TSTP Solution File: GRP181-3 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP181-3 : 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 : n005.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 : Sun May  5 05:53:55 EDT 2024

% Result   : Unsatisfiable 7.76s 1.47s
% Output   : Refutation 7.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  308
% Syntax   : Number of formulae    : 1032 (  41 unt;   0 def)
%            Number of atoms       : 2793 ( 742 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 3236 (1475   ~;1473   |;   0   &)
%                                         ( 288 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :  290 ( 288 usr; 289 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   : 1517 (1517   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f33945,plain,
    $false,
    inference(avatar_sat_refutation,[],[f25,f29,f33,f37,f41,f46,f51,f55,f59,f63,f67,f81,f86,f90,f108,f112,f116,f164,f169,f173,f177,f181,f269,f273,f307,f325,f329,f373,f377,f381,f385,f389,f465,f469,f515,f519,f523,f528,f532,f536,f540,f545,f549,f553,f557,f561,f565,f1282,f1286,f1290,f1294,f1483,f1487,f1491,f1495,f1499,f1503,f1507,f1511,f1515,f1519,f1523,f1568,f1572,f1576,f1580,f1584,f1588,f1967,f3034,f3038,f3186,f3190,f3194,f3198,f3202,f3208,f3212,f3216,f3220,f4057,f4328,f4332,f4695,f4700,f4705,f4710,f4714,f4720,f4724,f4728,f4732,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f7280,f7996,f8000,f8005,f8010,f8140,f8145,f8150,f8155,f8707,f8711,f8716,f8877,f8882,f8887,f9046,f9051,f9055,f9104,f9108,f9112,f9116,f9120,f9124,f9128,f9132,f9136,f9140,f9144,f9148,f9152,f9156,f9160,f9164,f9168,f10945,f11450,f11454,f11458,f11462,f11466,f11470,f11475,f11479,f11483,f11487,f11491,f11495,f11499,f11503,f11507,f11511,f11515,f11520,f11524,f11528,f11532,f11536,f11540,f11544,f11548,f11552,f11556,f11560,f11565,f11569,f11573,f11577,f11581,f11585,f11589,f11593,f11597,f11601,f11605,f22936,f22940,f22944,f22948,f22952,f22956,f22960,f22964,f22968,f22972,f22976,f22980,f22984,f22988,f22992,f22996,f23000,f23004,f23008,f23012,f24131,f26149,f26633,f26637,f26641,f26645,f26649,f28447,f28453,f28459,f28465,f28471,f28475,f28479,f28483,f28706,f28710,f28714,f28718,f28722,f28726,f28730,f28734,f28739,f28743,f28971,f28976,f28980,f28985,f28989,f28993,f32211,f32968,f32972,f32976,f32980,f33152,f33156,f33160,f33164,f33168,f33172,f33176,f33180,f33184,f33188,f33334,f33338,f33342,f33346,f33350,f33354,f33358,f33362,f33366,f33370,f33374,f33378,f33382,f33386,f33390,f33394,f33398,f33402,f33406,f33410,f33414,f33534,f33538,f33542,f33546,f33550,f33554,f33558,f33563,f33942,f33944]) ).

fof(f33944,plain,
    ( spl0_1
    | ~ spl0_6
    | ~ spl0_25
    | ~ spl0_89
    | ~ spl0_127
    | ~ spl0_228
    | ~ spl0_238
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f33858,f33561,f28968,f28704,f8705,f4718,f305,f43,f22]) ).

fof(f22,plain,
    ( spl0_1
  <=> a = b ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f43,plain,
    ( spl0_6
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(b,c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f305,plain,
    ( spl0_25
  <=> ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f4718,plain,
    ( spl0_89
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f8705,plain,
    ( spl0_127
  <=> ! [X0] : inverse(inverse(X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f28704,plain,
    ( spl0_228
  <=> ! [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_228])]) ).

fof(f28968,plain,
    ( spl0_238
  <=> least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f33561,plain,
    ( spl0_287
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(identity,multiply(X1,X0))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f33858,plain,
    ( a = b
    | ~ spl0_6
    | ~ spl0_25
    | ~ spl0_89
    | ~ spl0_127
    | ~ spl0_228
    | ~ spl0_238
    | ~ spl0_287 ),
    inference(forward_demodulation,[],[f33857,f30203]) ).

fof(f30203,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,X0),least_upper_bound(identity,multiply(inverse(X0),X1))) = X1
    | ~ spl0_25
    | ~ spl0_89
    | ~ spl0_127
    | ~ spl0_228 ),
    inference(forward_demodulation,[],[f30066,f9057]) ).

fof(f9057,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = inverse(inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_89
    | ~ spl0_127 ),
    inference(superposition,[],[f8706,f4719]) ).

fof(f4719,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0))
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f4718]) ).

fof(f8706,plain,
    ( ! [X0] : inverse(inverse(X0)) = X0
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f8705]) ).

fof(f30066,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(greatest_lower_bound(X0,X1))),least_upper_bound(identity,multiply(inverse(X0),X1))) = X1
    | ~ spl0_25
    | ~ spl0_228 ),
    inference(superposition,[],[f306,f28705]) ).

fof(f28705,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X1,X0)),X0)
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f28704]) ).

fof(f306,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f33857,plain,
    ( b = multiply(greatest_lower_bound(a,c),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_6
    | ~ spl0_127
    | ~ spl0_238
    | ~ spl0_287 ),
    inference(forward_demodulation,[],[f33856,f45]) ).

fof(f45,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(b,c)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f33856,plain,
    ( b = multiply(greatest_lower_bound(b,c),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_127
    | ~ spl0_238
    | ~ spl0_287 ),
    inference(forward_demodulation,[],[f33649,f8706]) ).

fof(f33649,plain,
    ( b = multiply(greatest_lower_bound(b,inverse(inverse(c))),least_upper_bound(identity,multiply(inverse(c),a)))
    | ~ spl0_238
    | ~ spl0_287 ),
    inference(superposition,[],[f33562,f28970]) ).

fof(f28970,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a))
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f28968]) ).

fof(f33562,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f33561]) ).

fof(f33942,plain,
    ( spl0_288
    | ~ spl0_25
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f1365,f1284,f305,f33940]) ).

fof(f33940,plain,
    ( spl0_288
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(X0,inverse(X1))),least_upper_bound(identity,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f1284,plain,
    ( spl0_49
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1365,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,inverse(X1))),least_upper_bound(identity,multiply(X0,X1))) = X1
    | ~ spl0_25
    | ~ spl0_49 ),
    inference(superposition,[],[f306,f1285]) ).

fof(f1285,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f1284]) ).

fof(f33563,plain,
    ( spl0_287
    | ~ spl0_14
    | ~ spl0_127
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f33559,f33556,f8705,f88,f33561]) ).

fof(f88,plain,
    ( spl0_14
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f33556,plain,
    ( spl0_286
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X0),X1)),least_upper_bound(identity,multiply(X1,X0))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f33559,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,inverse(X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_14
    | ~ spl0_127
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f33557,f9068]) ).

fof(f9068,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,inverse(X1)) = inverse(least_upper_bound(inverse(X0),X1))
    | ~ spl0_14
    | ~ spl0_127 ),
    inference(superposition,[],[f89,f8706]) ).

fof(f89,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f33557,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X0),X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f33556]) ).

fof(f33558,plain,
    ( spl0_286
    | ~ spl0_25
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1319,f1280,f305,f33556]) ).

fof(f1280,plain,
    ( spl0_48
  <=> ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1319,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X0),X1)),least_upper_bound(identity,multiply(X1,X0))) = X0
    | ~ spl0_25
    | ~ spl0_48 ),
    inference(superposition,[],[f306,f1281]) ).

