4189,f107]) ).

fof(f4189,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(X1,X0)),identity) = greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X0,identity)))
    | ~ spl0_36
    | ~ spl0_89 ),
    inference(superposition,[],[f4048,f454]) ).

fof(f454,plain,
    ( ! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(inverse(X0),identity)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f453]) ).

fof(f4048,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2)
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f4047]) ).

fof(f47859,plain,
    ( spl0_357
    | ~ spl0_32
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f4074,f4043,f412,f47857]) ).

fof(f47857,plain,
    ( spl0_357
  <=> ! [X2,X0,X1] : multiply(inverse(X2),X1) = multiply(inverse(multiply(X0,X2)),multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f412,plain,
    ( spl0_32
  <=> ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f4043,plain,
    ( spl0_88
  <=> ! [X2,X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X2)) = multiply(inverse(multiply(X1,X0)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f4074,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X2),X1) = multiply(inverse(multiply(X0,X2)),multiply(X0,X1))
    | ~ spl0_32
    | ~ spl0_88 ),
    inference(superposition,[],[f4044,f413]) ).

fof(f413,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f412]) ).

fof(f4044,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X2)) = multiply(inverse(multiply(X1,X0)),X2)
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f4043]) ).

fof(f47855,plain,
    ( spl0_356
    | ~ spl0_8
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f3979,f2424,f58,f47853]) ).

fof(f47853,plain,
    ( spl0_356
  <=> ! [X0] : multiply(b,X0) = least_upper_bound(multiply(b,X0),multiply(greatest_lower_bound(a,c),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f2424,plain,
    ( spl0_87
  <=> ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f3979,plain,
    ( ! [X0] : multiply(b,X0) = least_upper_bound(multiply(b,X0),multiply(greatest_lower_bound(a,c),X0))
    | ~ spl0_8
    | ~ spl0_87 ),
    inference(superposition,[],[f2425,f60]) ).

fof(f2425,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f2424]) ).

fof(f47851,plain,
    ( spl0_355
    | ~ spl0_9
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f3778,f2416,f63,f47849]) ).

fof(f47849,plain,
    ( spl0_355
  <=> ! [X0] : multiply(b,X0) = greatest_lower_bound(multiply(b,X0),multiply(least_upper_bound(a,c),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f63,plain,
    ( spl0_9
  <=> least_upper_bound(a,c) = least_upper_bound(b,c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f2416,plain,
    ( spl0_85
  <=> ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f3778,plain,
    ( ! [X0] : multiply(b,X0) = greatest_lower_bound(multiply(b,X0),multiply(least_upper_bound(a,c),X0))
    | ~ spl0_9
    | ~ spl0_85 ),
    inference(superposition,[],[f2417,f65]) ).

fof(f65,plain,
    ( least_upper_bound(a,c) = least_upper_bound(b,c)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f2417,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f2416]) ).

fof(f47847,plain,
    ( spl0_354
    | ~ spl0_8
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f3576,f2408,f58,f47844]) ).

fof(f47844,plain,
    ( spl0_354
  <=> greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f2408,plain,
    ( spl0_83
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f3576,plain,
    ( greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a))
    | ~ spl0_8
    | ~ spl0_83 ),
    inference(forward_demodulation,[],[f3528,f2409]) ).

fof(f2409,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0))
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f2408]) ).

fof(f3528,plain,
    ( greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),greatest_lower_bound(a,c))
    | ~ spl0_8
    | ~ spl0_83 ),
    inference(superposition,[],[f2409,f60]) ).

fof(f47842,plain,
    ( spl0_353
    | ~ spl0_8
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f3443,f2404,f58,f47840]) ).

fof(f47840,plain,
    ( spl0_353
  <=> ! [X0] : multiply(X0,b) = least_upper_bound(multiply(X0,b),multiply(X0,greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f2404,plain,
    ( spl0_82
  <=> ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f3443,plain,
    ( ! [X0] : multiply(X0,b) = least_upper_bound(multiply(X0,b),multiply(X0,greatest_lower_bound(a,c)))
    | ~ spl0_8
    | ~ spl0_82 ),
    inference(superposition,[],[f2405,f60]) ).

fof(f2405,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f2404]) ).

fof(f47838,plain,
    ( spl0_352
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_35
    | ~ spl0_39
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f3286,f2359,f579,f449,f106,f98,f35,f47836]) ).

fof(f47836,plain,
    ( spl0_352
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f449,plain,
    ( spl0_35
  <=> ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f579,plain,
    ( spl0_39
  <=> ! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f3286,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(least_upper_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_35
    | ~ spl0_39
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3285,f643]) ).

fof(f643,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,inverse(X0))) = inverse(least_upper_bound(identity,multiply(X0,inverse(X1))))
    | ~ spl0_35
    | ~ spl0_39 ),
    inference(superposition,[],[f450,f580]) ).

fof(f580,plain,
    ( ! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1))
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f450,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f449]) ).

fof(f3285,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(identity,multiply(X1,inverse(X0)))) = multiply(X0,inverse(least_upper_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_35
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3284,f36]) ).

fof(f3284,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(identity,multiply(X1,inverse(X0)))) = multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_35
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3283,f450]) ).

fof(f3283,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1))) = greatest_lower_bound(identity,inverse(multiply(X1,inverse(X0))))
    | ~ spl0_15
    | ~ spl0_17
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3230,f99]) ).

fof(f3230,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1))) = greatest_lower_bound(identity,multiply(inverse(inverse(X0)),inverse(X1)))
    | ~ spl0_17
    | ~ spl0_80 ),
    inference(superposition,[],[f2360,f107]) ).

fof(f47834,plain,
    ( spl0_351
    | ~ spl0_3
    | ~ spl0_48
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f3282,f2359,f615,f35,f47832]) ).

fof(f47832,plain,
    ( spl0_351
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(least_upper_bound(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f615,plain,
    ( spl0_48
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f3282,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(least_upper_bound(X1,X0)))
    | ~ spl0_3
    | ~ spl0_48
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3229,f36]) ).

fof(f3229,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(inverse(X0)),inverse(X1))) = multiply(inverse(inverse(X0)),inverse(least_upper_bound(X1,X0)))
    | ~ spl0_48
    | ~ spl0_80 ),
    inference(superposition,[],[f2360,f616]) ).

fof(f616,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0))
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f615]) ).

fof(f47830,plain,
    ( spl0_350
    | ~ spl0_8
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f3236,f2359,f58,f47827]) ).

fof(f47827,plain,
    ( spl0_350
  <=> multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f3236,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c))
    | ~ spl0_8
    | ~ spl0_80 ),
    inference(superposition,[],[f2360,f60]) ).

fof(f47825,plain,
    ( spl0_349
    | ~ spl0_9
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f3186,f2355,f63,f47822]) ).

fof(f2355,plain,
    ( spl0_79
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f3186,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a))
    | ~ spl0_9
    | ~ spl0_79 ),
    inference(forward_demodulation,[],[f3146,f2356]) ).

fof(f2356,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0))
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f2355]) ).

fof(f3146,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_79 ),
    inference(superposition,[],[f2356,f65]) ).

fof(f47820,plain,
    ( spl0_348
    | ~ spl0_3
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f8259,f7418,f35,f47818]) ).

fof(f47818,plain,
    ( spl0_348
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = inverse(inverse(greatest_lower_bound(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f8259,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = inverse(inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_3
    | ~ spl0_127 ),
    inference(superposition,[],[f36,f7419]) ).

fof(f47816,plain,
    ( spl0_347
    | ~ spl0_9
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f3073,f2351,f63,f47814]) ).

fof(f47814,plain,
    ( spl0_347
  <=> ! [X0] : multiply(X0,b) = greatest_lower_bound(multiply(X0,b),multiply(X0,least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f2351,plain,
    ( spl0_78
  <=> ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f3073,plain,
    ( ! [X0] : multiply(X0,b) = greatest_lower_bound(multiply(X0,b),multiply(X0,least_upper_bound(a,c)))
    | ~ spl0_9
    | ~ spl0_78 ),
    inference(superposition,[],[f2352,f65]) ).

fof(f2352,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f2351]) ).

fof(f47812,plain,
    ( spl0_346
    | ~ spl0_3
    | ~ spl0_16
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2932,f2343,f102,f35,f47810]) ).

fof(f47810,plain,
    ( spl0_346
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f2343,plain,
    ( spl0_76
  <=> ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f2932,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_16
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2890,f36]) ).

fof(f2890,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(inverse(X0)),inverse(X1))) = multiply(inverse(inverse(X0)),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_16
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f103]) ).

fof(f2344,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f2343]) ).

fof(f47808,plain,
    ( spl0_345
    | ~ spl0_3
    | ~ spl0_44
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2931,f2343,f599,f35,f47806]) ).

fof(f47806,plain,
    ( spl0_345
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(greatest_lower_bound(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f599,plain,
    ( spl0_44
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f2931,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X0,inverse(X1))) = multiply(X0,inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_3
    | ~ spl0_44
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2889,f36]) ).

fof(f2889,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(inverse(X0)),inverse(X1))) = multiply(inverse(inverse(X0)),inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_44
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f600]) ).

fof(f600,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0))
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f47804,plain,
    ( spl0_344
    | ~ spl0_9
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2896,f2343,f63,f47801]) ).

fof(f47801,plain,
    ( spl0_344
  <=> least_upper_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f2896,plain,
    ( least_upper_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f65]) ).

fof(f47799,plain,
    ( spl0_343
    | ~ spl0_9
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f2807,f2339,f63,f47797]) ).

fof(f47797,plain,
    ( spl0_343
  <=> ! [X0] : least_upper_bound(X0,b) = greatest_lower_bound(least_upper_bound(X0,b),least_upper_bound(X0,least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f2339,plain,
    ( spl0_75
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,least_upper_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f2807,plain,
    ( ! [X0] : least_upper_bound(X0,b) = greatest_lower_bound(least_upper_bound(X0,b),least_upper_bound(X0,least_upper_bound(a,c)))
    | ~ spl0_9
    | ~ spl0_75 ),
    inference(superposition,[],[f2340,f65]) ).

fof(f2340,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,least_upper_bound(X1,X2)))
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f2339]) ).

fof(f47795,plain,
    ( spl0_342
    | ~ spl0_9
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f2648,f2335,f63,f47793]) ).

fof(f47793,plain,
    ( spl0_342
  <=> ! [X0] : least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f2335,plain,
    ( spl0_74
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f2648,plain,
    ( ! [X0] : least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(least_upper_bound(a,c),X0)))
    | ~ spl0_9
    | ~ spl0_74 ),
    inference(superposition,[],[f2336,f65]) ).

fof(f2336,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X0,X1),X2)))
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f2335]) ).

fof(f47791,plain,
    ( spl0_341
    | ~ spl0_8
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f2572,f2331,f58,f47789]) ).

fof(f47789,plain,
    ( spl0_341
  <=> ! [X0] : greatest_lower_bound(X0,b) = least_upper_bound(greatest_lower_bound(X0,b),greatest_lower_bound(X0,greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f2331,plain,
    ( spl0_73
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f2572,plain,
    ( ! [X0] : greatest_lower_bound(X0,b) = least_upper_bound(greatest_lower_bound(X0,b),greatest_lower_bound(X0,greatest_lower_bound(a,c)))
    | ~ spl0_8
    | ~ spl0_73 ),
    inference(superposition,[],[f2332,f60]) ).

fof(f2332,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f2331]) ).

fof(f47787,plain,
    ( spl0_340
    | ~ spl0_8
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f2449,f2327,f58,f47785]) ).

fof(f47785,plain,
    ( spl0_340
  <=> ! [X0] : greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,c),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f2327,plain,
    ( spl0_72
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f2449,plain,
    ( ! [X0] : greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(c,least_upper_bound(greatest_lower_bound(a,c),X0)))
    | ~ spl0_8
    | ~ spl0_72 ),
    inference(superposition,[],[f2328,f60]) ).

fof(f2328,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X0,X1),X2)))
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f2327]) ).

fof(f47783,plain,
    ( spl0_339
    | ~ spl0_17
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f2149,f1988,f106,f47781]) ).

fof(f47781,plain,
    ( spl0_339
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(least_upper_bound(X0,X1)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f1988,plain,
    ( spl0_70
  <=> ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f2149,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(least_upper_bound(X0,X1)),X0)
    | ~ spl0_17
    | ~ spl0_70 ),
    inference(superposition,[],[f1989,f107]) ).

fof(f1989,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f1988]) ).

fof(f47779,plain,
    ( spl0_338
    | ~ spl0_48
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f2148,f1988,f615,f47777]) ).

fof(f47777,plain,
    ( spl0_338
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(least_upper_bound(X1,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f2148,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(least_upper_bound(X1,X0)),X0)
    | ~ spl0_48
    | ~ spl0_70 ),
    inference(superposition,[],[f1989,f616]) ).

fof(f47775,plain,
    ( spl0_337
    | ~ spl0_54
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f7465,f5536,f1152,f47772]) ).

fof(f47772,plain,
    ( spl0_337
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(c,greatest_lower_bound(a,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f1152,plain,
    ( spl0_54
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f5536,plain,
    ( spl0_106
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f7465,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(c,greatest_lower_bound(a,b))
    | ~ spl0_54
    | ~ spl0_106 ),
    inference(superposition,[],[f5538,f1153]) ).

fof(f1153,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2)
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f1152]) ).

fof(f5538,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,c),b)
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f5536]) ).

fof(f47770,plain,
    ( spl0_336
    | ~ spl0_16
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f2005,f1980,f102,f47768]) ).

fof(f47768,plain,
    ( spl0_336
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X0,X1)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f1980,plain,
    ( spl0_68
  <=> ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f2005,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X0,X1)),X0)
    | ~ spl0_16
    | ~ spl0_68 ),
    inference(superposition,[],[f1981,f103]) ).

fof(f1981,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1980]) ).

fof(f47766,plain,
    ( spl0_335
    | ~ spl0_44
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f2004,f1980,f599,f47764]) ).

fof(f47764,plain,
    ( spl0_335
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X1,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f2004,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X1,X0)),X0)
    | ~ spl0_44
    | ~ spl0_68 ),
    inference(superposition,[],[f1981,f600]) ).

fof(f47762,plain,
    ( spl0_334
    | ~ spl0_36
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1881,f1202,f453,f47760]) ).

fof(f47760,plain,
    ( spl0_334
  <=> ! [X0,X1] : greatest_lower_bound(multiply(inverse(X0),X1),X1) = multiply(inverse(least_upper_bound(X0,identity)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f1202,plain,
    ( spl0_66
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1881,plain,
    ( ! [X0,X1] : greatest_lower_bound(multiply(inverse(X0),X1),X1) = multiply(inverse(least_upper_bound(X0,identity)),X1)
    | ~ spl0_36
    | ~ spl0_66 ),
    inference(superposition,[],[f1203,f454]) ).

fof(f1203,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1202]) ).

fof(f47758,plain,
    ( spl0_333
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1877,f1198,f587,f579,f47756]) ).

fof(f47756,plain,
    ( spl0_333
  <=> ! [X0,X1] : multiply(X0,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X0,multiply(X0,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f587,plain,
    ( spl0_41
  <=> ! [X0,X1] : inverse(greatest_lower_bound(inverse(X0),X1)) = least_upper_bound(X0,inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1198,plain,
    ( spl0_65
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f1877,plain,
    ( ! [X0,X1] : multiply(X0,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X0,multiply(X0,inverse(X1)))
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1876,f580]) ).

fof(f1876,plain,
    ( ! [X0,X1] : least_upper_bound(X0,inverse(multiply(X1,inverse(X0)))) = multiply(X0,inverse(greatest_lower_bound(identity,X1)))
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1851,f580]) ).

fof(f1851,plain,
    ( ! [X0,X1] : least_upper_bound(X0,inverse(multiply(X1,inverse(X0)))) = inverse(multiply(greatest_lower_bound(identity,X1),inverse(X0)))
    | ~ spl0_41
    | ~ spl0_65 ),
    inference(superposition,[],[f588,f1199]) ).

fof(f1199,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f1198]) ).

fof(f588,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(inverse(X0),X1)) = least_upper_bound(X0,inverse(X1))
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f47754,plain,
    ( spl0_332
    | ~ spl0_35
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1804,f1198,f449,f47752]) ).

fof(f47752,plain,
    ( spl0_332
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(inverse(X0),X1)) = multiply(inverse(least_upper_bound(identity,X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1804,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(inverse(X0),X1)) = multiply(inverse(least_upper_bound(identity,X0)),X1)
    | ~ spl0_35
    | ~ spl0_65 ),
    inference(superposition,[],[f1199,f450]) ).

fof(f47750,plain,
    ( spl0_331
    | ~ spl0_34
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1723,f1194,f445,f47748]) ).

fof(f47748,plain,
    ( spl0_331
  <=> ! [X0,X1] : least_upper_bound(multiply(inverse(X0),X1),X1) = multiply(inverse(greatest_lower_bound(X0,identity)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f1194,plain,
    ( spl0_64
  <=> ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1723,plain,
    ( ! [X0,X1] : least_upper_bound(multiply(inverse(X0),X1),X1) = multiply(inverse(greatest_lower_bound(X0,identity)),X1)
    | ~ spl0_34
    | ~ spl0_64 ),
    inference(superposition,[],[f1195,f446]) ).

fof(f1195,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1194]) ).

fof(f47746,plain,
    ( spl0_330
    | ~ spl0_39
    | ~ spl0_46
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1715,f1186,f607,f579,f47744]) ).

fof(f47744,plain,
    ( spl0_330
  <=> ! [X0,X1] : multiply(X0,inverse(least_upper_bound(identity,X1))) = greatest_lower_bound(X0,multiply(X0,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f607,plain,
    ( spl0_46
  <=> ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f1186,plain,
    ( spl0_62
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1715,plain,
    ( ! [X0,X1] : multiply(X0,inverse(least_upper_bound(identity,X1))) = greatest_lower_bound(X0,multiply(X0,inverse(X1)))
    | ~ spl0_39
    | ~ spl0_46
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1714,f580]) ).

fof(f1714,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(multiply(X1,inverse(X0)))) = multiply(X0,inverse(least_upper_bound(identity,X1)))
    | ~ spl0_39
    | ~ spl0_46
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1698,f580]) ).

fof(f1698,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(multiply(X1,inverse(X0)))) = inverse(multiply(least_upper_bound(identity,X1),inverse(X0)))
    | ~ spl0_46
    | ~ spl0_62 ),
    inference(superposition,[],[f608,f1187]) ).

fof(f1187,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1186]) ).

fof(f608,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(inverse(X0),X1))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f47742,plain,
    ( spl0_329
    | ~ spl0_33
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1655,f1186,f441,f47740]) ).

fof(f47740,plain,
    ( spl0_329
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(inverse(X0),X1)) = multiply(inverse(greatest_lower_bound(identity,X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f1655,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(inverse(X0),X1)) = multiply(inverse(greatest_lower_bound(identity,X0)),X1)
    | ~ spl0_33
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f442]) ).

fof(f47738,plain,
    ( spl0_328
    | ~ spl0_34
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1579,f1182,f445,f47736]) ).

fof(f47736,plain,
    ( spl0_328
  <=> ! [X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(identity,X1)) = least_upper_bound(X1,inverse(greatest_lower_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f1579,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(identity,X1)) = least_upper_bound(X1,inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_34
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f446]) ).

fof(f47734,plain,
    ( spl0_327
    | ~ spl0_33
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1573,f1182,f441,f47732]) ).