fof(f1281,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f1280]) ).

fof(f33554,plain,
    ( spl0_285
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1276,f563,f559,f323,f53,f33552]) ).

fof(f33552,plain,
    ( spl0_285
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,multiply(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f53,plain,
    ( spl0_8
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f323,plain,
    ( spl0_26
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f559,plain,
    ( spl0_46
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f563,plain,
    ( spl0_47
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f1276,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,multiply(X0,X1)))
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1275,f54]) ).

fof(f54,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f1275,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,greatest_lower_bound(multiply(X0,X1),X1))
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1221,f331]) ).

fof(f331,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_8
    | ~ spl0_26 ),
    inference(superposition,[],[f324,f54]) ).

fof(f324,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f323]) ).

fof(f1221,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,greatest_lower_bound(multiply(X0,X1),X1)) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X0,identity)),X1)
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(superposition,[],[f560,f564]) ).

fof(f564,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f563]) ).

fof(f560,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f559]) ).

fof(f33550,plain,
    ( spl0_284
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1253,f563,f323,f53,f33548]) ).

fof(f33548,plain,
    ( spl0_284
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1253,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1252,f331]) ).

fof(f1252,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = multiply(greatest_lower_bound(identity,greatest_lower_bound(X0,identity)),X1)
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1251,f54]) ).

fof(f1251,plain,
    ( ! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = multiply(greatest_lower_bound(greatest_lower_bound(X0,identity),identity),X1)
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1200,f54]) ).

fof(f1200,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(greatest_lower_bound(X0,identity),identity),X1) = greatest_lower_bound(greatest_lower_bound(multiply(X0,X1),X1),X1)
    | ~ spl0_47 ),
    inference(superposition,[],[f564,f564]) ).

fof(f33546,plain,
    ( spl0_283
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1250,f563,f559,f323,f53,f33544]) ).

fof(f33544,plain,
    ( spl0_283
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1250,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_8
    | ~ spl0_26
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1249,f324]) ).

fof(f1249,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_8
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1199,f54]) ).

fof(f1199,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(greatest_lower_bound(identity,X0),identity),X1) = greatest_lower_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_46
    | ~ spl0_47 ),
    inference(superposition,[],[f564,f560]) ).

fof(f33542,plain,
    ( spl0_282
    | ~ spl0_26
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1181,f559,f323,f33540]) ).

fof(f33540,plain,
    ( spl0_282
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,multiply(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f1181,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,multiply(X0,X1)))
    | ~ spl0_26
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f1140,f324]) ).

fof(f1140,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),X1) = greatest_lower_bound(X1,greatest_lower_bound(X1,multiply(X0,X1)))
    | ~ spl0_46 ),
    inference(superposition,[],[f560,f560]) ).

fof(f33538,plain,
    ( spl0_281
    | ~ spl0_40
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1166,f559,f534,f33536]) ).

fof(f33536,plain,
    ( spl0_281
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(multiply(greatest_lower_bound(identity,X1),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f534,plain,
    ( spl0_40
  <=> ! [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_40])]) ).

fof(f1166,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(multiply(greatest_lower_bound(identity,X1),X0),X2))
    | ~ spl0_40
    | ~ spl0_46 ),
    inference(superposition,[],[f535,f560]) ).

fof(f535,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f33534,plain,
    ( spl0_280
    | ~ spl0_26
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1129,f559,f323,f33532]) ).

fof(f33532,plain,
    ( spl0_280
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1129,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X0),X1))
    | ~ spl0_26
    | ~ spl0_46 ),
    inference(superposition,[],[f560,f324]) ).

fof(f33414,plain,
    ( spl0_279
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1108,f551,f547,f327,f57,f33412]) ).

fof(f33412,plain,
    ( spl0_279
  <=> ! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,least_upper_bound(X1,multiply(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f57,plain,
    ( spl0_9
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f327,plain,
    ( spl0_27
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f547,plain,
    ( spl0_43
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f551,plain,
    ( spl0_44
  <=> ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f1108,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,least_upper_bound(X1,multiply(X0,X1)))
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1107,f58]) ).

fof(f58,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f57]) ).

fof(f1107,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,least_upper_bound(multiply(X0,X1),X1))
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1066,f351]) ).

fof(f351,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_9
    | ~ spl0_27 ),
    inference(superposition,[],[f328,f58]) ).

fof(f328,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f1066,plain,
    ( ! [X0,X1] : least_upper_bound(X1,least_upper_bound(multiply(X0,X1),X1)) = multiply(least_upper_bound(identity,least_upper_bound(X0,identity)),X1)
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(superposition,[],[f548,f552]) ).

fof(f552,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f551]) ).

fof(f548,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f547]) ).

fof(f33410,plain,
    ( spl0_278
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1091,f551,f327,f57,f33408]) ).

fof(f33408,plain,
    ( spl0_278
  <=> ! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f1091,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1090,f351]) ).

fof(f1090,plain,
    ( ! [X0,X1] : least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = multiply(least_upper_bound(identity,least_upper_bound(X0,identity)),X1)
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1089,f58]) ).

fof(f1089,plain,
    ( ! [X0,X1] : least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = multiply(least_upper_bound(least_upper_bound(X0,identity),identity),X1)
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1047,f58]) ).

fof(f1047,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(least_upper_bound(X0,identity),identity),X1) = least_upper_bound(least_upper_bound(multiply(X0,X1),X1),X1)
    | ~ spl0_44 ),
    inference(superposition,[],[f552,f552]) ).

fof(f33406,plain,
    ( spl0_277
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1088,f551,f547,f327,f57,f33404]) ).

fof(f33404,plain,
    ( spl0_277
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1088,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_9
    | ~ spl0_27
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1087,f328]) ).

fof(f1087,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,least_upper_bound(identity,X0)),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_9
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1046,f58]) ).

fof(f1046,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(least_upper_bound(identity,X0),identity),X1) = least_upper_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(superposition,[],[f552,f548]) ).

fof(f33402,plain,
    ( spl0_276
    | ~ spl0_27
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1035,f547,f327,f33400]) ).

fof(f33400,plain,
    ( spl0_276
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,least_upper_bound(X1,multiply(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f1035,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,least_upper_bound(X1,multiply(X0,X1)))
    | ~ spl0_27
    | ~ spl0_43 ),
    inference(forward_demodulation,[],[f1000,f328]) ).

fof(f1000,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,least_upper_bound(identity,X0)),X1) = least_upper_bound(X1,least_upper_bound(X1,multiply(X0,X1)))
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f548]) ).

fof(f33398,plain,
    ( spl0_275
    | ~ spl0_36
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1021,f547,f517,f33396]) ).

fof(f33396,plain,
    ( spl0_275
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(multiply(least_upper_bound(identity,X1),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f517,plain,
    ( spl0_36
  <=> ! [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_36])]) ).

fof(f1021,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(multiply(least_upper_bound(identity,X1),X0),X2))
    | ~ spl0_36
    | ~ spl0_43 ),
    inference(superposition,[],[f518,f548]) ).

fof(f518,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f517]) ).

fof(f33394,plain,
    ( spl0_274
    | ~ spl0_27
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f993,f547,f327,f33392]) ).

fof(f33392,plain,
    ( spl0_274
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(least_upper_bound(identity,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f993,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(least_upper_bound(identity,X0),X1))
    | ~ spl0_27
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f328]) ).

fof(f33390,plain,
    ( spl0_273
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f966,f543,f327,f114,f33388]) ).

fof(f33388,plain,
    ( spl0_273
  <=> ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X0,least_upper_bound(X0,least_upper_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f114,plain,
    ( spl0_17
  <=> ! [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_17])]) ).

fof(f543,plain,
    ( spl0_42
  <=> ! [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_42])]) ).

fof(f966,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X0,least_upper_bound(X0,least_upper_bound(X1,X2)))
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f906,f115]) ).

fof(f115,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f906,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X0,least_upper_bound(least_upper_bound(X0,X1),X2))
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f328]) ).

fof(f544,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1))
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f33386,plain,
    ( spl0_272
    | ~ spl0_36
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f953,f543,f517,f33384]) ).

fof(f33384,plain,
    ( spl0_272
  <=> ! [X0,X3,X2,X1] : greatest_lower_bound(X0,X3) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,least_upper_bound(X2,X0)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f953,plain,
    ( ! [X2,X3,X0,X1] : greatest_lower_bound(X0,X3) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,least_upper_bound(X2,X0)),X3))
    | ~ spl0_36
    | ~ spl0_42 ),
    inference(superposition,[],[f518,f544]) ).

fof(f33382,plain,
    ( spl0_271
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f951,f543,f327,f33380]) ).

fof(f33380,plain,
    ( spl0_271
  <=> ! [X2,X0,X1] : least_upper_bound(X1,least_upper_bound(X2,X0)) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f951,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X1,least_upper_bound(X2,X0)) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0)))
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(superposition,[],[f328,f544]) ).

fof(f33378,plain,
    ( spl0_270
    | ~ spl0_36
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f937,f543,f517,f33376]) ).

fof(f33376,plain,
    ( spl0_270
  <=> ! [X0,X3,X2,X1] : greatest_lower_bound(X0,X3) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X2,least_upper_bound(X0,X1)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f937,plain,
    ( ! [X2,X3,X0,X1] : greatest_lower_bound(X0,X3) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X2,least_upper_bound(X0,X1)),X3))
    | ~ spl0_36
    | ~ spl0_42 ),
    inference(superposition,[],[f518,f544]) ).

fof(f33374,plain,
    ( spl0_269
    | ~ spl0_69
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f8156,f7994,f1964,f33372]) ).

fof(f33372,plain,
    ( spl0_269
  <=> ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(X0,identity))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f1964,plain,
    ( spl0_69
  <=> identity = inverse(identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f7994,plain,
    ( spl0_119
  <=> ! [X0,X1] : inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f8156,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(X0,identity)))
    | ~ spl0_69
    | ~ spl0_119 ),
    inference(superposition,[],[f7995,f1966]) ).

fof(f1966,plain,
    ( identity = inverse(identity)
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f1964]) ).

fof(f7995,plain,
    ( ! [X0,X1] : inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f7994]) ).

fof(f33370,plain,
    ( spl0_268
    | ~ spl0_24
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f934,f543,f271,f33368]) ).

fof(f33368,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] : least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f271,plain,
    ( spl0_24
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f934,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X1,X2) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,least_upper_bound(X0,X1)))
    | ~ spl0_24
    | ~ spl0_42 ),
    inference(superposition,[],[f272,f544]) ).

fof(f272,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f33366,plain,
    ( spl0_267
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f878,f543,f327,f33364]) ).

fof(f33364,plain,
    ( spl0_267
  <=> ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f878,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X2,X0))
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f328]) ).

fof(f33362,plain,
    ( spl0_266
    | ~ spl0_38
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f831,f534,f526,f33360]) ).

fof(f33360,plain,
    ( spl0_266
  <=> ! [X0,X3,X2,X1] : least_upper_bound(X0,X3) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f526,plain,
    ( spl0_38
  <=> ! [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_38])]) ).

fof(f831,plain,
    ( ! [X2,X3,X0,X1] : least_upper_bound(X0,X3) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),X3))
    | ~ spl0_38
    | ~ spl0_40 ),
    inference(superposition,[],[f535,f527]) ).

fof(f527,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1))
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f526]) ).

fof(f33358,plain,
    ( spl0_265
    | ~ spl0_38
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f830,f534,f526,f33356]) ).

fof(f33356,plain,
    ( spl0_265
  <=> ! [X0,X3,X2,X1] : least_upper_bound(X0,X3) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,greatest_lower_bound(X2,X0)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f830,plain,
    ( ! [X2,X3,X0,X1] : least_upper_bound(X0,X3) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,greatest_lower_bound(X2,X0)),X3))
    | ~ spl0_38
    | ~ spl0_40 ),
    inference(superposition,[],[f535,f527]) ).

fof(f33354,plain,
    ( spl0_264
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f819,f530,f327,f114,f33352]) ).

fof(f33352,plain,
    ( spl0_264
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,least_upper_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f530,plain,
    ( spl0_39
  <=> ! [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_39])]) ).

fof(f819,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,least_upper_bound(X1,X2)))
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(forward_demodulation,[],[f818,f328]) ).

fof(f818,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,least_upper_bound(X0,least_upper_bound(X1,X2))))
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(forward_demodulation,[],[f795,f115]) ).

fof(f795,plain,
    ( ! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X1,least_upper_bound(X0,least_upper_bound(least_upper_bound(X0,X1),X2)))
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f328]) ).

fof(f531,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f530]) ).

fof(f33350,plain,
    ( spl0_263
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f809,f530,f327,f114,f33348]) ).

fof(f33348,plain,
    ( spl0_263
  <=> ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f809,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2))
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(forward_demodulation,[],[f778,f115]) ).

fof(f778,plain,
    ( ! [X2,X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2))
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f328]) ).

fof(f33346,plain,
    ( spl0_262
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f800,f530,f65,f33344]) ).

fof(f33344,plain,
    ( spl0_262
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,least_upper_bound(X0,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f65,plain,
    ( spl0_11
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f800,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,least_upper_bound(X0,X2)))
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(superposition,[],[f66,f531]) ).

fof(f66,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f33342,plain,
    ( spl0_261
    | ~ spl0_23
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f794,f530,f267,f33340]) ).

fof(f33340,plain,
    ( spl0_261
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,greatest_lower_bound(X2,least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f267,plain,
    ( spl0_23
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f794,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,greatest_lower_bound(X2,least_upper_bound(X0,X1))))
    | ~ spl0_23
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f268]) ).

fof(f268,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f33338,plain,
    ( spl0_260
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f793,f530,f61,f33336]) ).

fof(f33336,plain,
    ( spl0_260
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f61,plain,
    ( spl0_10
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f793,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,least_upper_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)))
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f62]) ).

fof(f62,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f61]) ).

fof(f33334,plain,
    ( spl0_259
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f751,f526,f323,f110,f33332]) ).

fof(f33332,plain,
    ( spl0_259
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f110,plain,
    ( spl0_16
  <=> ! [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_16])]) ).

fof(f751,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,greatest_lower_bound(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f691,f111]) ).

fof(f111,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f691,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,greatest_lower_bound(greatest_lower_bound(X0,X1),X2))
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f324]) ).

fof(f33188,plain,
    ( spl0_258
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f737,f526,f323,f33186]) ).

fof(f33186,plain,
    ( spl0_258
  <=> ! [X2,X0,X1] : greatest_lower_bound(X1,greatest_lower_bound(X2,X0)) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f737,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X1,greatest_lower_bound(X2,X0)) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0)))
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(superposition,[],[f324,f527]) ).

fof(f33184,plain,
    ( spl0_257
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f721,f526,f267,f33182]) ).

fof(f33182,plain,
    ( spl0_257
  <=> ! [X2,X0,X1] : greatest_lower_bound(X1,X2) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f721,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X1,X2) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,greatest_lower_bound(X0,X1)))
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(superposition,[],[f268,f527]) ).

fof(f33180,plain,
    ( spl0_256
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f663,f526,f323,f33178]) ).

fof(f33178,plain,
    ( spl0_256
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f663,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X2,X0))
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f324]) ).

fof(f33176,plain,
    ( spl0_255
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f611,f513,f323,f110,f33174]) ).