fof(f47732,plain,
    ( spl0_327
  <=> ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(X1,inverse(greatest_lower_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f1573,plain,
    ( ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(X1,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_33
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f442]) ).

fof(f47730,plain,
    ( spl0_326
    | ~ spl0_58
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f7433,f4932,f1169,f47727]) ).

fof(f47727,plain,
    ( spl0_326
  <=> least_upper_bound(a,c) = least_upper_bound(c,least_upper_bound(a,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1169,plain,
    ( spl0_58
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f4932,plain,
    ( spl0_99
  <=> least_upper_bound(a,c) = least_upper_bound(least_upper_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f7433,plain,
    ( least_upper_bound(a,c) = least_upper_bound(c,least_upper_bound(a,b))
    | ~ spl0_58
    | ~ spl0_99 ),
    inference(superposition,[],[f4934,f1170]) ).

fof(f1170,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f1169]) ).

fof(f4934,plain,
    ( least_upper_bound(a,c) = least_upper_bound(least_upper_bound(a,c),b)
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f4932]) ).

fof(f47725,plain,
    ( spl0_325
    | ~ spl0_34
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1549,f1182,f445,f47723]) ).

fof(f47723,plain,
    ( spl0_325
  <=> ! [X0,X1] : least_upper_bound(X1,inverse(greatest_lower_bound(X0,identity))) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f1549,plain,
    ( ! [X0,X1] : least_upper_bound(X1,inverse(greatest_lower_bound(X0,identity))) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0)))
    | ~ spl0_34
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f446]) ).

fof(f47721,plain,
    ( spl0_324
    | ~ spl0_33
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1543,f1182,f441,f47719]) ).

fof(f47719,plain,
    ( spl0_324
  <=> ! [X0,X1] : least_upper_bound(X1,inverse(greatest_lower_bound(identity,X0))) = least_upper_bound(inverse(X0),least_upper_bound(X1,identity)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1543,plain,
    ( ! [X0,X1] : least_upper_bound(X1,inverse(greatest_lower_bound(identity,X0))) = least_upper_bound(inverse(X0),least_upper_bound(X1,identity))
    | ~ spl0_33
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f442]) ).

fof(f47717,plain,
    ( spl0_323
    | ~ spl0_51
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f1502,f1173,f1114,f47715]) ).

fof(f47715,plain,
    ( spl0_323
  <=> ! [X0,X1] : least_upper_bound(b,X1) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f1114,plain,
    ( spl0_51
  <=> ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(a,greatest_lower_bound(c,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1173,plain,
    ( spl0_59
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1502,plain,
    ( ! [X0,X1] : least_upper_bound(b,X1) = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,greatest_lower_bound(c,X0)),X1))
    | ~ spl0_51
    | ~ spl0_59 ),
    inference(superposition,[],[f1174,f1115]) ).

fof(f1115,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(a,greatest_lower_bound(c,X0))
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f1114]) ).

fof(f1174,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f1173]) ).

fof(f47713,plain,
    ( spl0_322
    | ~ spl0_33
    | ~ spl0_58
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1466,f1182,f1169,f441,f47711]) ).

fof(f47711,plain,
    ( spl0_322
  <=> ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f1466,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0)))
    | ~ spl0_33
    | ~ spl0_58
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f1432,f1183]) ).

fof(f1432,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1) = least_upper_bound(inverse(X0),least_upper_bound(identity,X1))
    | ~ spl0_33
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f442]) ).

fof(f47709,plain,
    ( spl0_321
    | ~ spl0_34
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1438,f1169,f445,f47707]) ).

fof(f47707,plain,
    ( spl0_321
  <=> ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,identity)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f1438,plain,
    ( ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,identity)),X1)
    | ~ spl0_34
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f446]) ).

fof(f47705,plain,
    ( spl0_320
    | ~ spl0_36
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1352,f1165,f453,f47703]) ).

fof(f47703,plain,
    ( spl0_320
  <=> ! [X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(identity,X1)) = greatest_lower_bound(X1,inverse(least_upper_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f1352,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(identity,X1)) = greatest_lower_bound(X1,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_36
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f454]) ).

fof(f47701,plain,
    ( spl0_319
    | ~ spl0_35
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1346,f1165,f449,f47699]) ).

fof(f47699,plain,
    ( spl0_319
  <=> ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(X1,inverse(least_upper_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f1346,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(X1,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_35
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f450]) ).

fof(f47697,plain,
    ( spl0_318
    | ~ spl0_36
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1322,f1165,f453,f47695]) ).

fof(f47695,plain,
    ( spl0_318
  <=> ! [X0,X1] : greatest_lower_bound(X1,inverse(least_upper_bound(X0,identity))) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f1322,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,inverse(least_upper_bound(X0,identity))) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0)))
    | ~ spl0_36
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f454]) ).

fof(f47693,plain,
    ( spl0_317
    | ~ spl0_35
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1316,f1165,f449,f47691]) ).

fof(f47691,plain,
    ( spl0_317
  <=> ! [X0,X1] : greatest_lower_bound(X1,inverse(least_upper_bound(identity,X0))) = greatest_lower_bound(inverse(X0),greatest_lower_bound(X1,identity)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f1316,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,inverse(least_upper_bound(identity,X0))) = greatest_lower_bound(inverse(X0),greatest_lower_bound(X1,identity))
    | ~ spl0_35
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f450]) ).

fof(f47689,plain,
    ( spl0_316
    | ~ spl0_52
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1276,f1156,f1118,f47687]) ).

fof(f47687,plain,
    ( spl0_316
  <=> ! [X0,X1] : greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f1118,plain,
    ( spl0_52
  <=> ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(a,least_upper_bound(c,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1156,plain,
    ( spl0_55
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f1276,plain,
    ( ! [X0,X1] : greatest_lower_bound(b,X1) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,least_upper_bound(c,X0)),X1))
    | ~ spl0_52
    | ~ spl0_55 ),
    inference(superposition,[],[f1157,f1119]) ).

fof(f1119,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(a,least_upper_bound(c,X0))
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1118]) ).

fof(f1157,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1156]) ).

fof(f47685,plain,
    ( spl0_315
    | ~ spl0_30
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f3921,f2420,f374,f47683]) ).

fof(f47683,plain,
    ( spl0_315
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(greatest_lower_bound(X0,X1),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f374,plain,
    ( spl0_30
  <=> ! [X0] : multiply(X0,identity) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f2420,plain,
    ( spl0_86
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f3921,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(greatest_lower_bound(X0,X1),identity)
    | ~ spl0_30
    | ~ spl0_86 ),
    inference(forward_demodulation,[],[f3867,f375]) ).

fof(f375,plain,
    ( ! [X0] : multiply(X0,identity) = X0
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f374]) ).

fof(f3867,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,X1),identity) = greatest_lower_bound(multiply(X1,identity),X0)
    | ~ spl0_30
    | ~ spl0_86 ),
    inference(superposition,[],[f2421,f375]) ).

fof(f2421,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f2420]) ).

fof(f47681,plain,
    ( spl0_314
    | ~ spl0_35
    | ~ spl0_54
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1244,f1165,f1152,f449,f47679]) ).

fof(f47679,plain,
    ( spl0_314
  <=> ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f1244,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0)))
    | ~ spl0_35
    | ~ spl0_54
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1211,f1166]) ).

fof(f1211,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1) = greatest_lower_bound(inverse(X0),greatest_lower_bound(identity,X1))
    | ~ spl0_35
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f450]) ).

fof(f47677,plain,
    ( spl0_313
    | ~ spl0_36
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1217,f1152,f453,f47675]) ).

fof(f47675,plain,
    ( spl0_313
  <=> ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,identity)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f1217,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,identity)),X1)
    | ~ spl0_36
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f454]) ).

fof(f47673,plain,
    ( spl0_312
    | ~ spl0_38
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1147,f1118,f531,f47671]) ).

fof(f47671,plain,
    ( spl0_312
  <=> ! [X0] : least_upper_bound(a,least_upper_bound(c,X0)) = least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f531,plain,
    ( spl0_38
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1147,plain,
    ( ! [X0] : least_upper_bound(a,least_upper_bound(c,X0)) = least_upper_bound(b,least_upper_bound(a,least_upper_bound(c,X0)))
    | ~ spl0_38
    | ~ spl0_52 ),
    inference(superposition,[],[f532,f1119]) ).

fof(f532,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f531]) ).

fof(f47669,plain,
    ( spl0_311
    | ~ spl0_37
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f1130,f1114,f527,f47667]) ).

fof(f47667,plain,
    ( spl0_311
  <=> ! [X0] : greatest_lower_bound(a,greatest_lower_bound(c,X0)) = greatest_lower_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f527,plain,
    ( spl0_37
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1130,plain,
    ( ! [X0] : greatest_lower_bound(a,greatest_lower_bound(c,X0)) = greatest_lower_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0)))
    | ~ spl0_37
    | ~ spl0_51 ),
    inference(superposition,[],[f528,f1115]) ).

fof(f528,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f527]) ).

fof(f47665,plain,
    ( spl0_310
    | ~ spl0_32
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f974,f611,f412,f47663]) ).

fof(f47663,plain,
    ( spl0_310
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),multiply(least_upper_bound(X0,inverse(X1)),X2)) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f611,plain,
    ( spl0_47
  <=> ! [X0,X1] : inverse(least_upper_bound(X1,inverse(X0))) = greatest_lower_bound(inverse(X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f974,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),multiply(least_upper_bound(X0,inverse(X1)),X2)) = X2
    | ~ spl0_32
    | ~ spl0_47 ),
    inference(superposition,[],[f413,f612]) ).

fof(f612,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,inverse(X0))) = greatest_lower_bound(inverse(X1),X0)
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f611]) ).

fof(f47661,plain,
    ( spl0_309
    | ~ spl0_20
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f944,f607,f453,f158,f47659]) ).

fof(f47659,plain,
    ( spl0_309
  <=> ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,inverse(X1)),identity) = greatest_lower_bound(X0,inverse(least_upper_bound(X1,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f158,plain,
    ( spl0_20
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f944,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,inverse(X1)),identity) = greatest_lower_bound(X0,inverse(least_upper_bound(X1,identity)))
    | ~ spl0_20
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f943,f608]) ).

fof(f943,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,inverse(X1)),identity) = inverse(least_upper_bound(inverse(X0),least_upper_bound(X1,identity)))
    | ~ spl0_20
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f917,f159]) ).

fof(f159,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f158]) ).

fof(f917,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,inverse(X1)),identity) = inverse(least_upper_bound(least_upper_bound(inverse(X0),X1),identity))
    | ~ spl0_36
    | ~ spl0_46 ),
    inference(superposition,[],[f454,f608]) ).

fof(f47657,plain,
    ( spl0_308
    | ~ spl0_32
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f913,f607,f412,f47655]) ).

fof(f47655,plain,
    ( spl0_308
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),multiply(least_upper_bound(inverse(X0),X1),X2)) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f913,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),multiply(least_upper_bound(inverse(X0),X1),X2)) = X2
    | ~ spl0_32
    | ~ spl0_46 ),
    inference(superposition,[],[f413,f608]) ).

fof(f47653,plain,
    ( spl0_307
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f784,f595,f412,f47651]) ).

fof(f47651,plain,
    ( spl0_307
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X1),multiply(greatest_lower_bound(X0,inverse(X1)),X2)) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f595,plain,
    ( spl0_43
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X1,inverse(X0))) = least_upper_bound(inverse(X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f784,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X1),multiply(greatest_lower_bound(X0,inverse(X1)),X2)) = X2
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f413,f596]) ).

fof(f596,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,inverse(X0))) = least_upper_bound(inverse(X1),X0)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f47649,plain,
    ( spl0_306
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f733,f587,f412,f47647]) ).

fof(f47647,plain,
    ( spl0_306
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),multiply(greatest_lower_bound(inverse(X0),X1),X2)) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f733,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),multiply(greatest_lower_bound(inverse(X0),X1),X2)) = X2
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(superposition,[],[f413,f588]) ).

fof(f47645,plain,
    ( spl0_305
    | ~ spl0_18
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f705,f583,f412,f142,f47643]) ).

fof(f47643,plain,
    ( spl0_305
  <=> ! [X2,X0,X1] : multiply(multiply(inverse(X1),X0),multiply(inverse(X0),multiply(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f142,plain,
    ( spl0_18
  <=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f705,plain,
    ( ! [X2,X0,X1] : multiply(multiply(inverse(X1),X0),multiply(inverse(X0),multiply(X1,X2))) = X2
    | ~ spl0_18
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(forward_demodulation,[],[f681,f143]) ).

fof(f143,plain,
    ( ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f142]) ).

fof(f681,plain,
    ( ! [X2,X0,X1] : multiply(multiply(inverse(X1),X0),multiply(multiply(inverse(X0),X1),X2)) = X2
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f413,f584]) ).

fof(f47641,plain,
    ( spl0_304
    | ~ spl0_30
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f3675,f2412,f374,f47639]) ).

fof(f47639,plain,
    ( spl0_304
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = multiply(least_upper_bound(X0,X1),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f2412,plain,
    ( spl0_84
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f3675,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = multiply(least_upper_bound(X0,X1),identity)
    | ~ spl0_30
    | ~ spl0_84 ),
    inference(forward_demodulation,[],[f3623,f375]) ).

fof(f3623,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,X1),identity) = least_upper_bound(multiply(X1,identity),X0)
    | ~ spl0_30
    | ~ spl0_84 ),
    inference(superposition,[],[f2413,f375]) ).

fof(f2413,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f2412]) ).

fof(f47637,plain,
    ( spl0_303
    | ~ spl0_18
    | ~ spl0_32
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f653,f579,f412,f142,f47635]) ).

fof(f47635,plain,
    ( spl0_303
  <=> ! [X2,X0,X1] : multiply(multiply(X1,inverse(X0)),multiply(X0,multiply(inverse(X1),X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f653,plain,
    ( ! [X2,X0,X1] : multiply(multiply(X1,inverse(X0)),multiply(X0,multiply(inverse(X1),X2))) = X2
    | ~ spl0_18
    | ~ spl0_32
    | ~ spl0_39 ),
    inference(forward_demodulation,[],[f640,f143]) ).

fof(f640,plain,
    ( ! [X2,X0,X1] : multiply(multiply(X1,inverse(X0)),multiply(multiply(X0,inverse(X1)),X2)) = X2
    | ~ spl0_32
    | ~ spl0_39 ),
    inference(superposition,[],[f413,f580]) ).

fof(f47633,plain,
    ( spl0_302
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f525,f453,f154,f68,f47631]) ).

fof(f47631,plain,
    ( spl0_302
  <=> ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(X0,identity)),X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f154,plain,
    ( spl0_19
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f525,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(least_upper_bound(X0,identity)),X1) = greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X0)))
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f516,f180]) ).

fof(f180,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1))
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f69]) ).

fof(f155,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f154]) ).

fof(f516,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(identity,X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,identity)),X1)
    | ~ spl0_19
    | ~ spl0_36 ),
    inference(superposition,[],[f155,f454]) ).

fof(f47629,plain,
    ( spl0_301
    | ~ spl0_19
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f504,f449,f154,f47627]) ).

fof(f47627,plain,
    ( spl0_301
  <=> ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f504,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(inverse(least_upper_bound(identity,X0)),X1)
    | ~ spl0_19
    | ~ spl0_35 ),
    inference(superposition,[],[f155,f450]) ).

fof(f47625,plain,
    ( spl0_300
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f499,f445,f158,f72,f47623]) ).

fof(f47623,plain,
    ( spl0_300
  <=> ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(X0,identity)),X1) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f499,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(greatest_lower_bound(X0,identity)),X1) = least_upper_bound(identity,least_upper_bound(X1,inverse(X0)))
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f490,f199]) ).

fof(f199,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1))
    | ~ spl0_11
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f73]) ).

fof(f490,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(identity,X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,identity)),X1)
    | ~ spl0_20
    | ~ spl0_34 ),
    inference(superposition,[],[f159,f446]) ).

fof(f47621,plain,
    ( spl0_299
    | ~ spl0_20
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f460,f441,f158,f47619]) ).

fof(f47619,plain,
    ( spl0_299
  <=> ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f460,plain,
    ( ! [X0,X1] : least_upper_bound(identity,least_upper_bound(inverse(X0),X1)) = least_upper_bound(inverse(greatest_lower_bound(identity,X0)),X1)
    | ~ spl0_20
    | ~ spl0_33 ),
    inference(superposition,[],[f159,f442]) ).

fof(f47617,plain,
    ( spl0_298
    | ~ spl0_10
    | ~ spl0_14
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f328,f223,f84,f68,f47615]) ).

fof(f47615,plain,
    ( spl0_298
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,inverse(X0))) = multiply(greatest_lower_bound(X1,X0),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f84,plain,
    ( spl0_14
  <=> ! [X0] : identity = multiply(X0,inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f223,plain,
    ( spl0_24
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f328,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,inverse(X0))) = multiply(greatest_lower_bound(X1,X0),inverse(X0))
    | ~ spl0_10
    | ~ spl0_14
    | ~ spl0_24 ),
    inference(forward_demodulation,[],[f315,f69]) ).

fof(f315,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,X0),inverse(X0)) = greatest_lower_bound(multiply(X1,inverse(X0)),identity)
    | ~ spl0_14
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f85]) ).

fof(f85,plain,
    ( ! [X0] : identity = multiply(X0,inverse(X0))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f84]) ).

fof(f224,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f47613,plain,
    ( spl0_297
    | ~ spl0_14
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f310,f223,f84,f47611]) ).

fof(f47611,plain,
    ( spl0_297
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X0,X1),inverse(X0)) = greatest_lower_bound(identity,multiply(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f310,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,X1),inverse(X0)) = greatest_lower_bound(identity,multiply(X1,inverse(X0)))
    | ~ spl0_14
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f85]) ).

fof(f47609,plain,
    ( spl0_296
    | ~ spl0_11
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f304,f219,f84,f72,f47607]) ).

fof(f47607,plain,
    ( spl0_296
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X1,inverse(X0))) = multiply(least_upper_bound(X1,X0),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f219,plain,
    ( spl0_23
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f304,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,inverse(X0))) = multiply(least_upper_bound(X1,X0),inverse(X0))
    | ~ spl0_11
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f291,f73]) ).

fof(f291,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,X0),inverse(X0)) = least_upper_bound(multiply(X1,inverse(X0)),identity)
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f85]) ).

fof(f220,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f47605,plain,
    ( spl0_295
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f286,f219,f84,f47603]) ).

fof(f47603,plain,
    ( spl0_295
  <=> ! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X0)) = least_upper_bound(identity,multiply(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f286,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X0)) = least_upper_bound(identity,multiply(X1,inverse(X0)))
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f85]) ).

fof(f47018,plain,
    ( spl0_294
    | ~ spl0_30
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f3409,f2404,f374,f47016]) ).

fof(f47016,plain,
    ( spl0_294
  <=> ! [X0,X1] : least_upper_bound(X0,multiply(X0,greatest_lower_bound(identity,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f3409,plain,
    ( ! [X0,X1] : least_upper_bound(X0,multiply(X0,greatest_lower_bound(identity,X1))) = X0
    | ~ spl0_30
    | ~ spl0_82 ),
    inference(superposition,[],[f2405,f375]) ).

fof(f44879,plain,
    ( spl0_293
    | ~ spl0_10
    | ~ spl0_32
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1965,f1202,f412,f68,f44877]) ).

fof(f44877,plain,
    ( spl0_293
  <=> ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f1965,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_10
    | ~ spl0_32
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1911,f69]) ).

fof(f1911,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(multiply(X0,X1),X1)) = X1
    | ~ spl0_32
    | ~ spl0_66 ),
    inference(superposition,[],[f413,f1203]) ).

fof(f44875,plain,
    ( spl0_292
    | ~ spl0_32
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1836,f1198,f412,f44873]) ).

fof(f44873,plain,
    ( spl0_292
  <=> ! [X0,X1] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f1836,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_65 ),
    inference(superposition,[],[f413,f1199]) ).

fof(f44871,plain,
    ( spl0_291
    | ~ spl0_11
    | ~ spl0_32
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1796,f1194,f412,f72,f44869]) ).

fof(f44869,plain,
    ( spl0_291
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f1796,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_11
    | ~ spl0_32
    | ~ spl0_64 ),
    inference(forward_demodulation,[],[f1751,f73]) ).

fof(f1751,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(multiply(X0,X1),X1)) = X1
    | ~ spl0_32
    | ~ spl0_64 ),
    inference(superposition,[],[f413,f1195]) ).

fof(f44867,plain,
    ( spl0_290
    | ~ spl0_32
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1685,f1186,f412,f44865]) ).

fof(f44865,plain,
    ( spl0_290
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(identity,X0)),least_upper_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f1685,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(identity,X0)),least_upper_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_62 ),
    inference(superposition,[],[f413,f1187]) ).

fof(f44863,plain,
    ( spl0_289
    | ~ spl0_18
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f420,f412,f142,f44861]) ).

fof(f44861,plain,
    ( spl0_289
  <=> ! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f420,plain,
    ( ! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2
    | ~ spl0_18
    | ~ spl0_32 ),
    inference(superposition,[],[f413,f143]) ).

fof(f44518,plain,
    ( spl0_288
    | ~ spl0_30
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f3044,f2351,f374,f44516]) ).

fof(f44516,plain,
    ( spl0_288
  <=> ! [X0,X1] : greatest_lower_bound(X0,multiply(X0,least_upper_bound(identity,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f3044,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,multiply(X0,least_upper_bound(identity,X1))) = X0
    | ~ spl0_30
    | ~ spl0_78 ),
    inference(superposition,[],[f2352,f375]) ).

fof(f35587,plain,
    ( spl0_287
    | ~ spl0_7
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f4969,f4928,f52,f35585]) ).

fof(f35585,plain,
    ( spl0_287
  <=> ! [X0,X1] : identity = inverse(multiply(least_upper_bound(X1,inverse(X0)),greatest_lower_bound(X0,inverse(X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f52,plain,
    ( spl0_7
  <=> ! [X0] : identity = multiply(inverse(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f4928,plain,
    ( spl0_98
  <=> ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = inverse(multiply(least_upper_bound(X1,inverse(X2)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f4969,plain,
    ( ! [X0,X1] : identity = inverse(multiply(least_upper_bound(X1,inverse(X0)),greatest_lower_bound(X0,inverse(X1))))
    | ~ spl0_7
    | ~ spl0_98 ),
    inference(superposition,[],[f4929,f53]) ).

fof(f53,plain,
    ( ! [X0] : identity = multiply(inverse(X0),X0)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f4929,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = inverse(multiply(least_upper_bound(X1,inverse(X2)),X0))
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f4928]) ).

fof(f35582,plain,
    ( spl0_286
    | ~ spl0_7
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f4803,f4764,f52,f35580]) ).

fof(f35580,plain,
    ( spl0_286
  <=> ! [X0,X1] : identity = inverse(multiply(least_upper_bound(inverse(X1),X0),greatest_lower_bound(inverse(X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f4803,plain,
    ( ! [X0,X1] : identity = inverse(multiply(least_upper_bound(inverse(X1),X0),greatest_lower_bound(inverse(X0),X1)))
    | ~ spl0_7
    | ~ spl0_96 ),
    inference(superposition,[],[f4765,f53]) ).

fof(f35577,plain,
    ( spl0_285
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f4653,f4617,f52,f35575]) ).

fof(f35575,plain,
    ( spl0_285
  <=> ! [X0,X1] : identity = inverse(multiply(greatest_lower_bound(X1,inverse(X0)),least_upper_bound(X0,inverse(X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f4617,plain,
    ( spl0_94
  <=> ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = inverse(multiply(greatest_lower_bound(X1,inverse(X2)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f4653,plain,
    ( ! [X0,X1] : identity = inverse(multiply(greatest_lower_bound(X1,inverse(X0)),least_upper_bound(X0,inverse(X1))))
    | ~ spl0_7
    | ~ spl0_94 ),
    inference(superposition,[],[f4618,f53]) ).

fof(f4618,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = inverse(multiply(greatest_lower_bound(X1,inverse(X2)),X0))
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f4617]) ).

fof(f35399,plain,
    ( spl0_284
    | ~ spl0_7
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f4492,f4453,f52,f35397]) ).

fof(f35397,plain,
    ( spl0_284
  <=> ! [X0,X1] : identity = inverse(multiply(greatest_lower_bound(inverse(X1),X0),least_upper_bound(inverse(X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f4492,plain,
    ( ! [X0,X1] : identity = inverse(multiply(greatest_lower_bound(inverse(X1),X0),least_upper_bound(inverse(X0),X1)))
    | ~ spl0_7
    | ~ spl0_92 ),
    inference(superposition,[],[f4454,f53]) ).

fof(f35395,plain,
    ( spl0_283
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f4376,f4051,f102,f44,f35393]) ).

fof(f35393,plain,
    ( spl0_283
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f44,plain,
    ( spl0_5
  <=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f4376,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),inverse(X0))
    | ~ spl0_5
    | ~ spl0_16
    | ~ spl0_90 ),
    inference(forward_demodulation,[],[f4309,f103]) ).

fof(f4309,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(X1),inverse(X0)) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),inverse(X0))
    | ~ spl0_5
    | ~ spl0_90 ),
    inference(superposition,[],[f4052,f45]) ).

fof(f45,plain,
    ( ! [X0] : least_upper_bound(X0,X0) = X0
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f35391,plain,
    ( spl0_282
    | ~ spl0_13
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f4335,f4051,f80,f35389]) ).

fof(f35389,plain,
    ( spl0_282
  <=> ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f80,plain,
    ( spl0_13
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f4335,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2))
    | ~ spl0_13
    | ~ spl0_90 ),
    inference(superposition,[],[f81,f4052]) ).

fof(f81,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f35387,plain,
    ( spl0_281
    | ~ spl0_6
    | ~ spl0_17
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f4258,f4047,f106,f48,f35385]) ).

fof(f35385,plain,
    ( spl0_281
  <=> ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(least_upper_bound(X1,X0)),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f48,plain,
    ( spl0_6
  <=> ! [X0] : greatest_lower_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f4258,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(least_upper_bound(X1,X0)),inverse(X0))
    | ~ spl0_6
    | ~ spl0_17
    | ~ spl0_89 ),
    inference(forward_demodulation,[],[f4191,f107]) ).

fof(f4191,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(X1),inverse(X0)) = greatest_lower_bound(inverse(least_upper_bound(X1,X0)),inverse(X0))
    | ~ spl0_6
    | ~ spl0_89 ),
    inference(superposition,[],[f4048,f49]) ).

fof(f49,plain,
    ( ! [X0] : greatest_lower_bound(X0,X0) = X0
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f35383,plain,
    ( spl0_280
    | ~ spl0_12
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f4217,f4047,f76,f35381]) ).

fof(f35381,plain,
    ( spl0_280
  <=> ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f76,plain,
    ( spl0_12
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f4217,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2))
    | ~ spl0_12
    | ~ spl0_89 ),
    inference(superposition,[],[f77,f4048]) ).

fof(f77,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f35379,plain,
    ( spl0_279
    | ~ spl0_32
    | ~ spl0_43
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f2313,f1992,f595,f412,f35377]) ).

fof(f35377,plain,
    ( spl0_279
  <=> ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),greatest_lower_bound(identity,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1992,plain,
    ( spl0_71
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f2313,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),greatest_lower_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_43
    | ~ spl0_71 ),
    inference(forward_demodulation,[],[f2288,f596]) ).

fof(f2288,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,inverse(X1))),greatest_lower_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_71 ),
    inference(superposition,[],[f413,f1993]) ).

fof(f1993,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0)
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f1992]) ).

fof(f35375,plain,
    ( spl0_278
    | ~ spl0_32
    | ~ spl0_41
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f2203,f1988,f587,f412,f35373]) ).

fof(f35373,plain,
    ( spl0_278
  <=> ! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),greatest_lower_bound(identity,multiply(X1,X0))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f2203,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),greatest_lower_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_32
    | ~ spl0_41
    | ~ spl0_70 ),
    inference(forward_demodulation,[],[f2174,f588]) ).

fof(f2174,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(inverse(X0),X1)),greatest_lower_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_32
    | ~ spl0_70 ),
    inference(superposition,[],[f413,f1989]) ).

fof(f35371,plain,
    ( spl0_277
    | ~ spl0_32
    | ~ spl0_47
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f2126,f1984,f611,f412,f35369]) ).

fof(f1984,plain,
    ( spl0_69
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f2126,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),least_upper_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_47
    | ~ spl0_69 ),
    inference(forward_demodulation,[],[f2101,f612]) ).

fof(f2101,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,inverse(X1))),least_upper_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_32
    | ~ spl0_69 ),
    inference(superposition,[],[f413,f1985]) ).

fof(f1985,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f1984]) ).

fof(f35367,plain,
    ( spl0_276
    | ~ spl0_32
    | ~ spl0_46
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f2058,f1980,f607,f412,f35365]) ).

fof(f35365,plain,
    ( spl0_276
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(identity,multiply(X1,X0))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f2058,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_32
    | ~ spl0_46
    | ~ spl0_68 ),
    inference(forward_demodulation,[],[f2030,f608]) ).

fof(f2030,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X0),X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_32
    | ~ spl0_68 ),
    inference(superposition,[],[f413,f1981]) ).

fof(f35363,plain,
    ( spl0_275
    | ~ spl0_45
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1845,f1198,f603,f35361]) ).

fof(f35361,plain,
    ( spl0_275
  <=> ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(multiply(greatest_lower_bound(identity,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f603,plain,
    ( spl0_45
  <=> ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1845,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(multiply(greatest_lower_bound(identity,X1),X0)))
    | ~ spl0_45
    | ~ spl0_65 ),
    inference(superposition,[],[f604,f1199]) ).

fof(f604,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f35159,plain,
    ( spl0_274
    | ~ spl0_49
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1692,f1186,f619,f35157]) ).

fof(f35157,plain,
    ( spl0_274
  <=> ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(multiply(least_upper_bound(identity,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f619,plain,
    ( spl0_49
  <=> ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1692,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(multiply(least_upper_bound(identity,X1),X0)))
    | ~ spl0_49
    | ~ spl0_62 ),
    inference(superposition,[],[f620,f1187]) ).

fof(f620,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f619]) ).

fof(f35155,plain,
    ( spl0_273
    | ~ spl0_49
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1618,f1182,f619,f35153]) ).

fof(f35153,plain,
    ( spl0_273
  <=> ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X1,least_upper_bound(X2,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f1618,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X1,least_upper_bound(X2,X0))))
    | ~ spl0_49
    | ~ spl0_61 ),
    inference(superposition,[],[f620,f1183]) ).

fof(f35151,plain,
    ( spl0_272
    | ~ spl0_49
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1601,f1182,f619,f35149]) ).

fof(f35149,plain,
    ( spl0_272
  <=> ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X2,least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f1601,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X2,least_upper_bound(X0,X1))))
    | ~ spl0_49
    | ~ spl0_61 ),
    inference(superposition,[],[f620,f1183]) ).

fof(f35147,plain,
    ( spl0_271
    | ~ spl0_35
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f1491,f1173,f449,f35145]) ).

fof(f35145,plain,
    ( spl0_271
  <=> ! [X0,X1] : least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f1491,plain,
    ( ! [X0,X1] : least_upper_bound(identity,X1) = least_upper_bound(identity,least_upper_bound(inverse(least_upper_bound(identity,X0)),X1))
    | ~ spl0_35
    | ~ spl0_59 ),
    inference(superposition,[],[f1174,f450]) ).

fof(f35143,plain,
    ( spl0_270
    | ~ spl0_45
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1390,f1165,f603,f35141]) ).

fof(f35141,plain,
    ( spl0_270
  <=> ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X1,greatest_lower_bound(X2,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f1390,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X1,greatest_lower_bound(X2,X0))))
    | ~ spl0_45
    | ~ spl0_57 ),
    inference(superposition,[],[f604,f1166]) ).

fof(f35139,plain,
    ( spl0_269
    | ~ spl0_45
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1374,f1165,f603,f35137]) ).

fof(f35137,plain,
    ( spl0_269
  <=> ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X2,greatest_lower_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f1374,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X2,greatest_lower_bound(X0,X1))))
    | ~ spl0_45
    | ~ spl0_57 ),
    inference(superposition,[],[f604,f1166]) ).

fof(f35135,plain,
    ( spl0_268
    | ~ spl0_33
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1266,f1156,f441,f35133]) ).

fof(f35133,plain,
    ( spl0_268
  <=> ! [X0,X1] : greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(identity,X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f1266,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,X1) = greatest_lower_bound(identity,greatest_lower_bound(inverse(greatest_lower_bound(identity,X0)),X1))
    | ~ spl0_33
    | ~ spl0_55 ),
    inference(superposition,[],[f1157,f442]) ).

fof(f35131,plain,
    ( spl0_267
    | ~ spl0_49
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1148,f1118,f619,f35129]) ).

fof(f35129,plain,
    ( spl0_267
  <=> ! [X0] : inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,least_upper_bound(c,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f1148,plain,
    ( ! [X0] : inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,least_upper_bound(c,X0))))
    | ~ spl0_49
    | ~ spl0_52 ),
    inference(superposition,[],[f620,f1119]) ).

fof(f35127,plain,
    ( spl0_266
    | ~ spl0_45
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f1131,f1114,f603,f35125]) ).

fof(f35125,plain,
    ( spl0_266
  <=> ! [X0] : inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,greatest_lower_bound(c,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f1131,plain,
    ( ! [X0] : inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,greatest_lower_bound(c,X0))))
    | ~ spl0_45
    | ~ spl0_51 ),
    inference(superposition,[],[f604,f1115]) ).

fof(f35123,plain,
    ( spl0_265
    | ~ spl0_31
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f1091,f619,f378,f35121]) ).

fof(f35121,plain,
    ( spl0_265
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f378,plain,
    ( spl0_31
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1091,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),inverse(X0))
    | ~ spl0_31
    | ~ spl0_49 ),
    inference(superposition,[],[f379,f620]) ).

fof(f379,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f378]) ).

fof(f35119,plain,
    ( spl0_264
    | ~ spl0_67
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f9998,f8791,f1717,f35117]) ).

fof(f35117,plain,
    ( spl0_264
  <=> ! [X0] : identity = least_upper_bound(inverse(least_upper_bound(X0,identity)),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f1717,plain,
    ( spl0_67
  <=> ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f8791,plain,
    ( spl0_140
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f9998,plain,
    ( ! [X0] : identity = least_upper_bound(inverse(least_upper_bound(X0,identity)),identity)
    | ~ spl0_67
    | ~ spl0_140 ),
    inference(superposition,[],[f8792,f1718]) ).

fof(f1718,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1717]) ).

fof(f8792,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f8791]) ).

fof(f35115,plain,
    ( spl0_263
    | ~ spl0_37
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1038,f615,f527,f35113]) ).

fof(f35113,plain,
    ( spl0_263
  <=> ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f1038,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X1,X0)))
    | ~ spl0_37
    | ~ spl0_48 ),
    inference(superposition,[],[f528,f616]) ).

fof(f35111,plain,
    ( spl0_262
    | ~ spl0_29
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f869,f603,f370,f35109]) ).

fof(f35109,plain,
    ( spl0_262
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f370,plain,
    ( spl0_29
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f869,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),inverse(X0))
    | ~ spl0_29
    | ~ spl0_45 ),
    inference(superposition,[],[f371,f604]) ).

fof(f371,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f370]) ).

fof(f35107,plain,
    ( spl0_261
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f825,f599,f531,f35105]) ).

fof(f35105,plain,
    ( spl0_261
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f825,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(superposition,[],[f532,f600]) ).

fof(f35103,plain,
    ( spl0_260
    | ~ spl0_16
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f565,f531,f102,f35101]) ).

fof(f35101,plain,
    ( spl0_260
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f565,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_16
    | ~ spl0_38 ),
    inference(superposition,[],[f532,f103]) ).

fof(f35099,plain,
    ( spl0_259
    | ~ spl0_17
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f543,f527,f106,f35097]) ).

fof(f35097,plain,
    ( spl0_259
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f543,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_17
    | ~ spl0_37 ),
    inference(superposition,[],[f528,f107]) ).

fof(f35095,plain,
    ( spl0_258
    | ~ spl0_10
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f280,f215,f84,f68,f35093]) ).

fof(f35093,plain,
    ( spl0_258
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f215,plain,
    ( spl0_22
  <=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f280,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,inverse(X0)))
    | ~ spl0_10
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f265,f69]) ).

fof(f265,plain,
    ( ! [X0,X1] : multiply(X0,greatest_lower_bound(X1,inverse(X0))) = greatest_lower_bound(multiply(X0,X1),identity)
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f85]) ).

fof(f216,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f35091,plain,
    ( spl0_257
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f260,f215,f84,f35089]) ).

fof(f35089,plain,
    ( spl0_257
  <=> ! [X0,X1] : multiply(X0,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(identity,multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f260,plain,
    ( ! [X0,X1] : multiply(X0,greatest_lower_bound(inverse(X0),X1)) = greatest_lower_bound(identity,multiply(X0,X1))
    | ~ spl0_14
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f85]) ).

fof(f35087,plain,
    ( spl0_256
    | ~ spl0_11
    | ~ spl0_14
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f249,f211,f84,f72,f35085]) ).

fof(f35085,plain,
    ( spl0_256
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X0,X1)) = multiply(X0,least_upper_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f211,plain,
    ( spl0_21
  <=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f249,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X0,X1)) = multiply(X0,least_upper_bound(X1,inverse(X0)))
    | ~ spl0_11
    | ~ spl0_14
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f234,f73]) ).

fof(f234,plain,
    ( ! [X0,X1] : multiply(X0,least_upper_bound(X1,inverse(X0))) = least_upper_bound(multiply(X0,X1),identity)
    | ~ spl0_14
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f85]) ).

fof(f212,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f35083,plain,
    ( spl0_255
    | ~ spl0_14
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f229,f211,f84,f35081]) ).

fof(f35081,plain,
    ( spl0_255
  <=> ! [X0,X1] : multiply(X0,least_upper_bound(inverse(X0),X1)) = least_upper_bound(identity,multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f229,plain,
    ( ! [X0,X1] : multiply(X0,least_upper_bound(inverse(X0),X1)) = least_upper_bound(identity,multiply(X0,X1))
    | ~ spl0_14
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f85]) ).

fof(f34651,plain,
    ( spl0_254
    | ~ spl0_63
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f9997,f8791,f1190,f34649]) ).

fof(f34649,plain,
    ( spl0_254
  <=> ! [X0] : identity = least_upper_bound(inverse(least_upper_bound(identity,X0)),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f1190,plain,
    ( spl0_63
  <=> ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f9997,plain,
    ( ! [X0] : identity = least_upper_bound(inverse(least_upper_bound(identity,X0)),identity)
    | ~ spl0_63
    | ~ spl0_140 ),
    inference(superposition,[],[f8792,f1191]) ).