fof(f33174,plain,
    ( spl0_255
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f513,plain,
    ( spl0_35
  <=> ! [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_35])]) ).

fof(f611,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f610,f324]) ).

fof(f610,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))))
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f586,f111]) ).

fof(f586,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X1,greatest_lower_bound(X0,greatest_lower_bound(greatest_lower_bound(X0,X1),X2)))
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f324]) ).

fof(f514,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f513]) ).

fof(f33172,plain,
    ( spl0_254
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f601,f513,f323,f110,f33170]) ).

fof(f33170,plain,
    ( spl0_254
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f601,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2))
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(forward_demodulation,[],[f569,f111]) ).

fof(f569,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2))
    | ~ spl0_26
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f324]) ).

fof(f33168,plain,
    ( spl0_253
    | ~ spl0_10
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f593,f513,f61,f33166]) ).

fof(f33166,plain,
    ( spl0_253
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f593,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X1,greatest_lower_bound(X0,X2)))
    | ~ spl0_10
    | ~ spl0_35 ),
    inference(superposition,[],[f62,f514]) ).

fof(f33164,plain,
    ( spl0_252
    | ~ spl0_24
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f588,f513,f271,f33162]) ).

fof(f33162,plain,
    ( spl0_252
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,least_upper_bound(X2,greatest_lower_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f588,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,least_upper_bound(X2,greatest_lower_bound(X0,X1))))
    | ~ spl0_24
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f272]) ).

fof(f33160,plain,
    ( spl0_251
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f587,f513,f65,f33158]) ).

fof(f33158,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f587,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,greatest_lower_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)))
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f66]) ).

fof(f33156,plain,
    ( spl0_250
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f299,f271,f110,f33154]) ).

fof(f33154,plain,
    ( spl0_250
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f299,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X0,X1))))
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f111]) ).

fof(f33152,plain,
    ( spl0_249
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f294,f271,f175,f33150]) ).

fof(f33150,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] : multiply(X2,X1) = greatest_lower_bound(multiply(X2,X1),multiply(least_upper_bound(X0,X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f175,plain,
    ( spl0_21
  <=> ! [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_21])]) ).

fof(f294,plain,
    ( ! [X2,X0,X1] : multiply(X2,X1) = greatest_lower_bound(multiply(X2,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f176]) ).

fof(f176,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f32980,plain,
    ( spl0_248
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f293,f271,f162,f32978]) ).

fof(f32978,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] : multiply(X0,X2) = greatest_lower_bound(multiply(X0,X2),multiply(X0,least_upper_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f162,plain,
    ( spl0_18
  <=> ! [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_18])]) ).

fof(f293,plain,
    ( ! [X2,X0,X1] : multiply(X0,X2) = greatest_lower_bound(multiply(X0,X2),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_18
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f163]) ).

fof(f163,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f162]) ).

fof(f32976,plain,
    ( spl0_247
    | ~ spl0_17
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f284,f267,f114,f32974]) ).

fof(f32974,plain,
    ( spl0_247
  <=> ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f284,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X0,X1))))
    | ~ spl0_17
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f115]) ).

fof(f32972,plain,
    ( spl0_246
    | ~ spl0_22
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f279,f267,f179,f32970]) ).

fof(f32970,plain,
    ( spl0_246
  <=> ! [X2,X0,X1] : multiply(X2,X1) = least_upper_bound(multiply(X2,X1),multiply(greatest_lower_bound(X0,X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f179,plain,
    ( spl0_22
  <=> ! [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_22])]) ).

fof(f279,plain,
    ( ! [X2,X0,X1] : multiply(X2,X1) = least_upper_bound(multiply(X2,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_22
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f180]) ).

fof(f180,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f32968,plain,
    ( spl0_245
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f278,f267,f171,f32966]) ).

fof(f32966,plain,
    ( spl0_245
  <=> ! [X2,X0,X1] : multiply(X0,X2) = least_upper_bound(multiply(X0,X2),multiply(X0,greatest_lower_bound(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f171,plain,
    ( spl0_20
  <=> ! [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_20])]) ).

fof(f278,plain,
    ( ! [X2,X0,X1] : multiply(X0,X2) = least_upper_bound(multiply(X0,X2),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f172]) ).

fof(f172,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f32211,plain,
    ( spl0_244
    | ~ spl0_25
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f6038,f5348,f305,f32209]) ).

fof(f32209,plain,
    ( spl0_244
  <=> ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f5348,plain,
    ( spl0_99
  <=> ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f6038,plain,
    ( ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1
    | ~ spl0_25
    | ~ spl0_99 ),
    inference(superposition,[],[f5349,f306]) ).

fof(f5349,plain,
    ( ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1)
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f5348]) ).

fof(f28993,plain,
    ( spl0_243
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f2973,f1586,f43,f28991]) ).

fof(f28991,plain,
    ( spl0_243
  <=> ! [X0] : multiply(b,X0) = least_upper_bound(multiply(b,X0),multiply(greatest_lower_bound(a,c),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f1586,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f2973,plain,
    ( ! [X0] : multiply(b,X0) = least_upper_bound(multiply(b,X0),multiply(greatest_lower_bound(a,c),X0))
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(superposition,[],[f1587,f45]) ).

fof(f1587,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1586]) ).

fof(f28989,plain,
    ( spl0_242
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f2758,f1578,f48,f28987]) ).

fof(f28987,plain,
    ( spl0_242
  <=> ! [X0] : multiply(b,X0) = greatest_lower_bound(multiply(b,X0),multiply(least_upper_bound(a,c),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f48,plain,
    ( spl0_7
  <=> least_upper_bound(a,c) = least_upper_bound(b,c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1578,plain,
    ( spl0_66
  <=> ! [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_66])]) ).

fof(f2758,plain,
    ( ! [X0] : multiply(b,X0) = greatest_lower_bound(multiply(b,X0),multiply(least_upper_bound(a,c),X0))
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(superposition,[],[f1579,f50]) ).

fof(f50,plain,
    ( least_upper_bound(a,c) = least_upper_bound(b,c)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f1579,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1578]) ).

fof(f28985,plain,
    ( spl0_241
    | ~ spl0_6
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f2607,f1570,f43,f28982]) ).

fof(f28982,plain,
    ( spl0_241
  <=> greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f1570,plain,
    ( spl0_64
  <=> ! [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_64])]) ).

fof(f2607,plain,
    ( greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a))
    | ~ spl0_6
    | ~ spl0_64 ),
    inference(forward_demodulation,[],[f2571,f1571]) ).

fof(f1571,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0))
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1570]) ).

fof(f2571,plain,
    ( greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),greatest_lower_bound(a,c))
    | ~ spl0_6
    | ~ spl0_64 ),
    inference(superposition,[],[f1571,f45]) ).

fof(f28980,plain,
    ( spl0_240
    | ~ spl0_6
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f2494,f1566,f43,f28978]) ).

fof(f28978,plain,
    ( spl0_240
  <=> ! [X0] : multiply(X0,b) = least_upper_bound(multiply(X0,b),multiply(X0,greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f1566,plain,
    ( spl0_63
  <=> ! [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_63])]) ).

fof(f2494,plain,
    ( ! [X0] : multiply(X0,b) = least_upper_bound(multiply(X0,b),multiply(X0,greatest_lower_bound(a,c)))
    | ~ spl0_6
    | ~ spl0_63 ),
    inference(superposition,[],[f1567,f45]) ).

fof(f1567,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1566]) ).

fof(f28976,plain,
    ( spl0_239
    | ~ spl0_6
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f2302,f1517,f43,f28973]) ).

fof(f28973,plain,
    ( spl0_239
  <=> multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f1517,plain,
    ( spl0_61
  <=> ! [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_61])]) ).