fof(f1191,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1190]) ).

fof(f30393,plain,
    ( spl0_253
    | ~ spl0_53
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9863,f8787,f1135,f30391]) ).

fof(f30391,plain,
    ( spl0_253
  <=> ! [X0] : identity = greatest_lower_bound(inverse(greatest_lower_bound(X0,identity)),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f1135,plain,
    ( spl0_53
  <=> ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f9863,plain,
    ( ! [X0] : identity = greatest_lower_bound(inverse(greatest_lower_bound(X0,identity)),identity)
    | ~ spl0_53
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f1136]) ).

fof(f1136,plain,
    ( ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f1135]) ).

fof(f26695,plain,
    ( spl0_252
    | ~ spl0_50
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9862,f8787,f757,f26693]) ).

fof(f26693,plain,
    ( spl0_252
  <=> ! [X0] : identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X0)),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f757,plain,
    ( spl0_50
  <=> ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f9862,plain,
    ( ! [X0] : identity = greatest_lower_bound(inverse(greatest_lower_bound(identity,X0)),identity)
    | ~ spl0_50
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f758]) ).

fof(f758,plain,
    ( ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f757]) ).

fof(f21730,plain,
    ( spl0_251
    | ~ spl0_24
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f3878,f2420,f223,f21728]) ).

fof(f21728,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = multiply(greatest_lower_bound(X2,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f3878,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = multiply(greatest_lower_bound(X2,X0),X1)
    | ~ spl0_24
    | ~ spl0_86 ),
    inference(superposition,[],[f2421,f224]) ).

fof(f21726,plain,
    ( spl0_250
    | ~ spl0_23
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f3634,f2412,f219,f21724]) ).

fof(f21724,plain,
    ( spl0_250
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = multiply(least_upper_bound(X2,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f3634,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = multiply(least_upper_bound(X2,X0),X1)
    | ~ spl0_23
    | ~ spl0_84 ),
    inference(superposition,[],[f2413,f220]) ).

fof(f21722,plain,
    ( spl0_249
    | ~ spl0_22
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f3344,f2400,f215,f21720]) ).

fof(f21720,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f2400,plain,
    ( spl0_81
  <=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f3344,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1))
    | ~ spl0_22
    | ~ spl0_81 ),
    inference(superposition,[],[f2401,f216]) ).

fof(f2401,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f2400]) ).

fof(f21718,plain,
    ( spl0_248
    | ~ spl0_21
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f2983,f2347,f211,f21716]) ).

fof(f21716,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f2347,plain,
    ( spl0_77
  <=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f2983,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1))
    | ~ spl0_21
    | ~ spl0_77 ),
    inference(superposition,[],[f2348,f212]) ).

fof(f2348,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f2347]) ).

fof(f21714,plain,
    ( spl0_247
    | ~ spl0_5
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_38
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f2855,f2339,f531,f158,f72,f44,f21712]) ).

fof(f21712,plain,
    ( spl0_247
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2855,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X1))
    | ~ spl0_5
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_38
    | ~ spl0_75 ),
    inference(forward_demodulation,[],[f2854,f557]) ).

fof(f557,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(superposition,[],[f532,f73]) ).

fof(f2854,plain,
    ( ! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = greatest_lower_bound(least_upper_bound(X0,least_upper_bound(X1,X0)),least_upper_bound(X0,X1))
    | ~ spl0_5
    | ~ spl0_20
    | ~ spl0_75 ),
    inference(forward_demodulation,[],[f2815,f159]) ).

fof(f2815,plain,
    ( ! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = greatest_lower_bound(least_upper_bound(least_upper_bound(X0,X1),X0),least_upper_bound(X0,X1))
    | ~ spl0_5
    | ~ spl0_75 ),
    inference(superposition,[],[f2340,f45]) ).

fof(f21543,plain,
    ( spl0_246
    | ~ spl0_29
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f2631,f2335,f370,f21541]) ).

fof(f21541,plain,
    ( spl0_246
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X2))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2631,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X2))) = X0
    | ~ spl0_29
    | ~ spl0_74 ),
    inference(superposition,[],[f2336,f371]) ).

fof(f21539,plain,
    ( spl0_245
    | ~ spl0_12
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f2630,f2335,f76,f21537]) ).

fof(f21537,plain,
    ( spl0_245
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f2630,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2))) = X0
    | ~ spl0_12
    | ~ spl0_74 ),
    inference(superposition,[],[f2336,f77]) ).

fof(f21535,plain,
    ( spl0_244
    | ~ spl0_6
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_37
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f2617,f2331,f527,f154,f68,f48,f21533]) ).

fof(f21533,plain,
    ( spl0_244
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2617,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X1))
    | ~ spl0_6
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_37
    | ~ spl0_73 ),
    inference(forward_demodulation,[],[f2616,f535]) ).

fof(f535,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_10
    | ~ spl0_37 ),
    inference(superposition,[],[f528,f69]) ).

fof(f2616,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = least_upper_bound(greatest_lower_bound(X0,greatest_lower_bound(X1,X0)),greatest_lower_bound(X0,X1))
    | ~ spl0_6
    | ~ spl0_19
    | ~ spl0_73 ),
    inference(forward_demodulation,[],[f2580,f155]) ).

fof(f2580,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X0,X1),X0),greatest_lower_bound(X0,X1))
    | ~ spl0_6
    | ~ spl0_73 ),
    inference(superposition,[],[f2332,f49]) ).

fof(f21531,plain,
    ( spl0_243
    | ~ spl0_31
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f2437,f2327,f378,f21529]) ).

fof(f21529,plain,
    ( spl0_243
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X2))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2437,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X2))) = X0
    | ~ spl0_31
    | ~ spl0_72 ),
    inference(superposition,[],[f2328,f379]) ).

fof(f21527,plain,
    ( spl0_242
    | ~ spl0_13
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f2436,f2327,f80,f21525]) ).

fof(f21525,plain,
    ( spl0_242
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f2436,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2))) = X0
    | ~ spl0_13
    | ~ spl0_72 ),
    inference(superposition,[],[f2328,f81]) ).

fof(f21523,plain,
    ( spl0_241
    | ~ spl0_10
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1879,f1202,f68,f21521]) ).

fof(f21521,plain,
    ( spl0_241
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(multiply(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f1879,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(multiply(X0,X1),X1)
    | ~ spl0_10
    | ~ spl0_66 ),
    inference(superposition,[],[f1203,f69]) ).

fof(f21519,plain,
    ( spl0_240
    | ~ spl0_10
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1806,f1198,f68,f21517]) ).

fof(f21517,plain,
    ( spl0_240
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(X0,X1)) = multiply(greatest_lower_bound(X0,identity),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f1806,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(X0,X1)) = multiply(greatest_lower_bound(X0,identity),X1)
    | ~ spl0_10
    | ~ spl0_65 ),
    inference(superposition,[],[f1199,f69]) ).

fof(f21515,plain,
    ( spl0_239
    | ~ spl0_11
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1721,f1194,f72,f21513]) ).

fof(f21513,plain,
    ( spl0_239
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(multiply(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f1721,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(multiply(X0,X1),X1)
    | ~ spl0_11
    | ~ spl0_64 ),
    inference(superposition,[],[f1195,f73]) ).

fof(f21511,plain,
    ( spl0_238
    | ~ spl0_11
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1657,f1186,f72,f21509]) ).

fof(f21509,plain,
    ( spl0_238
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(X0,X1)) = multiply(least_upper_bound(X0,identity),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f1657,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(X0,X1)) = multiply(least_upper_bound(X0,identity),X1)
    | ~ spl0_11
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f73]) ).

fof(f21507,plain,
    ( spl0_237
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1568,f1182,f370,f21505]) ).

fof(f21505,plain,
    ( spl0_237
  <=> ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f1568,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2))
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f371]) ).

fof(f21338,plain,
    ( spl0_236
    | ~ spl0_12
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1567,f1182,f76,f21336]) ).

fof(f21336,plain,
    ( spl0_236
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X2,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f1567,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X2,X0)
    | ~ spl0_12
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f77]) ).

fof(f21334,plain,
    ( spl0_235
    | ~ spl0_11
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1559,f1182,f72,f21332]) ).

fof(f21332,plain,
    ( spl0_235
  <=> ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(least_upper_bound(X1,X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f1559,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(least_upper_bound(X1,X2),X0)
    | ~ spl0_11
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f73]) ).

fof(f21330,plain,
    ( spl0_234
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1538,f1182,f370,f21328]) ).

fof(f21328,plain,
    ( spl0_234
  <=> ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f1538,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X2,X0))
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f371]) ).

fof(f21326,plain,
    ( spl0_233
    | ~ spl0_12
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1537,f1182,f76,f21324]) ).

fof(f21324,plain,
    ( spl0_233
  <=> ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f1537,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0))
    | ~ spl0_12
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f77]) ).

fof(f21322,plain,
    ( spl0_232
    | ~ spl0_11
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f1503,f1173,f72,f21320]) ).

fof(f21320,plain,
    ( spl0_232
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(X2,greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f1503,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(X2,greatest_lower_bound(X0,X1)))
    | ~ spl0_11
    | ~ spl0_59 ),
    inference(superposition,[],[f1174,f73]) ).

fof(f21318,plain,
    ( spl0_231
    | ~ spl0_11
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1446,f1169,f72,f21316]) ).

fof(f21316,plain,
    ( spl0_231
  <=> ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X1,least_upper_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f1446,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X1,least_upper_bound(X0,X2))
    | ~ spl0_11
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f73]) ).

fof(f21314,plain,
    ( spl0_230
    | ~ spl0_20
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1444,f1169,f158,f21312]) ).

fof(f21312,plain,
    ( spl0_230
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f1444,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2))
    | ~ spl0_20
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f159]) ).

fof(f21310,plain,
    ( spl0_229
    | ~ spl0_29
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1430,f1169,f370,f21308]) ).

fof(f21308,plain,
    ( spl0_229
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f1430,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X0,X2))
    | ~ spl0_29
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f371]) ).

fof(f21306,plain,
    ( spl0_228
    | ~ spl0_12
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1429,f1169,f76,f21304]) ).

fof(f21304,plain,
    ( spl0_228
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f1429,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X0,X2))
    | ~ spl0_12
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f77]) ).

fof(f21302,plain,
    ( spl0_227
    | ~ spl0_31
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1345,f1165,f378,f21300]) ).

fof(f21300,plain,
    ( spl0_227
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f1345,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2))
    | ~ spl0_31
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f379]) ).

fof(f21135,plain,
    ( spl0_226
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1344,f1165,f80,f21133]) ).

fof(f21133,plain,
    ( spl0_226
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X2,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f1344,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X2,X0)
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f81]) ).

fof(f21131,plain,
    ( spl0_225
    | ~ spl0_10
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1332,f1165,f68,f21129]) ).

fof(f21129,plain,
    ( spl0_225
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f1332,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X0)
    | ~ spl0_10
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f69]) ).

fof(f21127,plain,
    ( spl0_224
    | ~ spl0_31
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1315,f1165,f378,f21125]) ).

fof(f21125,plain,
    ( spl0_224
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f1315,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X2,X0))
    | ~ spl0_31
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f379]) ).

fof(f21123,plain,
    ( spl0_223
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1314,f1165,f80,f21121]) ).

fof(f21121,plain,
    ( spl0_223
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f1314,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X2,X0))
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f81]) ).

fof(f21119,plain,
    ( spl0_222
    | ~ spl0_10
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1277,f1156,f68,f21117]) ).

fof(f21117,plain,
    ( spl0_222
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(X2,least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f1277,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(X2,least_upper_bound(X0,X1)))
    | ~ spl0_10
    | ~ spl0_55 ),
    inference(superposition,[],[f1157,f69]) ).

fof(f21115,plain,
    ( spl0_221
    | ~ spl0_10
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1225,f1152,f68,f21113]) ).

fof(f21113,plain,
    ( spl0_221
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f1225,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2))
    | ~ spl0_10
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f69]) ).

fof(f21111,plain,
    ( spl0_220
    | ~ spl0_19
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1223,f1152,f154,f21109]) ).

fof(f21109,plain,
    ( spl0_220
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1223,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2))
    | ~ spl0_19
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f155]) ).

fof(f21107,plain,
    ( spl0_219
    | ~ spl0_31
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1210,f1152,f378,f21105]) ).

fof(f21105,plain,
    ( spl0_219
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f1210,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X0,X2))
    | ~ spl0_31
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f379]) ).

fof(f21103,plain,
    ( spl0_218
    | ~ spl0_13
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1209,f1152,f80,f21101]) ).

fof(f21101,plain,
    ( spl0_218
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f1209,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X0,X2))
    | ~ spl0_13
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f81]) ).

fof(f21099,plain,
    ( spl0_217
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f408,f378,f154,f21097]) ).

fof(f21097,plain,
    ( spl0_217
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f408,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2))
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(superposition,[],[f155,f379]) ).

fof(f21095,plain,
    ( spl0_216
    | ~ spl0_29
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f9987,f8791,f370,f21093]) ).

fof(f21093,plain,
    ( spl0_216
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f9987,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,X0),X0) = X0
    | ~ spl0_29
    | ~ spl0_140 ),
    inference(superposition,[],[f8792,f371]) ).

fof(f21091,plain,
    ( spl0_215
    | ~ spl0_20
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f392,f370,f158,f21089]) ).

fof(f21089,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f392,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2))
    | ~ spl0_20
    | ~ spl0_29 ),
    inference(superposition,[],[f159,f371]) ).

fof(f19633,plain,
    ( spl0_214
    | ~ spl0_12
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f9986,f8791,f76,f19631]) ).

fof(f19631,plain,
    ( spl0_214
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,X1),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f9986,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,X1),X0) = X0
    | ~ spl0_12
    | ~ spl0_140 ),
    inference(superposition,[],[f8792,f77]) ).

fof(f18212,plain,
    ( spl0_213
    | ~ spl0_31
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9858,f8787,f378,f18210]) ).

fof(f18210,plain,
    ( spl0_213
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f9858,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,X0),X0) = X0
    | ~ spl0_31
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f379]) ).

fof(f15838,plain,
    ( spl0_212
    | ~ spl0_13
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9857,f8787,f80,f15836]) ).

fof(f15836,plain,
    ( spl0_212
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f9857,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),X0) = X0
    | ~ spl0_13
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f81]) ).

fof(f15747,plain,
    ( spl0_211
    | ~ spl0_25
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f2649,f2335,f253,f15745]) ).

fof(f15745,plain,
    ( spl0_211
  <=> ! [X0] : b = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f253,plain,
    ( spl0_25
  <=> b = least_upper_bound(b,greatest_lower_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f2649,plain,
    ( ! [X0] : b = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X0)))
    | ~ spl0_25
    | ~ spl0_74 ),
    inference(superposition,[],[f2336,f255]) ).

fof(f255,plain,
    ( b = least_upper_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f15743,plain,
    ( spl0_210
    | ~ spl0_26
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f2450,f2327,f332,f15741]) ).

fof(f15741,plain,
    ( spl0_210
  <=> ! [X0] : b = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f332,plain,
    ( spl0_26
  <=> b = greatest_lower_bound(b,least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f2450,plain,
    ( ! [X0] : b = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X0)))
    | ~ spl0_26
    | ~ spl0_72 ),
    inference(superposition,[],[f2328,f334]) ).

fof(f334,plain,
    ( b = greatest_lower_bound(b,least_upper_bound(a,c))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f332]) ).

fof(f15739,plain,
    ( spl0_209
    | ~ spl0_14
    | ~ spl0_35
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1952,f1202,f449,f84,f15737]) ).

fof(f15737,plain,
    ( spl0_209
  <=> ! [X0] : inverse(least_upper_bound(identity,X0)) = multiply(greatest_lower_bound(X0,identity),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f1952,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = multiply(greatest_lower_bound(X0,identity),inverse(X0))
    | ~ spl0_14
    | ~ spl0_35
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1895,f450]) ).

fof(f1895,plain,
    ( ! [X0] : greatest_lower_bound(identity,inverse(X0)) = multiply(greatest_lower_bound(X0,identity),inverse(X0))
    | ~ spl0_14
    | ~ spl0_66 ),
    inference(superposition,[],[f1203,f85]) ).

fof(f15735,plain,
    ( spl0_208
    | ~ spl0_14
    | ~ spl0_36
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1869,f1198,f453,f84,f15733]) ).

fof(f15733,plain,
    ( spl0_208
  <=> ! [X0] : inverse(least_upper_bound(X0,identity)) = multiply(greatest_lower_bound(identity,X0),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f1869,plain,
    ( ! [X0] : inverse(least_upper_bound(X0,identity)) = multiply(greatest_lower_bound(identity,X0),inverse(X0))
    | ~ spl0_14
    | ~ spl0_36
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1823,f454]) ).

fof(f1823,plain,
    ( ! [X0] : greatest_lower_bound(inverse(X0),identity) = multiply(greatest_lower_bound(identity,X0),inverse(X0))
    | ~ spl0_14
    | ~ spl0_65 ),
    inference(superposition,[],[f1199,f85]) ).

fof(f15731,plain,
    ( spl0_207
    | ~ spl0_14
    | ~ spl0_33
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1783,f1194,f441,f84,f15729]) ).

fof(f15729,plain,
    ( spl0_207
  <=> ! [X0] : inverse(greatest_lower_bound(identity,X0)) = multiply(least_upper_bound(X0,identity),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f1783,plain,
    ( ! [X0] : inverse(greatest_lower_bound(identity,X0)) = multiply(least_upper_bound(X0,identity),inverse(X0))
    | ~ spl0_14
    | ~ spl0_33
    | ~ spl0_64 ),
    inference(forward_demodulation,[],[f1735,f442]) ).

fof(f1735,plain,
    ( ! [X0] : least_upper_bound(identity,inverse(X0)) = multiply(least_upper_bound(X0,identity),inverse(X0))
    | ~ spl0_14
    | ~ spl0_64 ),
    inference(superposition,[],[f1195,f85]) ).

fof(f15727,plain,
    ( spl0_206
    | ~ spl0_14
    | ~ spl0_34
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1712,f1186,f445,f84,f15725]) ).

fof(f15725,plain,
    ( spl0_206
  <=> ! [X0] : inverse(greatest_lower_bound(X0,identity)) = multiply(least_upper_bound(identity,X0),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f1712,plain,
    ( ! [X0] : inverse(greatest_lower_bound(X0,identity)) = multiply(least_upper_bound(identity,X0),inverse(X0))
    | ~ spl0_14
    | ~ spl0_34
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1672,f446]) ).

fof(f1672,plain,
    ( ! [X0] : least_upper_bound(inverse(X0),identity) = multiply(least_upper_bound(identity,X0),inverse(X0))
    | ~ spl0_14
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f85]) ).

fof(f15723,plain,
    ( spl0_205
    | ~ spl0_25
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1583,f1182,f253,f15721]) ).

fof(f15721,plain,
    ( spl0_205
  <=> ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(X0,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1583,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(X0,b)
    | ~ spl0_25
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f255]) ).

fof(f15719,plain,
    ( spl0_204
    | ~ spl0_9
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1582,f1182,f63,f15717]) ).

fof(f15717,plain,
    ( spl0_204
  <=> ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(X0,least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f1582,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(X0,least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f65]) ).

fof(f15715,plain,
    ( spl0_203
    | ~ spl0_25
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1553,f1182,f253,f15713]) ).

fof(f15713,plain,
    ( spl0_203
  <=> ! [X0] : least_upper_bound(X0,b) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X0,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1553,plain,
    ( ! [X0] : least_upper_bound(X0,b) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X0,b))
    | ~ spl0_25
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f255]) ).