fof(f2302,plain,
    ( multiply(inverse(b),greatest_lower_bound(a,c)) = greatest_lower_bound(identity,multiply(inverse(b),c))
    | ~ spl0_6
    | ~ spl0_61 ),
    inference(superposition,[],[f1518,f45]) ).

fof(f1518,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1517]) ).

fof(f28971,plain,
    ( spl0_238
    | ~ spl0_7
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f2261,f1513,f48,f28968]) ).

fof(f1513,plain,
    ( spl0_60
  <=> ! [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_60])]) ).

fof(f2261,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = least_upper_bound(identity,multiply(inverse(c),a))
    | ~ spl0_7
    | ~ spl0_60 ),
    inference(forward_demodulation,[],[f2229,f1514]) ).

fof(f1514,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0))
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f1513]) ).

fof(f2229,plain,
    ( least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_60 ),
    inference(superposition,[],[f1514,f50]) ).

fof(f28743,plain,
    ( spl0_237
    | ~ spl0_7
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f2162,f1509,f48,f28741]) ).

fof(f28741,plain,
    ( spl0_237
  <=> ! [X0] : multiply(X0,b) = greatest_lower_bound(multiply(X0,b),multiply(X0,least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f1509,plain,
    ( spl0_59
  <=> ! [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_59])]) ).

fof(f2162,plain,
    ( ! [X0] : multiply(X0,b) = greatest_lower_bound(multiply(X0,b),multiply(X0,least_upper_bound(a,c)))
    | ~ spl0_7
    | ~ spl0_59 ),
    inference(superposition,[],[f1510,f50]) ).

fof(f1510,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f1509]) ).

fof(f28739,plain,
    ( spl0_236
    | ~ spl0_7
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f1988,f1501,f48,f28736]) ).

fof(f28736,plain,
    ( spl0_236
  <=> least_upper_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f1501,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f1988,plain,
    ( least_upper_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_57 ),
    inference(superposition,[],[f1502,f50]) ).

fof(f1502,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1501]) ).

fof(f28734,plain,
    ( spl0_235
    | ~ spl0_7
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f1906,f1497,f48,f28732]) ).

fof(f28732,plain,
    ( spl0_235
  <=> ! [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_235])]) ).

fof(f1497,plain,
    ( spl0_56
  <=> ! [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_56])]) ).

fof(f1906,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_7
    | ~ spl0_56 ),
    inference(superposition,[],[f1498,f50]) ).

fof(f1498,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_56 ),
    inference(avatar_component_clause,[],[f1497]) ).

fof(f28730,plain,
    ( spl0_234
    | ~ spl0_7
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1791,f1493,f48,f28728]) ).

fof(f28728,plain,
    ( spl0_234
  <=> ! [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_234])]) ).

fof(f1493,plain,
    ( spl0_55
  <=> ! [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_55])]) ).

fof(f1791,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_7
    | ~ spl0_55 ),
    inference(superposition,[],[f1494,f50]) ).

fof(f1494,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_55 ),
    inference(avatar_component_clause,[],[f1493]) ).

fof(f28726,plain,
    ( spl0_233
    | ~ spl0_6
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1718,f1489,f43,f28724]) ).

fof(f28724,plain,
    ( spl0_233
  <=> ! [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_233])]) ).

fof(f1489,plain,
    ( spl0_54
  <=> ! [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_54])]) ).

fof(f1718,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_6
    | ~ spl0_54 ),
    inference(superposition,[],[f1490,f45]) ).

fof(f1490,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_54 ),
    inference(avatar_component_clause,[],[f1489]) ).

fof(f28722,plain,
    ( spl0_232
    | ~ spl0_6
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f1608,f1485,f43,f28720]) ).

fof(f28720,plain,
    ( spl0_232
  <=> ! [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_232])]) ).

fof(f1485,plain,
    ( spl0_53
  <=> ! [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_53])]) ).

fof(f1608,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_6
    | ~ spl0_53 ),
    inference(superposition,[],[f1486,f45]) ).

fof(f1486,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_53 ),
    inference(avatar_component_clause,[],[f1485]) ).

fof(f28718,plain,
    ( spl0_231
    | ~ spl0_14
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f1388,f1288,f88,f28716]) ).

fof(f28716,plain,
    ( spl0_231
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(X0,X1)),X0) = greatest_lower_bound(identity,multiply(inverse(X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f1288,plain,
    ( spl0_50
  <=> ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1388,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,X1)),X0) = greatest_lower_bound(identity,multiply(inverse(X1),X0))
    | ~ spl0_14
    | ~ spl0_50 ),
    inference(superposition,[],[f1289,f89]) ).

fof(f1289,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f1288]) ).

fof(f28714,plain,
    ( spl0_230
    | ~ spl0_31
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f1387,f1288,f383,f28712]) ).

fof(f28712,plain,
    ( spl0_230
  <=> ! [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_230])]) ).

fof(f383,plain,
    ( spl0_31
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1387,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(least_upper_bound(X1,X0)),X0)
    | ~ spl0_31
    | ~ spl0_50 ),
    inference(superposition,[],[f1289,f384]) ).

fof(f384,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0))
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f383]) ).

fof(f28710,plain,
    ( spl0_229
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1296,f1280,f79,f28708]) ).

fof(f28708,plain,
    ( spl0_229
  <=> ! [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_229])]) ).

fof(f79,plain,
    ( spl0_12
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1296,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X0,X1)),X0)
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(superposition,[],[f1281,f80]) ).

fof(f80,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f79]) ).

fof(f28706,plain,
    ( spl0_228
    | ~ spl0_28
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1295,f1280,f371,f28704]) ).

fof(f371,plain,
    ( spl0_28
  <=> ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1295,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X1),X0)) = multiply(inverse(greatest_lower_bound(X1,X0)),X0)
    | ~ spl0_28
    | ~ spl0_48 ),
    inference(superposition,[],[f1281,f372]) ).

fof(f372,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0))
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f28483,plain,
    ( spl0_227
    | ~ spl0_33
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f843,f534,f463,f28481]) ).

fof(f28481,plain,
    ( spl0_227
  <=> ! [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_227])]) ).

fof(f463,plain,
    ( spl0_33
  <=> ! [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_33])]) ).

fof(f843,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_33
    | ~ spl0_40 ),
    inference(superposition,[],[f535,f464]) ).

fof(f464,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(a,greatest_lower_bound(c,X0))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f28479,plain,
    ( spl0_226
    | ~ spl0_34
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f631,f517,f467,f28477]) ).

fof(f28477,plain,
    ( spl0_226
  <=> ! [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_226])]) ).

fof(f467,plain,
    ( spl0_34
  <=> ! [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_34])]) ).

fof(f631,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_34
    | ~ spl0_36 ),
    inference(superposition,[],[f518,f468]) ).

fof(f468,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(a,least_upper_bound(c,X0))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f467]) ).

fof(f28475,plain,
    ( spl0_225
    | ~ spl0_27
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f492,f467,f327,f28473]) ).

fof(f28473,plain,
    ( spl0_225
  <=> ! [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_225])]) ).

fof(f492,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_27
    | ~ spl0_34 ),
    inference(superposition,[],[f328,f468]) ).

fof(f28471,plain,
    ( spl0_224
    | ~ spl0_26
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f479,f463,f323,f28469]) ).

fof(f28469,plain,
    ( spl0_224
  <=> ! [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_224])]) ).

fof(f479,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_26
    | ~ spl0_33 ),
    inference(superposition,[],[f324,f464]) ).

fof(f28465,plain,
    ( spl0_223
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f447,f387,f79,f28463]) ).

fof(f28463,plain,
    ( spl0_223
  <=> ! [X0,X1] : inverse(inverse(X0)) = least_upper_bound(inverse(inverse(X0)),inverse(inverse(greatest_lower_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f387,plain,
    ( spl0_32
  <=> ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f447,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = least_upper_bound(inverse(inverse(X0)),inverse(inverse(greatest_lower_bound(X0,X1))))
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(superposition,[],[f388,f80]) ).

fof(f388,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f387]) ).

fof(f28459,plain,
    ( spl0_222
    | ~ spl0_28
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f446,f387,f371,f28457]) ).

fof(f28457,plain,
    ( spl0_222
  <=> ! [X0,X1] : inverse(inverse(X0)) = least_upper_bound(inverse(inverse(X0)),inverse(inverse(greatest_lower_bound(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f446,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = least_upper_bound(inverse(inverse(X0)),inverse(inverse(greatest_lower_bound(X1,X0))))
    | ~ spl0_28
    | ~ spl0_32 ),
    inference(superposition,[],[f388,f372]) ).

fof(f28453,plain,
    ( spl0_221
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f435,f383,f375,f28451]) ).

fof(f28451,plain,
    ( spl0_221
  <=> ! [X0,X1] : inverse(inverse(X0)) = greatest_lower_bound(inverse(inverse(X0)),inverse(inverse(least_upper_bound(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f375,plain,
    ( spl0_29
  <=> ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f435,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = greatest_lower_bound(inverse(inverse(X0)),inverse(inverse(least_upper_bound(X1,X0))))
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(superposition,[],[f376,f384]) ).

fof(f376,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f28447,plain,
    ( spl0_220
    | ~ spl0_14
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f410,f375,f88,f28445]) ).

fof(f28445,plain,
    ( spl0_220
  <=> ! [X0,X1] : inverse(inverse(X0)) = greatest_lower_bound(inverse(inverse(X0)),inverse(inverse(least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f410,plain,
    ( ! [X0,X1] : inverse(inverse(X0)) = greatest_lower_bound(inverse(inverse(X0)),inverse(inverse(least_upper_bound(X0,X1))))
    | ~ spl0_14
    | ~ spl0_29 ),
    inference(superposition,[],[f376,f89]) ).

fof(f26649,plain,
    ( spl0_219
    | ~ spl0_8
    | ~ spl0_25
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1268,f563,f305,f53,f26647]) ).

fof(f26647,plain,
    ( spl0_219
  <=> ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f1268,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_8
    | ~ spl0_25
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1218,f54]) ).

fof(f1218,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(X0,identity)),greatest_lower_bound(multiply(X0,X1),X1)) = X1
    | ~ spl0_25
    | ~ spl0_47 ),
    inference(superposition,[],[f306,f564]) ).

fof(f26645,plain,
    ( spl0_218
    | ~ spl0_25
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1155,f559,f305,f26643]) ).

fof(f26643,plain,
    ( spl0_218
  <=> ! [X0,X1] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f1155,plain,
    ( ! [X0,X1] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_25
    | ~ spl0_46 ),
    inference(superposition,[],[f306,f560]) ).

fof(f26641,plain,
    ( spl0_217
    | ~ spl0_9
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1106,f551,f305,f57,f26639]) ).

fof(f26639,plain,
    ( spl0_217
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f1106,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_9
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1065,f58]) ).

fof(f1065,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(X0,identity)),least_upper_bound(multiply(X0,X1),X1)) = X1
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(superposition,[],[f306,f552]) ).

fof(f26637,plain,
    ( spl0_216
    | ~ spl0_25
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1015,f547,f305,f26635]) ).

fof(f26635,plain,
    ( spl0_216
  <=> ! [X0,X1] : multiply(inverse(least_upper_bound(identity,X0)),least_upper_bound(X1,multiply(X0,X1))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f1015,plain,
    ( ! [X0,X1] : multiply(inverse(least_upper_bound(identity,X0)),least_upper_bound(X1,multiply(X0,X1))) = X1
    | ~ spl0_25
    | ~ spl0_43 ),
    inference(superposition,[],[f306,f548]) ).

fof(f26633,plain,
    ( spl0_215
    | ~ spl0_15
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f310,f305,f106,f26631]) ).

fof(f26631,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f106,plain,
    ( spl0_15
  <=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f310,plain,
    ( ! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2
    | ~ spl0_15
    | ~ spl0_25 ),
    inference(superposition,[],[f306,f107]) ).

fof(f107,plain,
    ( ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f26149,plain,
    ( spl0_214
    | ~ spl0_23
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f6326,f5360,f267,f26147]) ).

fof(f26147,plain,
    ( spl0_214
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f5360,plain,
    ( spl0_102
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f6326,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,X0),X0) = X0
    | ~ spl0_23
    | ~ spl0_102 ),
    inference(superposition,[],[f5361,f268]) ).

fof(f5361,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f5360]) ).

fof(f24131,plain,
    ( spl0_213
    | ~ spl0_10
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f6325,f5360,f61,f24129]) ).

fof(f24129,plain,
    ( spl0_213
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,X1),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f6325,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X0,X1),X0) = X0
    | ~ spl0_10
    | ~ spl0_102 ),
    inference(superposition,[],[f5361,f62]) ).

fof(f23012,plain,
    ( spl0_212
    | ~ spl0_3
    | ~ spl0_12
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f3164,f3036,f79,f31,f23010]) ).

fof(f23010,plain,
    ( spl0_212
  <=> ! [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_212])]) ).

fof(f31,plain,
    ( spl0_3
  <=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f3036,plain,
    ( spl0_71
  <=> ! [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_71])]) ).

fof(f3164,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),inverse(X0))
    | ~ spl0_3
    | ~ spl0_12
    | ~ spl0_71 ),
    inference(forward_demodulation,[],[f3117,f80]) ).

fof(f3117,plain,
    ( ! [X0,X1] : least_upper_bound(inverse(X1),inverse(X0)) = least_upper_bound(inverse(greatest_lower_bound(X1,X0)),inverse(X0))
    | ~ spl0_3
    | ~ spl0_71 ),
    inference(superposition,[],[f3037,f32]) ).

fof(f32,plain,
    ( ! [X0] : least_upper_bound(X0,X0) = X0
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f3037,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_71 ),
    inference(avatar_component_clause,[],[f3036]) ).

fof(f23008,plain,
    ( spl0_211
    | ~ spl0_11
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f3142,f3036,f65,f23006]) ).

fof(f23006,plain,
    ( spl0_211
  <=> ! [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_211])]) ).

fof(f3142,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),least_upper_bound(inverse(greatest_lower_bound(X0,X1)),X2))
    | ~ spl0_11
    | ~ spl0_71 ),
    inference(superposition,[],[f66,f3037]) ).

fof(f23004,plain,
    ( spl0_210
    | ~ spl0_4
    | ~ spl0_14
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f3092,f3032,f88,f35,f23002]) ).

fof(f23002,plain,
    ( spl0_210
  <=> ! [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_210])]) ).

fof(f35,plain,
    ( spl0_4
  <=> ! [X0] : greatest_lower_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f3032,plain,
    ( spl0_70
  <=> ! [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_70])]) ).

fof(f3092,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(least_upper_bound(X1,X0)),inverse(X0))
    | ~ spl0_4
    | ~ spl0_14
    | ~ spl0_70 ),
    inference(forward_demodulation,[],[f3045,f89]) ).

fof(f3045,plain,
    ( ! [X0,X1] : greatest_lower_bound(inverse(X1),inverse(X0)) = greatest_lower_bound(inverse(least_upper_bound(X1,X0)),inverse(X0))
    | ~ spl0_4
    | ~ spl0_70 ),
    inference(superposition,[],[f3033,f36]) ).