fof(f15669,plain,
    ( spl0_202
    | ~ spl0_9
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1552,f1182,f63,f15667]) ).

fof(f15667,plain,
    ( spl0_202
  <=> ! [X0] : least_upper_bound(X0,least_upper_bound(a,c)) = least_upper_bound(c,least_upper_bound(X0,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f1552,plain,
    ( ! [X0] : least_upper_bound(X0,least_upper_bound(a,c)) = least_upper_bound(c,least_upper_bound(X0,b))
    | ~ spl0_9
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f65]) ).

fof(f15665,plain,
    ( spl0_201
    | ~ spl0_9
    | ~ spl0_11
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1470,f1182,f1169,f1118,f72,f63,f15663]) ).

fof(f15663,plain,
    ( spl0_201
  <=> ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(a,least_upper_bound(X0,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1470,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(a,least_upper_bound(X0,c))
    | ~ spl0_9
    | ~ spl0_11
    | ~ spl0_52
    | ~ spl0_58
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f1469,f1139]) ).

fof(f1139,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(X0,c)) = least_upper_bound(a,least_upper_bound(X0,c))
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(superposition,[],[f1119,f73]) ).

fof(f1469,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(b,least_upper_bound(X0,c))
    | ~ spl0_9
    | ~ spl0_58
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f1441,f1183]) ).

fof(f1441,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(c,least_upper_bound(b,X0))
    | ~ spl0_9
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f65]) ).

fof(f15661,plain,
    ( spl0_200
    | ~ spl0_25
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f1442,f1169,f253,f15659]) ).

fof(f15659,plain,
    ( spl0_200
  <=> ! [X0] : least_upper_bound(b,X0) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1442,plain,
    ( ! [X0] : least_upper_bound(b,X0) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X0))
    | ~ spl0_25
    | ~ spl0_58 ),
    inference(superposition,[],[f1170,f255]) ).

fof(f15657,plain,
    ( spl0_199
    | ~ spl0_26
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1356,f1165,f332,f15655]) ).

fof(f15655,plain,
    ( spl0_199
  <=> ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(X0,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1356,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(X0,b)
    | ~ spl0_26
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f334]) ).

fof(f15653,plain,
    ( spl0_198
    | ~ spl0_8
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1355,f1165,f58,f15651]) ).

fof(f15651,plain,
    ( spl0_198
  <=> ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(X0,greatest_lower_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1355,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(X0,greatest_lower_bound(a,c))
    | ~ spl0_8
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f60]) ).

fof(f15649,plain,
    ( spl0_197
    | ~ spl0_26
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1326,f1165,f332,f15647]) ).

fof(f15647,plain,
    ( spl0_197
  <=> ! [X0] : greatest_lower_bound(X0,b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X0,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1326,plain,
    ( ! [X0] : greatest_lower_bound(X0,b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X0,b))
    | ~ spl0_26
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f334]) ).

fof(f15645,plain,
    ( spl0_196
    | ~ spl0_8
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1325,f1165,f58,f15643]) ).

fof(f15643,plain,
    ( spl0_196
  <=> ! [X0] : greatest_lower_bound(X0,greatest_lower_bound(a,c)) = greatest_lower_bound(c,greatest_lower_bound(X0,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f1325,plain,
    ( ! [X0] : greatest_lower_bound(X0,greatest_lower_bound(a,c)) = greatest_lower_bound(c,greatest_lower_bound(X0,b))
    | ~ spl0_8
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f60]) ).

fof(f15641,plain,
    ( spl0_195
    | ~ spl0_8
    | ~ spl0_10
    | ~ spl0_51
    | ~ spl0_54
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1248,f1165,f1152,f1114,f68,f58,f15639]) ).

fof(f15639,plain,
    ( spl0_195
  <=> ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(a,greatest_lower_bound(X0,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1248,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(a,greatest_lower_bound(X0,c))
    | ~ spl0_8
    | ~ spl0_10
    | ~ spl0_51
    | ~ spl0_54
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1247,f1122]) ).

fof(f1122,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(X0,c)) = greatest_lower_bound(a,greatest_lower_bound(X0,c))
    | ~ spl0_10
    | ~ spl0_51 ),
    inference(superposition,[],[f1115,f69]) ).

fof(f1247,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(b,greatest_lower_bound(X0,c))
    | ~ spl0_8
    | ~ spl0_54
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1220,f1166]) ).

fof(f1220,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(c,greatest_lower_bound(b,X0))
    | ~ spl0_8
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f60]) ).

fof(f15637,plain,
    ( spl0_194
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1221,f1152,f332,f15635]) ).

fof(f15635,plain,
    ( spl0_194
  <=> ! [X0] : greatest_lower_bound(b,X0) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f1221,plain,
    ( ! [X0] : greatest_lower_bound(b,X0) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,X0))
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(superposition,[],[f1153,f334]) ).

fof(f15633,plain,
    ( spl0_193
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1139,f1118,f72,f15631]) ).

fof(f15631,plain,
    ( spl0_193
  <=> ! [X0] : least_upper_bound(b,least_upper_bound(X0,c)) = least_upper_bound(a,least_upper_bound(X0,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f15587,plain,
    ( spl0_192
    | ~ spl0_10
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f1122,f1114,f68,f15585]) ).

fof(f15585,plain,
    ( spl0_192
  <=> ! [X0] : greatest_lower_bound(b,greatest_lower_bound(X0,c)) = greatest_lower_bound(a,greatest_lower_bound(X0,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f15583,plain,
    ( spl0_191
    | ~ spl0_14
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f777,f595,f84,f15581]) ).

fof(f15581,plain,
    ( spl0_191
  <=> ! [X0,X1] : identity = multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f777,plain,
    ( ! [X0,X1] : identity = multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(inverse(X0),X1))
    | ~ spl0_14
    | ~ spl0_43 ),
    inference(superposition,[],[f85,f596]) ).

fof(f15579,plain,
    ( spl0_190
    | ~ spl0_7
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f776,f595,f52,f15577]) ).

fof(f15577,plain,
    ( spl0_190
  <=> ! [X0,X1] : identity = multiply(least_upper_bound(inverse(X0),X1),greatest_lower_bound(X0,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f776,plain,
    ( ! [X0,X1] : identity = multiply(least_upper_bound(inverse(X0),X1),greatest_lower_bound(X0,inverse(X1)))
    | ~ spl0_7
    | ~ spl0_43 ),
    inference(superposition,[],[f53,f596]) ).

fof(f15575,plain,
    ( spl0_189
    | ~ spl0_14
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f726,f587,f84,f15573]) ).

fof(f15573,plain,
    ( spl0_189
  <=> ! [X0,X1] : identity = multiply(greatest_lower_bound(inverse(X0),X1),least_upper_bound(X0,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f726,plain,
    ( ! [X0,X1] : identity = multiply(greatest_lower_bound(inverse(X0),X1),least_upper_bound(X0,inverse(X1)))
    | ~ spl0_14
    | ~ spl0_41 ),
    inference(superposition,[],[f85,f588]) ).

fof(f15571,plain,
    ( spl0_188
    | ~ spl0_7
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f725,f587,f52,f15569]) ).

fof(f15569,plain,
    ( spl0_188
  <=> ! [X0,X1] : identity = multiply(least_upper_bound(X0,inverse(X1)),greatest_lower_bound(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f725,plain,
    ( ! [X0,X1] : identity = multiply(least_upper_bound(X0,inverse(X1)),greatest_lower_bound(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_41 ),
    inference(superposition,[],[f53,f588]) ).

fof(f15567,plain,
    ( spl0_187
    | ~ spl0_7
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f673,f583,f52,f15565]) ).

fof(f15565,plain,
    ( spl0_187
  <=> ! [X0,X1] : identity = multiply(multiply(inverse(X1),X0),multiply(inverse(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f673,plain,
    ( ! [X0,X1] : identity = multiply(multiply(inverse(X1),X0),multiply(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_40 ),
    inference(superposition,[],[f53,f584]) ).

fof(f15563,plain,
    ( spl0_186
    | ~ spl0_7
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f632,f579,f52,f15561]) ).

fof(f15561,plain,
    ( spl0_186
  <=> ! [X0,X1] : identity = multiply(multiply(X1,inverse(X0)),multiply(X0,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f632,plain,
    ( ! [X0,X1] : identity = multiply(multiply(X1,inverse(X0)),multiply(X0,inverse(X1)))
    | ~ spl0_7
    | ~ spl0_39 ),
    inference(superposition,[],[f53,f580]) ).

fof(f15559,plain,
    ( spl0_185
    | ~ spl0_33
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f562,f531,f441,f15557]) ).

fof(f15557,plain,
    ( spl0_185
  <=> ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f562,plain,
    ( ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_33
    | ~ spl0_38 ),
    inference(superposition,[],[f532,f442]) ).

fof(f15555,plain,
    ( spl0_184
    | ~ spl0_35
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f540,f527,f449,f15553]) ).

fof(f15553,plain,
    ( spl0_184
  <=> ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f540,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_35
    | ~ spl0_37 ),
    inference(superposition,[],[f528,f450]) ).

fof(f15551,plain,
    ( spl0_183
    | ~ spl0_18
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f349,f337,f142,f15549]) ).

fof(f15549,plain,
    ( spl0_183
  <=> ! [X0,X1] : inverse(multiply(X0,X1)) = inverse(multiply(X0,multiply(X1,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f337,plain,
    ( spl0_27
  <=> ! [X0] : inverse(X0) = inverse(multiply(X0,identity)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f349,plain,
    ( ! [X0,X1] : inverse(multiply(X0,X1)) = inverse(multiply(X0,multiply(X1,identity)))
    | ~ spl0_18
    | ~ spl0_27 ),
    inference(superposition,[],[f338,f143]) ).

fof(f338,plain,
    ( ! [X0] : inverse(X0) = inverse(multiply(X0,identity))
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f337]) ).

fof(f15508,plain,
    ( spl0_182
    | ~ spl0_19
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f346,f332,f154,f15506]) ).

fof(f15506,plain,
    ( spl0_182
  <=> ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(b,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f346,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(b,X0)
    | ~ spl0_19
    | ~ spl0_26 ),
    inference(superposition,[],[f155,f334]) ).

fof(f15504,plain,
    ( spl0_181
    | ~ spl0_20
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f344,f253,f158,f15502]) ).

fof(f15502,plain,
    ( spl0_181
  <=> ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(b,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f344,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(b,X0)
    | ~ spl0_20
    | ~ spl0_25 ),
    inference(superposition,[],[f159,f255]) ).

fof(f13809,plain,
    ( spl0_180
    | ~ spl0_9
    | ~ spl0_140
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f10844,f8811,f8791,f63,f13806]) ).

fof(f13806,plain,
    ( spl0_180
  <=> least_upper_bound(a,c) = least_upper_bound(c,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f8811,plain,
    ( spl0_145
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f10844,plain,
    ( least_upper_bound(a,c) = least_upper_bound(c,b)
    | ~ spl0_9
    | ~ spl0_140
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f10758,f8792]) ).

fof(f10758,plain,
    ( least_upper_bound(c,b) = least_upper_bound(c,least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_145 ),
    inference(superposition,[],[f8812,f65]) ).

fof(f8812,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f8811]) ).

fof(f12011,plain,
    ( spl0_179
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_35
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f3562,f2408,f449,f374,f35,f12009]) ).

fof(f12009,plain,
    ( spl0_179
  <=> ! [X0] : greatest_lower_bound(identity,X0) = multiply(X0,inverse(least_upper_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f3562,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(X0,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_35
    | ~ spl0_83 ),
    inference(forward_demodulation,[],[f3561,f375]) ).

fof(f3561,plain,
    ( ! [X0] : greatest_lower_bound(identity,multiply(X0,identity)) = multiply(X0,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_3
    | ~ spl0_35
    | ~ spl0_83 ),
    inference(forward_demodulation,[],[f3513,f36]) ).

fof(f3513,plain,
    ( ! [X0] : greatest_lower_bound(identity,multiply(inverse(inverse(X0)),identity)) = multiply(inverse(inverse(X0)),inverse(least_upper_bound(identity,X0)))
    | ~ spl0_35
    | ~ spl0_83 ),
    inference(superposition,[],[f2409,f450]) ).

fof(f12007,plain,
    ( spl0_178
    | ~ spl0_30
    | ~ spl0_35
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f3484,f2404,f449,f374,f12005]) ).

fof(f12005,plain,
    ( spl0_178
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f3484,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(X1,inverse(least_upper_bound(identity,X0)))) = X1
    | ~ spl0_30
    | ~ spl0_35
    | ~ spl0_82 ),
    inference(forward_demodulation,[],[f3428,f375]) ).

fof(f3428,plain,
    ( ! [X0,X1] : multiply(X1,identity) = least_upper_bound(multiply(X1,identity),multiply(X1,inverse(least_upper_bound(identity,X0))))
    | ~ spl0_35
    | ~ spl0_82 ),
    inference(superposition,[],[f2405,f450]) ).

fof(f12003,plain,
    ( spl0_177
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_36
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f3292,f2359,f453,f374,f35,f12001]) ).

fof(f12001,plain,
    ( spl0_177
  <=> ! [X0] : greatest_lower_bound(identity,X0) = multiply(X0,inverse(least_upper_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f3292,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(X0,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_36
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3291,f375]) ).

fof(f3291,plain,
    ( ! [X0] : greatest_lower_bound(identity,multiply(X0,identity)) = multiply(X0,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_3
    | ~ spl0_36
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f3232,f36]) ).

fof(f3232,plain,
    ( ! [X0] : greatest_lower_bound(identity,multiply(inverse(inverse(X0)),identity)) = multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,identity)))
    | ~ spl0_36
    | ~ spl0_80 ),
    inference(superposition,[],[f2360,f454]) ).

fof(f11999,plain,
    ( spl0_176
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_33
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f3176,f2355,f441,f374,f35,f11997]) ).

fof(f11997,plain,
    ( spl0_176
  <=> ! [X0] : least_upper_bound(identity,X0) = multiply(X0,inverse(greatest_lower_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f3176,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(X0,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_33
    | ~ spl0_79 ),
    inference(forward_demodulation,[],[f3175,f375]) ).

fof(f3175,plain,
    ( ! [X0] : least_upper_bound(identity,multiply(X0,identity)) = multiply(X0,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_3
    | ~ spl0_33
    | ~ spl0_79 ),
    inference(forward_demodulation,[],[f3134,f36]) ).

fof(f3134,plain,
    ( ! [X0] : least_upper_bound(identity,multiply(inverse(inverse(X0)),identity)) = multiply(inverse(inverse(X0)),inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_33
    | ~ spl0_79 ),
    inference(superposition,[],[f2356,f442]) ).

fof(f11995,plain,
    ( spl0_175
    | ~ spl0_30
    | ~ spl0_33
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f3109,f2351,f441,f374,f11993]) ).

fof(f11993,plain,
    ( spl0_175
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(X1,inverse(greatest_lower_bound(identity,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f3109,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(X1,inverse(greatest_lower_bound(identity,X0)))) = X1
    | ~ spl0_30
    | ~ spl0_33
    | ~ spl0_78 ),
    inference(forward_demodulation,[],[f3061,f375]) ).

fof(f3061,plain,
    ( ! [X0,X1] : multiply(X1,identity) = greatest_lower_bound(multiply(X1,identity),multiply(X1,inverse(greatest_lower_bound(identity,X0))))
    | ~ spl0_33
    | ~ spl0_78 ),
    inference(superposition,[],[f2352,f442]) ).

fof(f11990,plain,
    ( spl0_174
    | ~ spl0_7
    | ~ spl0_25
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2939,f2343,f253,f52,f11987]) ).

fof(f11987,plain,
    ( spl0_174
  <=> identity = least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f2939,plain,
    ( identity = least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))
    | ~ spl0_7
    | ~ spl0_25
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2897,f53]) ).

fof(f2897,plain,
    ( least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))) = multiply(inverse(b),b)
    | ~ spl0_25
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f255]) ).

fof(f11985,plain,
    ( spl0_173
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_34
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2937,f2343,f445,f374,f35,f11983]) ).

fof(f11983,plain,
    ( spl0_173
  <=> ! [X0] : least_upper_bound(identity,X0) = multiply(X0,inverse(greatest_lower_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f2937,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(X0,inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_34
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2936,f375]) ).

fof(f2936,plain,
    ( ! [X0] : least_upper_bound(identity,multiply(X0,identity)) = multiply(X0,inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_3
    | ~ spl0_34
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2892,f36]) ).

fof(f2892,plain,
    ( ! [X0] : least_upper_bound(identity,multiply(inverse(inverse(X0)),identity)) = multiply(inverse(inverse(X0)),inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_34
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f446]) ).

fof(f11980,plain,
    ( spl0_172
    | ~ spl0_7
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f2935,f2343,f619,f579,f98,f52,f11978]) ).

fof(f11978,plain,
    ( spl0_172
  <=> ! [X0,X1] : identity = least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f2935,plain,
    ( ! [X0,X1] : identity = least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1))))
    | ~ spl0_7
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2934,f53]) ).

fof(f2934,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(X0)) = least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1))))
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2933,f580]) ).

fof(f2933,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(X0)) = least_upper_bound(identity,inverse(multiply(least_upper_bound(X0,X1),inverse(X0))))
    | ~ spl0_15
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(forward_demodulation,[],[f2891,f99]) ).

fof(f2891,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(X0)) = least_upper_bound(identity,multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1))))
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(superposition,[],[f2344,f620]) ).

fof(f11975,plain,
    ( spl0_171
    | ~ spl0_7
    | ~ spl0_49
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f2040,f1980,f619,f52,f11973]) ).

fof(f11973,plain,
    ( spl0_171
  <=> ! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f2040,plain,
    ( ! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0))
    | ~ spl0_7
    | ~ spl0_49
    | ~ spl0_68 ),
    inference(forward_demodulation,[],[f2006,f53]) ).

fof(f2006,plain,
    ( ! [X0,X1] : multiply(inverse(X0),X0) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0))
    | ~ spl0_49
    | ~ spl0_68 ),
    inference(superposition,[],[f1981,f620]) ).

fof(f11971,plain,
    ( spl0_170
    | ~ spl0_7
    | ~ spl0_36
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1935,f1202,f453,f52,f11969]) ).

fof(f11969,plain,
    ( spl0_170
  <=> ! [X0] : greatest_lower_bound(identity,X0) = multiply(inverse(least_upper_bound(X0,identity)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f1935,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(inverse(least_upper_bound(X0,identity)),X0)
    | ~ spl0_7
    | ~ spl0_36
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1887,f454]) ).

fof(f1887,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(greatest_lower_bound(inverse(X0),identity),X0)
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(superposition,[],[f1203,f53]) ).

fof(f11967,plain,
    ( spl0_169
    | ~ spl0_8
    | ~ spl0_139
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f10356,f8799,f8787,f58,f11964]) ).

fof(f11964,plain,
    ( spl0_169
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(c,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f8799,plain,
    ( spl0_142
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f10356,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(c,b)
    | ~ spl0_8
    | ~ spl0_139
    | ~ spl0_142 ),
    inference(forward_demodulation,[],[f10272,f8788]) ).

fof(f10272,plain,
    ( greatest_lower_bound(c,b) = greatest_lower_bound(c,greatest_lower_bound(a,c))
    | ~ spl0_8
    | ~ spl0_142 ),
    inference(superposition,[],[f8800,f60]) ).

fof(f8800,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f8799]) ).

fof(f11962,plain,
    ( spl0_168
    | ~ spl0_7
    | ~ spl0_35
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1860,f1198,f449,f52,f11960]) ).