fof(f36,plain,
    ( ! [X0] : greatest_lower_bound(X0,X0) = X0
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f3033,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_70 ),
    inference(avatar_component_clause,[],[f3032]) ).

fof(f23000,plain,
    ( spl0_209
    | ~ spl0_10
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f3070,f3032,f61,f22998]) ).

fof(f22998,plain,
    ( spl0_209
  <=> ! [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_209])]) ).

fof(f3070,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),greatest_lower_bound(inverse(least_upper_bound(X0,X1)),X2))
    | ~ spl0_10
    | ~ spl0_70 ),
    inference(superposition,[],[f62,f3033]) ).

fof(f22996,plain,
    ( spl0_208
    | ~ spl0_24
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f6213,f5352,f271,f22994]) ).

fof(f22994,plain,
    ( spl0_208
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f5352,plain,
    ( spl0_100
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f6213,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,X0),X0) = X0
    | ~ spl0_24
    | ~ spl0_100 ),
    inference(superposition,[],[f5353,f272]) ).

fof(f5353,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f5352]) ).

fof(f22992,plain,
    ( spl0_207
    | ~ spl0_29
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1162,f559,f375,f22990]) ).

fof(f22990,plain,
    ( spl0_207
  <=> ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(multiply(greatest_lower_bound(identity,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f1162,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(multiply(greatest_lower_bound(identity,X1),X0)))
    | ~ spl0_29
    | ~ spl0_46 ),
    inference(superposition,[],[f376,f560]) ).

fof(f22988,plain,
    ( spl0_206
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1020,f547,f387,f22986]) ).

fof(f22986,plain,
    ( spl0_206
  <=> ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(multiply(least_upper_bound(identity,X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f1020,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(multiply(least_upper_bound(identity,X1),X0)))
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f388,f548]) ).

fof(f22984,plain,
    ( spl0_205
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f952,f543,f387,f22982]) ).

fof(f22982,plain,
    ( spl0_205
  <=> ! [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_205])]) ).

fof(f952,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X1,least_upper_bound(X2,X0))))
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(superposition,[],[f388,f544]) ).

fof(f22980,plain,
    ( spl0_204
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f936,f543,f387,f22978]) ).

fof(f22978,plain,
    ( spl0_204
  <=> ! [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_204])]) ).

fof(f936,plain,
    ( ! [X2,X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X2,least_upper_bound(X0,X1))))
    | ~ spl0_32
    | ~ spl0_42 ),
    inference(superposition,[],[f388,f544]) ).

fof(f22976,plain,
    ( spl0_203
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f738,f526,f375,f22974]) ).

fof(f22974,plain,
    ( spl0_203
  <=> ! [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_203])]) ).

fof(f738,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X1,greatest_lower_bound(X2,X0))))
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(superposition,[],[f376,f527]) ).

fof(f22972,plain,
    ( spl0_202
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f723,f526,f375,f22970]) ).

fof(f22970,plain,
    ( spl0_202
  <=> ! [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_202])]) ).

fof(f723,plain,
    ( ! [X2,X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X2,greatest_lower_bound(X0,X1))))
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(superposition,[],[f376,f527]) ).

fof(f22968,plain,
    ( spl0_201
    | ~ spl0_32
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f493,f467,f387,f22966]) ).

fof(f22966,plain,
    ( spl0_201
  <=> ! [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_201])]) ).

fof(f493,plain,
    ( ! [X0] : inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,least_upper_bound(c,X0))))
    | ~ spl0_32
    | ~ spl0_34 ),
    inference(superposition,[],[f388,f468]) ).

fof(f22964,plain,
    ( spl0_200
    | ~ spl0_29
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f480,f463,f375,f22962]) ).

fof(f22962,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f480,plain,
    ( ! [X0] : inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,greatest_lower_bound(c,X0))))
    | ~ spl0_29
    | ~ spl0_33 ),
    inference(superposition,[],[f376,f464]) ).

fof(f22960,plain,
    ( spl0_199
    | ~ spl0_24
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f458,f387,f271,f22958]) ).

fof(f22958,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

fof(f458,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(least_upper_bound(X0,X1)),inverse(X0))
    | ~ spl0_24
    | ~ spl0_32 ),
    inference(superposition,[],[f272,f388]) ).

fof(f22956,plain,
    ( spl0_198
    | ~ spl0_26
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f434,f383,f323,f22954]) ).

fof(f22954,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f434,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X1,X0)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X1,X0)))
    | ~ spl0_26
    | ~ spl0_31 ),
    inference(superposition,[],[f324,f384]) ).

fof(f22952,plain,
    ( spl0_197
    | ~ spl0_11
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f6212,f5352,f65,f22950]) ).

fof(f22950,plain,
    ( spl0_197
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f6212,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),X0) = X0
    | ~ spl0_11
    | ~ spl0_100 ),
    inference(superposition,[],[f5353,f66]) ).

fof(f22948,plain,
    ( spl0_196
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f419,f375,f267,f22946]) ).

fof(f22946,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

fof(f419,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(greatest_lower_bound(X0,X1)),inverse(X0))
    | ~ spl0_23
    | ~ spl0_29 ),
    inference(superposition,[],[f268,f376]) ).

fof(f22944,plain,
    ( spl0_195
    | ~ spl0_27
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f396,f371,f327,f22942]) ).

fof(f22942,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

fof(f396,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X1,X0)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X1,X0)))
    | ~ spl0_27
    | ~ spl0_28 ),
    inference(superposition,[],[f328,f372]) ).

fof(f22940,plain,
    ( spl0_194
    | ~ spl0_12
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f358,f327,f79,f22938]) ).

fof(f22938,plain,
    ( spl0_194
  <=> ! [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_194])]) ).

fof(f358,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_12
    | ~ spl0_27 ),
    inference(superposition,[],[f328,f80]) ).

fof(f22936,plain,
    ( spl0_193
    | ~ spl0_14
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f338,f323,f88,f22934]) ).

fof(f22934,plain,
    ( spl0_193
  <=> ! [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_193])]) ).

fof(f338,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_14
    | ~ spl0_26 ),
    inference(superposition,[],[f324,f89]) ).

fof(f11605,plain,
    ( spl0_192
    | ~ spl0_22
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f2877,f1582,f179,f11603]) ).

fof(f11603,plain,
    ( spl0_192
  <=> ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = multiply(greatest_lower_bound(X2,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1582,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f2877,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = multiply(greatest_lower_bound(X2,X0),X1)
    | ~ spl0_22
    | ~ spl0_67 ),
    inference(superposition,[],[f1583,f180]) ).

fof(f1583,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1582]) ).

fof(f11601,plain,
    ( spl0_191
    | ~ spl0_21
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f2667,f1574,f175,f11599]) ).

fof(f11599,plain,
    ( spl0_191
  <=> ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = multiply(least_upper_bound(X2,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1574,plain,
    ( spl0_65
  <=> ! [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_65])]) ).

fof(f2667,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = multiply(least_upper_bound(X2,X0),X1)
    | ~ spl0_21
    | ~ spl0_65 ),
    inference(superposition,[],[f1575,f176]) ).

fof(f1575,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f1574]) ).

fof(f11597,plain,
    ( spl0_190
    | ~ spl0_20
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f2389,f1521,f171,f11595]) ).

fof(f11595,plain,
    ( spl0_190
  <=> ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1521,plain,
    ( spl0_62
  <=> ! [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_62])]) ).

fof(f2389,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = multiply(X0,greatest_lower_bound(X2,X1))
    | ~ spl0_20
    | ~ spl0_62 ),
    inference(superposition,[],[f1522,f172]) ).

fof(f1522,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1521]) ).

fof(f11593,plain,
    ( spl0_189
    | ~ spl0_18
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f2064,f1505,f162,f11591]) ).