fof(f11960,plain,
    ( spl0_168
  <=> ! [X0] : greatest_lower_bound(X0,identity) = multiply(inverse(least_upper_bound(identity,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1860,plain,
    ( ! [X0] : greatest_lower_bound(X0,identity) = multiply(inverse(least_upper_bound(identity,X0)),X0)
    | ~ spl0_7
    | ~ spl0_35
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1816,f450]) ).

fof(f1816,plain,
    ( ! [X0] : greatest_lower_bound(X0,identity) = multiply(greatest_lower_bound(identity,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_65 ),
    inference(superposition,[],[f1199,f53]) ).

fof(f11958,plain,
    ( spl0_167
    | ~ spl0_7
    | ~ spl0_34
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1773,f1194,f445,f52,f11956]) ).

fof(f11956,plain,
    ( spl0_167
  <=> ! [X0] : least_upper_bound(identity,X0) = multiply(inverse(greatest_lower_bound(X0,identity)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1773,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(inverse(greatest_lower_bound(X0,identity)),X0)
    | ~ spl0_7
    | ~ spl0_34
    | ~ spl0_64 ),
    inference(forward_demodulation,[],[f1729,f446]) ).

fof(f1729,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(least_upper_bound(inverse(X0),identity),X0)
    | ~ spl0_7
    | ~ spl0_64 ),
    inference(superposition,[],[f1195,f53]) ).

fof(f11954,plain,
    ( spl0_166
    | ~ spl0_7
    | ~ spl0_33
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1707,f1186,f441,f52,f11952]) ).

fof(f11952,plain,
    ( spl0_166
  <=> ! [X0] : least_upper_bound(X0,identity) = multiply(inverse(greatest_lower_bound(identity,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f1707,plain,
    ( ! [X0] : least_upper_bound(X0,identity) = multiply(inverse(greatest_lower_bound(identity,X0)),X0)
    | ~ spl0_7
    | ~ spl0_33
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1667,f442]) ).

fof(f1667,plain,
    ( ! [X0] : least_upper_bound(X0,identity) = multiply(least_upper_bound(identity,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f53]) ).

fof(f11950,plain,
    ( spl0_165
    | ~ spl0_9
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f1079,f619,f63,f11947]) ).

fof(f11947,plain,
    ( spl0_165
  <=> inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1079,plain,
    ( inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,c)))
    | ~ spl0_9
    | ~ spl0_49 ),
    inference(superposition,[],[f620,f65]) ).

fof(f11945,plain,
    ( spl0_164
    | ~ spl0_11
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f957,f611,f72,f11943]) ).

fof(f11943,plain,
    ( spl0_164
  <=> ! [X0,X1] : greatest_lower_bound(inverse(X0),X1) = inverse(least_upper_bound(inverse(X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f957,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(X0),X1) = inverse(least_upper_bound(inverse(X1),X0))
    | ~ spl0_11
    | ~ spl0_47 ),
    inference(superposition,[],[f612,f73]) ).

fof(f11941,plain,
    ( spl0_163
    | ~ spl0_11
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f899,f607,f72,f11939]) ).

fof(f11939,plain,
    ( spl0_163
  <=> ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f899,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(X1,inverse(X0)))
    | ~ spl0_11
    | ~ spl0_46 ),
    inference(superposition,[],[f608,f73]) ).

fof(f11937,plain,
    ( spl0_162
    | ~ spl0_8
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f859,f603,f58,f11934]) ).

fof(f11934,plain,
    ( spl0_162
  <=> inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f859,plain,
    ( inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,c)))
    | ~ spl0_8
    | ~ spl0_45 ),
    inference(superposition,[],[f604,f60]) ).

fof(f11932,plain,
    ( spl0_161
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f768,f595,f68,f11930]) ).

fof(f11930,plain,
    ( spl0_161
  <=> ! [X0,X1] : least_upper_bound(inverse(X0),X1) = inverse(greatest_lower_bound(inverse(X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f768,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(X0),X1) = inverse(greatest_lower_bound(inverse(X1),X0))
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(superposition,[],[f596,f69]) ).

fof(f11928,plain,
    ( spl0_160
    | ~ spl0_10
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f719,f587,f68,f11926]) ).

fof(f11926,plain,
    ( spl0_160
  <=> ! [X0,X1] : least_upper_bound(X0,inverse(X1)) = inverse(greatest_lower_bound(X1,inverse(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f719,plain,
    ( ! [X0,X1] : least_upper_bound(X0,inverse(X1)) = inverse(greatest_lower_bound(X1,inverse(X0)))
    | ~ spl0_10
    | ~ spl0_41 ),
    inference(superposition,[],[f588,f69]) ).

fof(f11924,plain,
    ( spl0_159
    | ~ spl0_16
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f402,f378,f102,f11922]) ).

fof(f11922,plain,
    ( spl0_159
  <=> ! [X0,X1] : inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f402,plain,
    ( ! [X0,X1] : inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_16
    | ~ spl0_31 ),
    inference(superposition,[],[f379,f103]) ).

fof(f11920,plain,
    ( spl0_158
    | ~ spl0_25
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f10024,f8791,f253,f11917]) ).

fof(f11917,plain,
    ( spl0_158
  <=> b = least_upper_bound(greatest_lower_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f10024,plain,
    ( b = least_upper_bound(greatest_lower_bound(a,c),b)
    | ~ spl0_25
    | ~ spl0_140 ),
    inference(superposition,[],[f8792,f255]) ).

fof(f11915,plain,
    ( spl0_157
    | ~ spl0_17
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f387,f370,f106,f11913]) ).

fof(f11913,plain,
    ( spl0_157
  <=> ! [X0,X1] : inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f387,plain,
    ( ! [X0,X1] : inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_17
    | ~ spl0_29 ),
    inference(superposition,[],[f371,f107]) ).

fof(f11910,plain,
    ( spl0_156
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f166,f142,f84,f11908]) ).

fof(f11908,plain,
    ( spl0_156
  <=> ! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f166,plain,
    ( ! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1))))
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(superposition,[],[f143,f85]) ).

fof(f10727,plain,
    ( spl0_155
    | ~ spl0_26
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f9889,f8787,f332,f10724]) ).

fof(f10724,plain,
    ( spl0_155
  <=> b = greatest_lower_bound(least_upper_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f9889,plain,
    ( b = greatest_lower_bound(least_upper_bound(a,c),b)
    | ~ spl0_26
    | ~ spl0_139 ),
    inference(superposition,[],[f8788,f334]) ).

fof(f9012,plain,
    ( spl0_154
    | ~ spl0_4
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f3381,f2400,f40,f9010]) ).

fof(f9010,plain,
    ( spl0_154
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(identity,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f40,plain,
    ( spl0_4
  <=> ! [X0] : multiply(identity,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f3381,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(identity,greatest_lower_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_81 ),
    inference(forward_demodulation,[],[f3325,f41]) ).

fof(f41,plain,
    ( ! [X0] : multiply(identity,X0) = X0
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f40]) ).

fof(f3325,plain,
    ( ! [X0,X1] : multiply(identity,greatest_lower_bound(X0,X1)) = greatest_lower_bound(multiply(identity,X1),X0)
    | ~ spl0_4
    | ~ spl0_81 ),
    inference(superposition,[],[f2401,f41]) ).

fof(f9008,plain,
    ( spl0_153
    | ~ spl0_4
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f3018,f2347,f40,f9006]) ).

fof(f9006,plain,
    ( spl0_153
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = multiply(identity,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f3018,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = multiply(identity,least_upper_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_77 ),
    inference(forward_demodulation,[],[f2966,f41]) ).

fof(f2966,plain,
    ( ! [X0,X1] : multiply(identity,least_upper_bound(X0,X1)) = least_upper_bound(multiply(identity,X1),X0)
    | ~ spl0_4
    | ~ spl0_77 ),
    inference(superposition,[],[f2348,f41]) ).

fof(f9004,plain,
    ( spl0_152
    | ~ spl0_4
    | ~ spl0_10
    | ~ spl0_13
    | ~ spl0_62
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1938,f1202,f1186,f80,f68,f40,f9002]) ).

fof(f9002,plain,
    ( spl0_152
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1938,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = X1
    | ~ spl0_4
    | ~ spl0_10
    | ~ spl0_13
    | ~ spl0_62
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1937,f41]) ).

fof(f1937,plain,
    ( ! [X0,X1] : multiply(identity,X1) = greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_10
    | ~ spl0_13
    | ~ spl0_62
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1936,f81]) ).

fof(f1936,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,least_upper_bound(identity,X0)),X1) = greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_10
    | ~ spl0_62
    | ~ spl0_66 ),
    inference(forward_demodulation,[],[f1888,f69]) ).

fof(f1888,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(least_upper_bound(identity,X0),identity),X1) = greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_62
    | ~ spl0_66 ),
    inference(superposition,[],[f1203,f1187]) ).

fof(f9000,plain,
    ( spl0_151
    | ~ spl0_4
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1875,f1198,f1194,f76,f72,f40,f8998]) ).

fof(f8998,plain,
    ( spl0_151
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1875,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = X1
    | ~ spl0_4
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1874,f41]) ).

fof(f1874,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1873,f77]) ).

fof(f1873,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,greatest_lower_bound(identity,X0)),X1) = least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_11
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(forward_demodulation,[],[f1838,f73]) ).

fof(f1838,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(greatest_lower_bound(identity,X0),identity),X1) = least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(superposition,[],[f1195,f1199]) ).

fof(f8996,plain,
    ( spl0_150
    | ~ spl0_31
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f1760,f1194,f378,f8994]) ).

fof(f8994,plain,
    ( spl0_150
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(least_upper_bound(X0,identity),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1760,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(least_upper_bound(X0,identity),X1)) = X1
    | ~ spl0_31
    | ~ spl0_64 ),
    inference(superposition,[],[f379,f1195]) ).

fof(f8992,plain,
    ( spl0_149
    | ~ spl0_4
    | ~ spl0_29
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1704,f1186,f370,f40,f8990]) ).

fof(f8990,plain,
    ( spl0_149
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1704,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1)) = X1
    | ~ spl0_4
    | ~ spl0_29
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1660,f41]) ).

fof(f1660,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1))
    | ~ spl0_29
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f371]) ).

fof(f8988,plain,
    ( spl0_148
    | ~ spl0_4
    | ~ spl0_12
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1703,f1186,f76,f40,f8986]) ).

fof(f8986,plain,
    ( spl0_148
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1703,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1)) = X1
    | ~ spl0_4
    | ~ spl0_12
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f1659,f41]) ).

fof(f1659,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1))
    | ~ spl0_12
    | ~ spl0_62 ),
    inference(superposition,[],[f1187,f77]) ).

fof(f8984,plain,
    ( spl0_147
    | ~ spl0_13
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1688,f1186,f80,f8982]) ).

fof(f8982,plain,
    ( spl0_147
  <=> ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1688,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0
    | ~ spl0_13
    | ~ spl0_62 ),
    inference(superposition,[],[f81,f1187]) ).

fof(f8817,plain,
    ( spl0_146
    | ~ spl0_5
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_38
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1629,f1182,f531,f158,f72,f44,f8815]) ).

fof(f8815,plain,
    ( spl0_146
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1629,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X1,X0))
    | ~ spl0_5
    | ~ spl0_11
    | ~ spl0_20
    | ~ spl0_38
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f1628,f557]) ).

fof(f1628,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,least_upper_bound(X1,X0)))
    | ~ spl0_5
    | ~ spl0_20
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f1558,f159]) ).

fof(f1558,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(least_upper_bound(X0,X1),X0))
    | ~ spl0_5
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f45]) ).

fof(f8813,plain,
    ( spl0_145
    | ~ spl0_38
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f1585,f1182,f531,f8811]) ).

fof(f1585,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_38
    | ~ spl0_61 ),
    inference(superposition,[],[f1183,f532]) ).

fof(f8809,plain,
    ( spl0_144
    | ~ spl0_6
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_37
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1400,f1165,f527,f154,f68,f48,f8807]) ).

fof(f8807,plain,
    ( spl0_144
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1400,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,X0))
    | ~ spl0_6
    | ~ spl0_10
    | ~ spl0_19
    | ~ spl0_37
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1399,f535]) ).

fof(f1399,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,greatest_lower_bound(X1,X0)))
    | ~ spl0_6
    | ~ spl0_19
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1331,f155]) ).

fof(f1331,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(greatest_lower_bound(X0,X1),X0))
    | ~ spl0_6
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f49]) ).

fof(f8805,plain,
    ( spl0_143
    | ~ spl0_12
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1370,f1165,f76,f8803]) ).

fof(f8803,plain,
    ( spl0_143
  <=> ! [X2,X0,X1] : least_upper_bound(X0,greatest_lower_bound(X2,greatest_lower_bound(X0,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1370,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,greatest_lower_bound(X2,greatest_lower_bound(X0,X1))) = X0
    | ~ spl0_12
    | ~ spl0_57 ),
    inference(superposition,[],[f77,f1166]) ).

fof(f8801,plain,
    ( spl0_142
    | ~ spl0_37
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1358,f1165,f527,f8799]) ).

fof(f1358,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_37
    | ~ spl0_57 ),
    inference(superposition,[],[f1166,f528]) ).

fof(f8797,plain,
    ( spl0_141
    | ~ spl0_13
    | ~ spl0_31
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1298,f1156,f378,f80,f8795]) ).

fof(f8795,plain,
    ( spl0_141
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X2,least_upper_bound(X0,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1298,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X2,least_upper_bound(X0,X1))) = X0
    | ~ spl0_13
    | ~ spl0_31
    | ~ spl0_55 ),
    inference(forward_demodulation,[],[f1281,f81]) ).

fof(f1281,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = greatest_lower_bound(X0,least_upper_bound(X2,least_upper_bound(X0,X1)))
    | ~ spl0_31
    | ~ spl0_55 ),
    inference(superposition,[],[f1157,f379]) ).

fof(f8793,plain,
    ( spl0_140
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f557,f531,f72,f8791]) ).

fof(f8789,plain,
    ( spl0_139
    | ~ spl0_10
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f535,f527,f68,f8787]) ).

fof(f8785,plain,
    ( spl0_138
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f407,f378,f370,f8783]) ).

fof(f8783,plain,
    ( spl0_138
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(least_upper_bound(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f407,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(least_upper_bound(X1,X0),X0)
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(superposition,[],[f371,f379]) ).

fof(f8781,plain,
    ( spl0_137
    | ~ spl0_20
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f403,f378,f158,f8779]) ).

fof(f8779,plain,
    ( spl0_137
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))) = X2
    | ~ spl0_20
    | ~ spl0_31 ),
    inference(superposition,[],[f379,f159]) ).

fof(f8777,plain,
    ( spl0_136
    | ~ spl0_3
    | ~ spl0_40
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f7672,f5714,f583,f35,f8775]) ).

fof(f8775,plain,
    ( spl0_136
  <=> ! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f7672,plain,
    ( ! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1
    | ~ spl0_3
    | ~ spl0_40
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f7671,f36]) ).

fof(f7671,plain,
    ( ! [X0,X1] : inverse(inverse(X1)) = multiply(multiply(X1,inverse(X0)),X0)
    | ~ spl0_3
    | ~ spl0_40
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f7592,f36]) ).

fof(f7592,plain,
    ( ! [X0,X1] : inverse(inverse(X1)) = multiply(inverse(inverse(multiply(X1,inverse(X0)))),X0)
    | ~ spl0_40
    | ~ spl0_116 ),
    inference(superposition,[],[f584,f5715]) ).

fof(f8773,plain,
    ( spl0_135
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f399,f378,f370,f8771]) ).

fof(f8771,plain,
    ( spl0_135
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(greatest_lower_bound(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f399,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(greatest_lower_bound(X1,X0),X0)
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(superposition,[],[f379,f371]) ).

fof(f8769,plain,
    ( spl0_134
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f398,f378,f76,f8767]) ).

fof(f8767,plain,
    ( spl0_134
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(greatest_lower_bound(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f398,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(greatest_lower_bound(X0,X1),X0)
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(superposition,[],[f379,f77]) ).

fof(f8765,plain,
    ( spl0_133
    | ~ spl0_19
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f388,f370,f154,f8763]) ).

fof(f8763,plain,
    ( spl0_133
  <=> ! [X2,X0,X1] : least_upper_bound(X2,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f388,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) = X2
    | ~ spl0_19
    | ~ spl0_29 ),
    inference(superposition,[],[f371,f155]) ).

fof(f8761,plain,
    ( spl0_132
    | ~ spl0_13
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f384,f370,f80,f8759]) ).

fof(f8759,plain,
    ( spl0_132
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f384,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0)
    | ~ spl0_13
    | ~ spl0_29 ),
    inference(superposition,[],[f371,f81]) ).

fof(f7995,plain,
    ( spl0_131
    | ~ spl0_3
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f7605,f5714,f412,f35,f7993]) ).

fof(f7993,plain,
    ( spl0_131
  <=> ! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f7605,plain,
    ( ! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0
    | ~ spl0_3
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f7509,f36]) ).

fof(f7509,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(X0,X1),inverse(X1))
    | ~ spl0_32
    | ~ spl0_116 ),
    inference(superposition,[],[f5715,f413]) ).

fof(f7432,plain,
    ( spl0_130
    | ~ spl0_13
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1144,f1118,f80,f7430]) ).

fof(f1144,plain,
    ( ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X0)))
    | ~ spl0_13
    | ~ spl0_52 ),
    inference(superposition,[],[f81,f1119]) ).

fof(f7428,plain,
    ( spl0_129
    | ~ spl0_12
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f1127,f1114,f76,f7426]) ).

fof(f1127,plain,
    ( ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0)))
    | ~ spl0_12
    | ~ spl0_51 ),
    inference(superposition,[],[f77,f1115]) ).

fof(f7424,plain,
    ( spl0_128
    | ~ spl0_17
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1023,f615,f106,f7422]) ).

fof(f7422,plain,
    ( spl0_128
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1023,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0))
    | ~ spl0_17
    | ~ spl0_48 ),
    inference(superposition,[],[f616,f107]) ).

fof(f7420,plain,
    ( spl0_127
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f819,f599,f102,f7418]) ).

fof(f819,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0))
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(superposition,[],[f600,f103]) ).

fof(f7416,plain,
    ( spl0_126
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f665,f583,f412,f7414]) ).

fof(f7414,plain,
    ( spl0_126
  <=> ! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f665,plain,
    ( ! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0)
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f584,f413]) ).

fof(f7412,plain,
    ( spl0_125
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f568,f531,f63,f7409]) ).

fof(f7409,plain,
    ( spl0_125
  <=> least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f568,plain,
    ( least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(superposition,[],[f532,f65]) ).

fof(f7407,plain,
    ( spl0_124
    | ~ spl0_8
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f546,f527,f58,f7404]) ).

fof(f7404,plain,
    ( spl0_124
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f546,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_8
    | ~ spl0_37 ),
    inference(superposition,[],[f528,f60]) ).

fof(f7402,plain,
    ( spl0_123
    | ~ spl0_11
    | ~ spl0_27
    | ~ spl0_30
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f524,f453,f374,f337,f72,f7400]) ).

fof(f7400,plain,
    ( spl0_123
  <=> ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f524,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity)
    | ~ spl0_11
    | ~ spl0_27
    | ~ spl0_30
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f523,f375]) ).

fof(f523,plain,
    ( ! [X0] : greatest_lower_bound(inverse(X0),identity) = inverse(least_upper_bound(identity,multiply(X0,identity)))
    | ~ spl0_11
    | ~ spl0_27
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f512,f73]) ).

fof(f512,plain,
    ( ! [X0] : greatest_lower_bound(inverse(X0),identity) = inverse(least_upper_bound(multiply(X0,identity),identity))
    | ~ spl0_27
    | ~ spl0_36 ),
    inference(superposition,[],[f454,f338]) ).

fof(f7398,plain,
    ( spl0_122
    | ~ spl0_10
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f513,f453,f68,f7396]) ).

fof(f7396,plain,
    ( spl0_122
  <=> ! [X0] : greatest_lower_bound(identity,inverse(X0)) = inverse(least_upper_bound(X0,identity)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f513,plain,
    ( ! [X0] : greatest_lower_bound(identity,inverse(X0)) = inverse(least_upper_bound(X0,identity))
    | ~ spl0_10
    | ~ spl0_36 ),
    inference(superposition,[],[f454,f69]) ).

fof(f7394,plain,
    ( spl0_121
    | ~ spl0_10
    | ~ spl0_27
    | ~ spl0_30
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f498,f445,f374,f337,f68,f7392]) ).

fof(f7392,plain,
    ( spl0_121
  <=> ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f498,plain,
    ( ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(inverse(X0),identity)
    | ~ spl0_10
    | ~ spl0_27
    | ~ spl0_30
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f497,f375]) ).

fof(f497,plain,
    ( ! [X0] : least_upper_bound(inverse(X0),identity) = inverse(greatest_lower_bound(identity,multiply(X0,identity)))
    | ~ spl0_10
    | ~ spl0_27
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f486,f69]) ).

fof(f486,plain,
    ( ! [X0] : least_upper_bound(inverse(X0),identity) = inverse(greatest_lower_bound(multiply(X0,identity),identity))
    | ~ spl0_27
    | ~ spl0_34 ),
    inference(superposition,[],[f446,f338]) ).

fof(f7002,plain,
    ( spl0_120
    | ~ spl0_18
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f277,f215,f142,f7000]) ).

fof(f7000,plain,
    ( spl0_120
  <=> ! [X0,X3,X2,X1] : greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3))) = multiply(X0,multiply(X1,greatest_lower_bound(X2,X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f277,plain,
    ( ! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3))) = multiply(X0,multiply(X1,greatest_lower_bound(X2,X3)))
    | ~ spl0_18
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f276,f143]) ).

fof(f276,plain,
    ( ! [X2,X3,X0,X1] : multiply(multiply(X0,X1),greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3)))
    | ~ spl0_18
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f261,f143]) ).

fof(f261,plain,
    ( ! [X2,X3,X0,X1] : multiply(multiply(X0,X1),greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X3))
    | ~ spl0_18
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f143]) ).

fof(f6998,plain,
    ( spl0_119
    | ~ spl0_11
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f487,f445,f72,f6996]) ).

fof(f6996,plain,
    ( spl0_119
  <=> ! [X0] : least_upper_bound(identity,inverse(X0)) = inverse(greatest_lower_bound(X0,identity)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f487,plain,
    ( ! [X0] : least_upper_bound(identity,inverse(X0)) = inverse(greatest_lower_bound(X0,identity))
    | ~ spl0_11
    | ~ spl0_34 ),
    inference(superposition,[],[f446,f73]) ).

fof(f6994,plain,
    ( spl0_118
    | ~ spl0_18
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f246,f211,f142,f6992]) ).

fof(f6992,plain,
    ( spl0_118
  <=> ! [X0,X3,X2,X1] : least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3))) = multiply(X0,multiply(X1,least_upper_bound(X2,X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f246,plain,
    ( ! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3))) = multiply(X0,multiply(X1,least_upper_bound(X2,X3)))
    | ~ spl0_18
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f245,f143]) ).

fof(f245,plain,
    ( ! [X2,X3,X0,X1] : multiply(multiply(X0,X1),least_upper_bound(X2,X3)) = least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3)))
    | ~ spl0_18
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f230,f143]) ).

fof(f230,plain,
    ( ! [X2,X3,X0,X1] : multiply(multiply(X0,X1),least_upper_bound(X2,X3)) = least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X3))
    | ~ spl0_18
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f143]) ).

fof(f5720,plain,
    ( spl0_117
    | ~ spl0_19
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f323,f223,f154,f5718]) ).

fof(f5718,plain,
    ( spl0_117
  <=> ! [X0,X3,X2,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X2,X1),X3)) = greatest_lower_bound(multiply(greatest_lower_bound(X0,X2),X1),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f323,plain,
    ( ! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X2,X1),X3)) = greatest_lower_bound(multiply(greatest_lower_bound(X0,X2),X1),X3)
    | ~ spl0_19
    | ~ spl0_24 ),
    inference(superposition,[],[f155,f224]) ).

fof(f5716,plain,
    ( spl0_116
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f438,f412,f98,f35,f5714]) ).

fof(f438,plain,
    ( ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0)))
    | ~ spl0_3
    | ~ spl0_15
    | ~ spl0_32 ),
    inference(forward_demodulation,[],[f422,f36]) ).

fof(f422,plain,
    ( ! [X0,X1] : inverse(X1) = multiply(inverse(inverse(X0)),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_32 ),
    inference(superposition,[],[f413,f99]) ).

fof(f5712,plain,
    ( spl0_115
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f316,f223,f142,f5710]) ).

fof(f5710,plain,
    ( spl0_115
  <=> ! [X0,X3,X2,X1] : multiply(greatest_lower_bound(X3,multiply(X0,X1)),X2) = greatest_lower_bound(multiply(X3,X2),multiply(X0,multiply(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f316,plain,
    ( ! [X2,X3,X0,X1] : multiply(greatest_lower_bound(X3,multiply(X0,X1)),X2) = greatest_lower_bound(multiply(X3,X2),multiply(X0,multiply(X1,X2)))
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f143]) ).

fof(f5708,plain,
    ( spl0_114
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f311,f223,f142,f5706]) ).

fof(f5706,plain,
    ( spl0_114
  <=> ! [X0,X3,X2,X1] : multiply(greatest_lower_bound(multiply(X0,X1),X3),X2) = greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(X3,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f311,plain,
    ( ! [X2,X3,X0,X1] : multiply(greatest_lower_bound(multiply(X0,X1),X3),X2) = greatest_lower_bound(multiply(X0,multiply(X1,X2)),multiply(X3,X2))
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f143]) ).

fof(f5704,plain,
    ( spl0_113
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f299,f219,f158,f5702]) ).

fof(f5702,plain,
    ( spl0_113
  <=> ! [X0,X3,X2,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X2,X1),X3)) = least_upper_bound(multiply(least_upper_bound(X0,X2),X1),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f299,plain,
    ( ! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X2,X1),X3)) = least_upper_bound(multiply(least_upper_bound(X0,X2),X1),X3)
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(superposition,[],[f159,f220]) ).

fof(f5700,plain,
    ( spl0_112
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f292,f219,f142,f5698]) ).

fof(f5698,plain,
    ( spl0_112
  <=> ! [X0,X3,X2,X1] : multiply(least_upper_bound(X3,multiply(X0,X1)),X2) = least_upper_bound(multiply(X3,X2),multiply(X0,multiply(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f292,plain,
    ( ! [X2,X3,X0,X1] : multiply(least_upper_bound(X3,multiply(X0,X1)),X2) = least_upper_bound(multiply(X3,X2),multiply(X0,multiply(X1,X2)))
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f143]) ).

fof(f5696,plain,
    ( spl0_111
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f287,f219,f142,f5694]) ).

fof(f5694,plain,
    ( spl0_111
  <=> ! [X0,X3,X2,X1] : multiply(least_upper_bound(multiply(X0,X1),X3),X2) = least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(X3,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f287,plain,
    ( ! [X2,X3,X0,X1] : multiply(least_upper_bound(multiply(X0,X1),X3),X2) = least_upper_bound(multiply(X0,multiply(X1,X2)),multiply(X3,X2))
    | ~ spl0_18
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f143]) ).

fof(f5692,plain,
    ( spl0_110
    | ~ spl0_19
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f271,f215,f154,f5690]) ).

fof(f5690,plain,
    ( spl0_110
  <=> ! [X0,X3,X2,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f271,plain,
    ( ! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3)
    | ~ spl0_19
    | ~ spl0_22 ),
    inference(superposition,[],[f155,f216]) ).

fof(f5688,plain,
    ( spl0_109
    | ~ spl0_20
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f240,f211,f158,f5686]) ).

fof(f5686,plain,
    ( spl0_109
  <=> ! [X0,X3,X2,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f240,plain,
    ( ! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3)
    | ~ spl0_20
    | ~ spl0_21 ),
    inference(superposition,[],[f159,f212]) ).

fof(f5548,plain,
    ( spl0_108
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_86
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f5544,f5541,f2420,f587,f579,f98,f5546]) ).

fof(f5546,plain,
    ( spl0_108
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1)) = inverse(multiply(X1,least_upper_bound(X0,inverse(X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f5541,plain,
    ( spl0_107
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1)) = greatest_lower_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f5544,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1)) = inverse(multiply(X1,least_upper_bound(X0,inverse(X2))))
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_86
    | ~ spl0_107 ),
    inference(forward_demodulation,[],[f5542,f3922]) ).

fof(f3922,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0))) = inverse(multiply(X1,least_upper_bound(X0,inverse(X2))))
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_41
    | ~ spl0_86 ),
    inference(forward_demodulation,[],[f3870,f738]) ).

fof(f738,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),inverse(X2)) = inverse(multiply(X2,least_upper_bound(X0,inverse(X1))))
    | ~ spl0_39
    | ~ spl0_41 ),
    inference(superposition,[],[f580,f588]) ).

fof(f3870,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = greatest_lower_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_86 ),
    inference(superposition,[],[f2421,f99]) ).

fof(f5542,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1)) = greatest_lower_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f5541]) ).

fof(f5543,plain,
    ( spl0_107
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f314,f223,f98,f5541]) ).

fof(f314,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1)) = greatest_lower_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f99]) ).

fof(f5539,plain,
    ( spl0_106
    | ~ spl0_25
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f405,f378,f253,f5536]) ).

fof(f405,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,c),b)
    | ~ spl0_25
    | ~ spl0_31 ),
    inference(superposition,[],[f379,f255]) ).

fof(f5385,plain,
    ( spl0_105
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_43
    | ~ spl0_86
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f5381,f5378,f2420,f595,f579,f98,f5383]) ).

fof(f5378,plain,
    ( spl0_104
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f5381,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,least_upper_bound(inverse(X2),X0)))
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_43
    | ~ spl0_86
    | ~ spl0_104 ),
    inference(forward_demodulation,[],[f5379,f3911]) ).

fof(f3911,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) = inverse(multiply(X1,least_upper_bound(inverse(X2),X0)))
    | ~ spl0_15
    | ~ spl0_39
    | ~ spl0_43
    | ~ spl0_86 ),
    inference(forward_demodulation,[],[f3850,f789]) ).

fof(f789,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),inverse(X2)) = inverse(multiply(X2,least_upper_bound(inverse(X0),X1)))
    | ~ spl0_39
    | ~ spl0_43 ),
    inference(superposition,[],[f580,f596]) ).

fof(f3850,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) = multiply(greatest_lower_bound(X2,inverse(X0)),inverse(X1))
    | ~ spl0_15
    | ~ spl0_86 ),
    inference(superposition,[],[f2421,f99]) ).

fof(f5379,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1)))
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f5378]) ).

fof(f5380,plain,
    ( spl0_104
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f309,f223,f98,f5378]) ).

fof(f309,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(inverse(X0),X2),inverse(X1)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1)))
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f99]) ).

fof(f5240,plain,
    ( spl0_103
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_84
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f5236,f5233,f2412,f595,f98,f5238]) ).

fof(f5238,plain,
    ( spl0_103
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X2,inverse(X0)),inverse(X1)) = inverse(multiply(X1,greatest_lower_bound(X0,inverse(X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f5233,plain,
    ( spl0_102
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X2,inverse(X0)),inverse(X1)) = least_upper_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f5236,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X2,inverse(X0)),inverse(X1)) = inverse(multiply(X1,greatest_lower_bound(X0,inverse(X2))))
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_84
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f5234,f3676]) ).

fof(f3676,plain,
    ( ! [X2,X0,X1] : least_upper_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0))) = inverse(multiply(X1,greatest_lower_bound(X0,inverse(X2))))
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_84 ),
    inference(forward_demodulation,[],[f3626,f779]) ).

fof(f779,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X1),inverse(X2)) = inverse(multiply(X2,greatest_lower_bound(X0,inverse(X1))))
    | ~ spl0_15
    | ~ spl0_43 ),
    inference(superposition,[],[f99,f596]) ).

fof(f3626,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = least_upper_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_84 ),
    inference(superposition,[],[f2413,f99]) ).

fof(f5234,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X2,inverse(X0)),inverse(X1)) = least_upper_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f5233]) ).

fof(f5235,plain,
    ( spl0_102
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f290,f219,f98,f5233]) ).

fof(f290,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X2,inverse(X0)),inverse(X1)) = least_upper_bound(multiply(X2,inverse(X1)),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f99]) ).

fof(f5082,plain,
    ( spl0_101
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_84
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f5078,f5075,f2412,f587,f98,f5080]) ).

fof(f5075,plain,
    ( spl0_100
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f5078,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = inverse(multiply(X1,greatest_lower_bound(inverse(X2),X0)))
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_84
    | ~ spl0_100 ),
    inference(forward_demodulation,[],[f5076,f3665]) ).

fof(f3665,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) = inverse(multiply(X1,greatest_lower_bound(inverse(X2),X0)))
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_84 ),
    inference(forward_demodulation,[],[f3606,f728]) ).

fof(f728,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,inverse(X1)),inverse(X2)) = inverse(multiply(X2,greatest_lower_bound(inverse(X0),X1)))
    | ~ spl0_15
    | ~ spl0_41 ),
    inference(superposition,[],[f99,f588]) ).

fof(f3606,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1))) = multiply(least_upper_bound(X2,inverse(X0)),inverse(X1))
    | ~ spl0_15
    | ~ spl0_84 ),
    inference(superposition,[],[f2413,f99]) ).

fof(f5076,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1)))
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f5075]) ).

fof(f5077,plain,
    ( spl0_100
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f285,f219,f98,f5075]) ).

fof(f285,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(inverse(X0),X2),inverse(X1)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(X2,inverse(X1)))
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f99]) ).

fof(f4935,plain,
    ( spl0_99
    | ~ spl0_26
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f390,f370,f332,f4932]) ).

fof(f390,plain,
    ( least_upper_bound(a,c) = least_upper_bound(least_upper_bound(a,c),b)
    | ~ spl0_26
    | ~ spl0_29 ),
    inference(superposition,[],[f371,f334]) ).

fof(f4930,plain,
    ( spl0_98
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_41
    | ~ spl0_81
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f4926,f4923,f2400,f587,f583,f98,f4928]) ).

fof(f4923,plain,
    ( spl0_97
  <=> ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f4926,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = inverse(multiply(least_upper_bound(X1,inverse(X2)),X0))
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_41
    | ~ spl0_81
    | ~ spl0_97 ),
    inference(forward_demodulation,[],[f4924,f3387]) ).

fof(f3387,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0))) = inverse(multiply(least_upper_bound(X1,inverse(X2)),X0))
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_41
    | ~ spl0_81 ),
    inference(forward_demodulation,[],[f3339,f739]) ).

fof(f739,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X2),greatest_lower_bound(inverse(X0),X1)) = inverse(multiply(least_upper_bound(X0,inverse(X1)),X2))
    | ~ spl0_40
    | ~ spl0_41 ),
    inference(superposition,[],[f584,f588]) ).

fof(f3339,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_81 ),
    inference(superposition,[],[f2401,f99]) ).

fof(f4924,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f4923]) ).

fof(f4925,plain,
    ( spl0_97
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f264,f215,f98,f4923]) ).

fof(f264,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f99]) ).

fof(f4766,plain,
    ( spl0_96
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_43
    | ~ spl0_81
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f4762,f4759,f2400,f595,f583,f98,f4764]) ).

fof(f4759,plain,
    ( spl0_95
  <=> ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f4762,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = inverse(multiply(least_upper_bound(inverse(X2),X1),X0))
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_43
    | ~ spl0_81
    | ~ spl0_95 ),
    inference(forward_demodulation,[],[f4760,f3379]) ).

fof(f3379,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) = inverse(multiply(least_upper_bound(inverse(X2),X1),X0))
    | ~ spl0_15
    | ~ spl0_40
    | ~ spl0_43
    | ~ spl0_81 ),
    inference(forward_demodulation,[],[f3320,f790]) ).

fof(f790,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X2),greatest_lower_bound(X0,inverse(X1))) = inverse(multiply(least_upper_bound(inverse(X0),X1),X2))
    | ~ spl0_40
    | ~ spl0_43 ),
    inference(superposition,[],[f584,f596]) ).

fof(f3320,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) = multiply(inverse(X0),greatest_lower_bound(X2,inverse(X1)))
    | ~ spl0_15
    | ~ spl0_81 ),
    inference(superposition,[],[f2401,f99]) ).

fof(f4760,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2))
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f4759]) ).

fof(f4761,plain,
    ( spl0_95
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f259,f215,f98,f4759]) ).

fof(f259,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2))
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f99]) ).

fof(f4619,plain,
    ( spl0_94
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_77
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f4615,f4612,f2347,f595,f98,f4617]) ).

fof(f4612,plain,
    ( spl0_93
  <=> ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = least_upper_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f4615,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = inverse(multiply(greatest_lower_bound(X1,inverse(X2)),X0))
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_77
    | ~ spl0_93 ),
    inference(forward_demodulation,[],[f4613,f3024]) ).

fof(f3024,plain,
    ( ! [X2,X0,X1] : least_upper_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0))) = inverse(multiply(greatest_lower_bound(X1,inverse(X2)),X0))
    | ~ spl0_15
    | ~ spl0_43
    | ~ spl0_77 ),
    inference(forward_demodulation,[],[f2980,f778]) ).

fof(f778,plain,
    ( ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(X0,inverse(X1)),X2)) = multiply(inverse(X2),least_upper_bound(inverse(X0),X1))
    | ~ spl0_15
    | ~ spl0_43 ),
    inference(superposition,[],[f99,f596]) ).

fof(f2980,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_77 ),
    inference(superposition,[],[f2348,f99]) ).

fof(f4613,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = least_upper_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f4612]) ).

fof(f4614,plain,
    ( spl0_93
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f233,f211,f98,f4612]) ).

fof(f233,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(X2,inverse(X1))) = least_upper_bound(multiply(inverse(X0),X2),inverse(multiply(X1,X0)))
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f99]) ).

fof(f4455,plain,
    ( spl0_92
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_77
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f4408,f4405,f2347,f587,f98,f4453]) ).

fof(f4405,plain,
    ( spl0_91
  <=> ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f4408,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = inverse(multiply(greatest_lower_bound(inverse(X2),X1),X0))
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_77
    | ~ spl0_91 ),
    inference(forward_demodulation,[],[f4406,f3016]) ).

fof(f3016,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) = inverse(multiply(greatest_lower_bound(inverse(X2),X1),X0))
    | ~ spl0_15
    | ~ spl0_41
    | ~ spl0_77 ),
    inference(forward_demodulation,[],[f2963,f727]) ).

fof(f727,plain,
    ( ! [X2,X0,X1] : inverse(multiply(greatest_lower_bound(inverse(X0),X1),X2)) = multiply(inverse(X2),least_upper_bound(X0,inverse(X1)))
    | ~ spl0_15
    | ~ spl0_41 ),
    inference(superposition,[],[f99,f588]) ).

fof(f2963,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2)) = multiply(inverse(X0),least_upper_bound(X2,inverse(X1)))
    | ~ spl0_15
    | ~ spl0_77 ),
    inference(superposition,[],[f2348,f99]) ).

fof(f4406,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2))
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f4405]) ).

fof(f4407,plain,
    ( spl0_91
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f228,f211,f98,f4405]) ).

fof(f228,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(multiply(X1,X0)),multiply(inverse(X0),X2))
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f99]) ).

fof(f4053,plain,
    ( spl0_90
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f195,f158,f102,f4051]) ).

fof(f195,plain,
    ( ! [X2,X0,X1] : least_upper_bound(inverse(X0),least_upper_bound(inverse(X1),X2)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2)
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f103]) ).

fof(f4049,plain,
    ( spl0_89
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f176,f154,f106,f4047]) ).

fof(f176,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(inverse(X0),greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2)
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f107]) ).

fof(f4045,plain,
    ( spl0_88
    | ~ spl0_15
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f163,f142,f98,f4043]) ).

fof(f163,plain,
    ( ! [X2,X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X2)) = multiply(inverse(multiply(X1,X0)),X2)
    | ~ spl0_15
    | ~ spl0_18 ),
    inference(superposition,[],[f143,f99]) ).

fof(f2426,plain,
    ( spl0_87
    | ~ spl0_12
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f324,f223,f76,f2424]) ).

fof(f324,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_12
    | ~ spl0_24 ),
    inference(superposition,[],[f77,f224]) ).

fof(f2422,plain,
    ( spl0_86
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f319,f223,f68,f2420]) ).

fof(f319,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f69]) ).

fof(f2418,plain,
    ( spl0_85
    | ~ spl0_13
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f300,f219,f80,f2416]) ).

fof(f300,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_13
    | ~ spl0_23 ),
    inference(superposition,[],[f81,f220]) ).

fof(f2414,plain,
    ( spl0_84
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f295,f219,f72,f2412]) ).

fof(f295,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f73]) ).

fof(f2410,plain,
    ( spl0_83
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f279,f215,f68,f52,f2408]) ).

fof(f279,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0))
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f263,f69]) ).

fof(f263,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_7
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f53]) ).

fof(f2406,plain,
    ( spl0_82
    | ~ spl0_12
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f272,f215,f76,f2404]) ).

fof(f272,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_12
    | ~ spl0_22 ),
    inference(superposition,[],[f77,f216]) ).

fof(f2402,plain,
    ( spl0_81
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f268,f215,f68,f2400]) ).

fof(f268,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f69]) ).

fof(f2361,plain,
    ( spl0_80
    | ~ spl0_7
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f258,f215,f52,f2359]) ).

fof(f258,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_22 ),
    inference(superposition,[],[f216,f53]) ).

fof(f2357,plain,
    ( spl0_79
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f248,f211,f72,f52,f2355]) ).

fof(f248,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0))
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f232,f73]) ).

fof(f232,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_7
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f53]) ).

fof(f2353,plain,
    ( spl0_78
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f241,f211,f80,f2351]) ).

fof(f241,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(superposition,[],[f81,f212]) ).

fof(f2349,plain,
    ( spl0_77
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f237,f211,f72,f2347]) ).

fof(f237,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f73]) ).

fof(f2345,plain,
    ( spl0_76
    | ~ spl0_7
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f227,f211,f52,f2343]) ).

fof(f227,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_21 ),
    inference(superposition,[],[f212,f53]) ).

fof(f2341,plain,
    ( spl0_75
    | ~ spl0_13
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f203,f158,f80,f2339]) ).

fof(f203,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,least_upper_bound(X1,X2)))
    | ~ spl0_13
    | ~ spl0_20 ),
    inference(superposition,[],[f81,f159]) ).

fof(f2337,plain,
    ( spl0_74
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f201,f158,f76,f2335]) ).

fof(f201,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X0,X1),X2)))
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f77]) ).

fof(f2333,plain,
    ( spl0_73
    | ~ spl0_12
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f184,f154,f76,f2331]) ).

fof(f184,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_12
    | ~ spl0_19 ),
    inference(superposition,[],[f77,f155]) ).

fof(f2329,plain,
    ( spl0_72
    | ~ spl0_13
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f182,f154,f80,f2327]) ).

fof(f182,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X0,X1),X2)))
    | ~ spl0_13
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f81]) ).

fof(f1994,plain,
    ( spl0_71
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f327,f223,f68,f52,f1992]) ).

fof(f327,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(forward_demodulation,[],[f313,f69]) ).

fof(f313,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,inverse(X0)),X0) = greatest_lower_bound(multiply(X1,X0),identity)
    | ~ spl0_7
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f53]) ).

fof(f1990,plain,
    ( spl0_70
    | ~ spl0_7
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f308,f223,f52,f1988]) ).

fof(f308,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
    | ~ spl0_7
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f53]) ).

fof(f1986,plain,
    ( spl0_69
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f303,f219,f72,f52,f1984]) ).

fof(f303,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(forward_demodulation,[],[f289,f73]) ).

fof(f289,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,inverse(X0)),X0) = least_upper_bound(multiply(X1,X0),identity)
    | ~ spl0_7
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f53]) ).

fof(f1982,plain,
    ( spl0_68
    | ~ spl0_7
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f284,f219,f52,f1980]) ).

fof(f284,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
    | ~ spl0_7
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f53]) ).

fof(f1719,plain,
    ( spl0_67
    | ~ spl0_29
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f515,f453,f370,f1717]) ).

fof(f515,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_29
    | ~ spl0_36 ),
    inference(superposition,[],[f371,f454]) ).

fof(f1204,plain,
    ( spl0_66
    | ~ spl0_4
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f312,f223,f40,f1202]) ).

fof(f312,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
    | ~ spl0_4
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f41]) ).

fof(f1200,plain,
    ( spl0_65
    | ~ spl0_4
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f307,f223,f40,f1198]) ).

fof(f307,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
    | ~ spl0_4
    | ~ spl0_24 ),
    inference(superposition,[],[f224,f41]) ).

fof(f1196,plain,
    ( spl0_64
    | ~ spl0_4
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f288,f219,f40,f1194]) ).

fof(f288,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
    | ~ spl0_4
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f41]) ).

fof(f1192,plain,
    ( spl0_63
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f505,f449,f76,f1190]) ).

fof(f505,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(superposition,[],[f77,f450]) ).

fof(f1188,plain,
    ( spl0_62
    | ~ spl0_4
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f283,f219,f40,f1186]) ).

fof(f283,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
    | ~ spl0_4
    | ~ spl0_23 ),
    inference(superposition,[],[f220,f41]) ).

fof(f1184,plain,
    ( spl0_61
    | ~ spl0_11
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f199,f158,f72,f1182]) ).

fof(f1179,plain,
    ( spl0_60
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f198,f158,f44,f1177]) ).

fof(f1177,plain,
    ( spl0_60
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f198,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1)))
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f45]) ).

fof(f1175,plain,
    ( spl0_59
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f194,f158,f76,f1173]) ).

fof(f194,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2)
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f77]) ).

fof(f1171,plain,
    ( spl0_58
    | ~ spl0_11
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f192,f158,f72,f1169]) ).

fof(f192,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2)
    | ~ spl0_11
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f73]) ).

fof(f1167,plain,
    ( spl0_57
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f180,f154,f68,f1165]) ).

fof(f1162,plain,
    ( spl0_56
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f179,f154,f48,f1160]) ).

fof(f1160,plain,
    ( spl0_56
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f179,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1)))
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f49]) ).

fof(f1158,plain,
    ( spl0_55
    | ~ spl0_13
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f175,f154,f80,f1156]) ).

fof(f175,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2)
    | ~ spl0_13
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f81]) ).

fof(f1154,plain,
    ( spl0_54
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f173,f154,f68,f1152]) ).

fof(f173,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2)
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f69]) ).

fof(f1137,plain,
    ( spl0_53
    | ~ spl0_31
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f489,f445,f378,f1135]) ).

fof(f489,plain,
    ( ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(X0,identity)))
    | ~ spl0_31
    | ~ spl0_34 ),
    inference(superposition,[],[f379,f446]) ).

fof(f1120,plain,
    ( spl0_52
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f209,f158,f63,f1118]) ).

fof(f209,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(a,least_upper_bound(c,X0))
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(forward_demodulation,[],[f197,f159]) ).

fof(f197,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(least_upper_bound(a,c),X0)
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f65]) ).

fof(f1116,plain,
    ( spl0_51
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f190,f154,f58,f1114]) ).

fof(f190,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(a,greatest_lower_bound(c,X0))
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(forward_demodulation,[],[f178,f155]) ).

fof(f178,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(greatest_lower_bound(a,c),X0)
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f60]) ).

fof(f759,plain,
    ( spl0_50
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f461,f441,f80,f757]) ).

fof(f461,plain,
    ( ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(superposition,[],[f81,f442]) ).

fof(f621,plain,
    ( spl0_49
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f138,f106,f76,f619]) ).

fof(f138,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(superposition,[],[f77,f107]) ).

fof(f617,plain,
    ( spl0_48
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f135,f106,f68,f615]) ).

fof(f135,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(superposition,[],[f107,f69]) ).

fof(f613,plain,
    ( spl0_47
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f133,f106,f35,f611]) ).

fof(f133,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,inverse(X0))) = greatest_lower_bound(inverse(X1),X0)
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(superposition,[],[f107,f36]) ).

fof(f609,plain,
    ( spl0_46
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f131,f106,f35,f607]) ).

fof(f131,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(inverse(X0),X1))
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(superposition,[],[f107,f36]) ).

fof(f605,plain,
    ( spl0_45
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f127,f102,f80,f603]) ).

fof(f127,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(superposition,[],[f81,f103]) ).

fof(f601,plain,
    ( spl0_44
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f124,f102,f72,f599]) ).

fof(f124,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(superposition,[],[f103,f73]) ).

fof(f597,plain,
    ( spl0_43
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f122,f102,f35,f595]) ).

fof(f122,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,inverse(X0))) = least_upper_bound(inverse(X1),X0)
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(superposition,[],[f103,f36]) ).

fof(f593,plain,
    ( spl0_42
    | ~ spl0_4
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f169,f142,f84,f40,f591]) ).

fof(f591,plain,
    ( spl0_42
  <=> ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f169,plain,
    ( ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1
    | ~ spl0_4
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f164,f41]) ).

fof(f164,plain,
    ( ! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1))
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(superposition,[],[f143,f85]) ).

fof(f589,plain,
    ( spl0_41
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f120,f102,f35,f587]) ).

fof(f120,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(inverse(X0),X1)) = least_upper_bound(X0,inverse(X1))
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(superposition,[],[f103,f36]) ).

fof(f585,plain,
    ( spl0_40
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f112,f98,f35,f583]) ).

fof(f112,plain,
    ( ! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0)
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(superposition,[],[f99,f36]) ).

fof(f581,plain,
    ( spl0_39
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f110,f98,f35,f579]) ).

fof(f110,plain,
    ( ! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1))
    | ~ spl0_3
    | ~ spl0_15 ),
    inference(superposition,[],[f99,f36]) ).

fof(f533,plain,
    ( spl0_38
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f191,f158,f44,f531]) ).

fof(f191,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(superposition,[],[f159,f45]) ).

fof(f529,plain,
    ( spl0_37
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f172,f154,f48,f527]) ).

fof(f172,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(superposition,[],[f155,f49]) ).

fof(f455,plain,
    ( spl0_36
    | ~ spl0_2
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f132,f106,f30,f453]) ).

fof(f30,plain,
    ( spl0_2
  <=> identity = inverse(identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f132,plain,
    ( ! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(inverse(X0),identity)
    | ~ spl0_2
    | ~ spl0_17 ),
    inference(superposition,[],[f107,f32]) ).

fof(f32,plain,
    ( identity = inverse(identity)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f30]) ).

fof(f451,plain,
    ( spl0_35
    | ~ spl0_2
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f130,f106,f30,f449]) ).

fof(f130,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0))
    | ~ spl0_2
    | ~ spl0_17 ),
    inference(superposition,[],[f107,f32]) ).

fof(f447,plain,
    ( spl0_34
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f121,f102,f30,f445]) ).

fof(f121,plain,
    ( ! [X0] : inverse(greatest_lower_bound(X0,identity)) = least_upper_bound(inverse(X0),identity)
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(superposition,[],[f103,f32]) ).

fof(f443,plain,
    ( spl0_33
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f119,f102,f30,f441]) ).

fof(f119,plain,
    ( ! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(X0))
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(superposition,[],[f103,f32]) ).

fof(f414,plain,
    ( spl0_32
    | ~ spl0_4
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f168,f142,f52,f40,f412]) ).

fof(f168,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_4
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f162,f41]) ).

fof(f162,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1)
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(superposition,[],[f143,f53]) ).

fof(f380,plain,
    ( spl0_31
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f92,f80,f72,f378]) ).

fof(f92,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(superposition,[],[f81,f73]) ).

fof(f376,plain,
    ( spl0_30
    | ~ spl0_3
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f360,f337,f35,f374]) ).

fof(f360,plain,
    ( ! [X0] : multiply(X0,identity) = X0
    | ~ spl0_3
    | ~ spl0_27 ),
    inference(forward_demodulation,[],[f350,f36]) ).

fof(f350,plain,
    ( ! [X0] : inverse(inverse(X0)) = multiply(X0,identity)
    | ~ spl0_3
    | ~ spl0_27 ),
    inference(superposition,[],[f36,f338]) ).

fof(f372,plain,
    ( spl0_29
    | ~ spl0_10
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f88,f76,f68,f370]) ).

fof(f88,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
    | ~ spl0_10
    | ~ spl0_12 ),
    inference(superposition,[],[f77,f69]) ).

fof(f343,plain,
    ( spl0_28
    | ~ spl0_2
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f116,f98,f40,f30,f341]) ).

fof(f341,plain,
    ( spl0_28
  <=> ! [X0] : inverse(X0) = multiply(inverse(X0),identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f116,plain,
    ( ! [X0] : inverse(X0) = multiply(inverse(X0),identity)
    | ~ spl0_2
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(forward_demodulation,[],[f111,f41]) ).

fof(f111,plain,
    ( ! [X0] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity)
    | ~ spl0_2
    | ~ spl0_15 ),
    inference(superposition,[],[f99,f32]) ).

fof(f339,plain,
    ( spl0_27
    | ~ spl0_2
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f115,f98,f40,f30,f337]) ).

fof(f115,plain,
    ( ! [X0] : inverse(X0) = inverse(multiply(X0,identity))
    | ~ spl0_2
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(forward_demodulation,[],[f109,f41]) ).

fof(f109,plain,
    ( ! [X0] : inverse(multiply(X0,identity)) = multiply(identity,inverse(X0))
    | ~ spl0_2
    | ~ spl0_15 ),
    inference(superposition,[],[f99,f32]) ).

fof(f335,plain,
    ( spl0_26
    | ~ spl0_9
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f95,f80,f63,f332]) ).

fof(f95,plain,
    ( b = greatest_lower_bound(b,least_upper_bound(a,c))
    | ~ spl0_9
    | ~ spl0_13 ),
    inference(superposition,[],[f81,f65]) ).

fof(f256,plain,
    ( spl0_25
    | ~ spl0_8
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f90,f76,f58,f253]) ).

fof(f90,plain,
    ( b = least_upper_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_8
    | ~ spl0_12 ),
    inference(superposition,[],[f77,f60]) ).

fof(f225,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f15,f223]) ).

fof(f15,axiom,
    ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).

fof(f221,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f14,f219]) ).

fof(f14,axiom,
    ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).

fof(f217,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f13,f215]) ).

fof(f13,axiom,
    ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).

fof(f213,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f12,f211]) ).

fof(f12,axiom,
    ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).

fof(f160,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f7,f158]) ).

fof(f7,axiom,
    ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).

fof(f156,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f6,f154]) ).

fof(f6,axiom,
    ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).

fof(f144,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f3,f142]) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

fof(f108,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f22,f106]) ).

fof(f22,axiom,
    ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_7) ).

fof(f104,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f21,f102]) ).

fof(f21,axiom,
    ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_6) ).

fof(f100,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f18,f98]) ).

fof(f18,axiom,
    ! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_3) ).

fof(f86,plain,
    ( spl0_14
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f56,f52,f35,f84]) ).

fof(f56,plain,
    ( ! [X0] : identity = multiply(X0,inverse(X0))
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(superposition,[],[f53,f36]) ).

fof(f82,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f11,f80]) ).

fof(f11,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).

fof(f78,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f10,f76]) ).

fof(f10,axiom,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).

fof(f74,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f5,f72]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).

fof(f70,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f4,f68]) ).

fof(f4,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).

fof(f66,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f20,f63]) ).

fof(f20,axiom,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_5) ).

fof(f61,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f19,f58]) ).

fof(f19,axiom,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).

fof(f54,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f2,f52]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f50,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f9,f48]) ).

fof(f9,axiom,
    ! [X0] : greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).

fof(f46,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f8,f44]) ).

fof(f8,axiom,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).

fof(f42,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f1,f40]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f37,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f17,f35]) ).

fof(f17,axiom,
    ! [X0] : inverse(inverse(X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).

fof(f33,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f16,f30]) ).

fof(f16,axiom,
    identity = inverse(identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).

fof(f28,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f23,f25]) ).

fof(f23,axiom,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem    : GRP181-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.05/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Apr 30 04:23:43 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (3847)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (3848)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (3851)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  TRYING [1]
% 0.20/0.37  TRYING [2]
% 0.20/0.37  TRYING [3]
% 0.20/0.37  TRYING [1]
% 0.20/0.38  % (3850)WARNING: value z3 for option sas not known
% 0.20/0.38  TRYING [2]
% 0.20/0.38  % (3849)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (3853)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.38  % (3852)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.38  % (3850)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38  % (3854)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.40  TRYING [3]
% 0.20/0.40  TRYING [4]
% 0.20/0.48  TRYING [4]
% 0.20/0.49  TRYING [5]
% 2.31/0.67  TRYING [5]
% 2.31/0.69  TRYING [6]
% 5.60/1.16  TRYING [6]
% 6.24/1.25  TRYING [7]
% 7.93/1.49  TRYING [1]
% 7.93/1.49  TRYING [2]
% 7.93/1.49  TRYING [3]
% 7.93/1.52  TRYING [4]
% 8.54/1.59  TRYING [5]
% 10.01/1.79  TRYING [6]
% 15.42/2.58  TRYING [7]
% 15.42/2.58  TRYING [7]
% 21.79/3.48  TRYING [8]
% 26.56/4.15  % (3852)First to succeed.
% 26.56/4.20  % (3852)Refutation found. Thanks to Tanya!
% 26.56/4.20  % SZS status Unsatisfiable for theBenchmark
% 26.56/4.20  % SZS output start Proof for theBenchmark
% See solution above
% 26.56/4.21  % (3852)------------------------------
% 26.56/4.21  % (3852)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 26.56/4.21  % (3852)Termination reason: Refutation
% 26.56/4.21  
% 26.56/4.21  % (3852)Memory used [KB]: 53124
% 26.56/4.21  % (3852)Time elapsed: 3.806 s
% 26.56/4.21  % (3852)Instructions burned: 7291 (million)
% 26.56/4.21  % (3852)------------------------------
% 26.56/4.21  % (3852)------------------------------
% 26.56/4.21  % (3847)Success in time 3.85 s
%------------------------------------------------------------------------------