fof(f11591,plain,
    ( spl0_189
  <=> ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1505,plain,
    ( spl0_58
  <=> ! [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_58])]) ).

fof(f2064,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1))
    | ~ spl0_18
    | ~ spl0_58 ),
    inference(superposition,[],[f1506,f163]) ).

fof(f1506,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f1505]) ).

fof(f11589,plain,
    ( spl0_188
    | ~ spl0_3
    | ~ spl0_9
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f1953,f1497,f327,f114,f57,f31,f11587]) ).

fof(f11587,plain,
    ( spl0_188
  <=> ! [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_188])]) ).

fof(f1953,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X1))
    | ~ spl0_3
    | ~ spl0_9
    | ~ spl0_17
    | ~ spl0_27
    | ~ spl0_56 ),
    inference(forward_demodulation,[],[f1952,f351]) ).

fof(f1952,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_3
    | ~ spl0_17
    | ~ spl0_56 ),
    inference(forward_demodulation,[],[f1914,f115]) ).

fof(f1914,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_3
    | ~ spl0_56 ),
    inference(superposition,[],[f1498,f32]) ).

fof(f11585,plain,
    ( spl0_187
    | ~ spl0_23
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1776,f1493,f267,f11583]) ).

fof(f11583,plain,
    ( spl0_187
  <=> ! [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_187])]) ).

fof(f1776,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X2))) = X0
    | ~ spl0_23
    | ~ spl0_55 ),
    inference(superposition,[],[f1494,f268]) ).

fof(f11581,plain,
    ( spl0_186
    | ~ spl0_10
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1775,f1493,f61,f11579]) ).

fof(f11579,plain,
    ( spl0_186
  <=> ! [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_186])]) ).

fof(f1775,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2))) = X0
    | ~ spl0_10
    | ~ spl0_55 ),
    inference(superposition,[],[f1494,f62]) ).

fof(f11577,plain,
    ( spl0_185
    | ~ spl0_4
    | ~ spl0_8
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f1762,f1489,f323,f110,f53,f35,f11575]) ).

fof(f11575,plain,
    ( spl0_185
  <=> ! [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_185])]) ).

fof(f1762,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = least_upper_bound(greatest_lower_bound(X1,X0),greatest_lower_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_8
    | ~ spl0_16
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(forward_demodulation,[],[f1761,f331]) ).

fof(f1761,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_4
    | ~ spl0_16
    | ~ spl0_54 ),
    inference(forward_demodulation,[],[f1726,f111]) ).

fof(f1726,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_4
    | ~ spl0_54 ),
    inference(superposition,[],[f1490,f36]) ).

fof(f11573,plain,
    ( spl0_184
    | ~ spl0_24
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f1599,f1485,f271,f11571]) ).

fof(f11571,plain,
    ( spl0_184
  <=> ! [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_184])]) ).

fof(f1599,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),least_upper_bound(X0,X2))) = X0
    | ~ spl0_24
    | ~ spl0_53 ),
    inference(superposition,[],[f1486,f272]) ).

fof(f11569,plain,
    ( spl0_183
    | ~ spl0_11
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f1598,f1485,f65,f11567]) ).

fof(f11567,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

fof(f1598,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2))) = X0
    | ~ spl0_11
    | ~ spl0_53 ),
    inference(superposition,[],[f1486,f66]) ).

fof(f11565,plain,
    ( spl0_182
    | ~ spl0_7
    | ~ spl0_87
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f7090,f5380,f4707,f48,f11562]) ).

fof(f11562,plain,
    ( spl0_182
  <=> least_upper_bound(a,c) = least_upper_bound(c,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f4707,plain,
    ( spl0_87
  <=> least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f5380,plain,
    ( spl0_107
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f7090,plain,
    ( least_upper_bound(a,c) = least_upper_bound(c,b)
    | ~ spl0_7
    | ~ spl0_87
    | ~ spl0_107 ),
    inference(forward_demodulation,[],[f7007,f4709]) ).

fof(f4709,plain,
    ( least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(a,c))
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f4707]) ).

fof(f7007,plain,
    ( least_upper_bound(c,b) = least_upper_bound(b,least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_107 ),
    inference(superposition,[],[f5381,f50]) ).

fof(f5381,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f5380]) ).

fof(f11560,plain,
    ( spl0_181
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1189,f563,f53,f11558]) ).

fof(f11558,plain,
    ( spl0_181
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(multiply(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1189,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(multiply(X0,X1),X1)
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(superposition,[],[f564,f54]) ).

fof(f11556,plain,
    ( spl0_180
    | ~ spl0_8
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1127,f559,f53,f11554]) ).

fof(f11554,plain,
    ( spl0_180
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(X0,X1)) = multiply(greatest_lower_bound(X0,identity),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1127,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(X0,X1)) = multiply(greatest_lower_bound(X0,identity),X1)
    | ~ spl0_8
    | ~ spl0_46 ),
    inference(superposition,[],[f560,f54]) ).

fof(f11552,plain,
    ( spl0_179
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1038,f551,f57,f11550]) ).

fof(f11550,plain,
    ( spl0_179
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(multiply(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1038,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(multiply(X0,X1),X1)
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(superposition,[],[f552,f58]) ).

fof(f11548,plain,
    ( spl0_178
    | ~ spl0_9
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f989,f547,f57,f11546]) ).

fof(f11546,plain,
    ( spl0_178
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(X0,X1)) = multiply(least_upper_bound(X0,identity),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f989,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(X0,X1)) = multiply(least_upper_bound(X0,identity),X1)
    | ~ spl0_9
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f58]) ).

fof(f11544,plain,
    ( spl0_177
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f905,f543,f267,f11542]) ).

fof(f11542,plain,
    ( spl0_177
  <=> ! [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_177])]) ).

fof(f905,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2))
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f268]) ).

fof(f11540,plain,
    ( spl0_176
    | ~ spl0_10
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f904,f543,f61,f11538]) ).

fof(f11538,plain,
    ( spl0_176
  <=> ! [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_176])]) ).

fof(f904,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X2,X0)
    | ~ spl0_10
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f62]) ).

fof(f11536,plain,
    ( spl0_175
    | ~ spl0_9
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f896,f543,f57,f11534]) ).

fof(f11534,plain,
    ( spl0_175
  <=> ! [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_175])]) ).

fof(f896,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(least_upper_bound(X1,X2),X0)
    | ~ spl0_9
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f58]) ).

fof(f11532,plain,
    ( spl0_174
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f877,f543,f267,f11530]) ).

fof(f11530,plain,
    ( spl0_174
  <=> ! [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_174])]) ).

fof(f877,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X2,X0))
    | ~ spl0_23
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f268]) ).

fof(f11528,plain,
    ( spl0_173
    | ~ spl0_10
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f876,f543,f61,f11526]) ).

fof(f11526,plain,
    ( spl0_173
  <=> ! [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_173])]) ).

fof(f876,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,X0) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0))
    | ~ spl0_10
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f62]) ).

fof(f11524,plain,
    ( spl0_172
    | ~ spl0_9
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f844,f534,f57,f11522]) ).

fof(f11522,plain,
    ( spl0_172
  <=> ! [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_172])]) ).

fof(f844,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(X2,greatest_lower_bound(X0,X1)))
    | ~ spl0_9
    | ~ spl0_40 ),
    inference(superposition,[],[f535,f58]) ).

fof(f11520,plain,
    ( spl0_171
    | ~ spl0_6
    | ~ spl0_86
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f6669,f5368,f4702,f43,f11517]) ).

fof(f11517,plain,
    ( spl0_171
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(c,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f4702,plain,
    ( spl0_86
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f5368,plain,
    ( spl0_104
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f6669,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(c,b)
    | ~ spl0_6
    | ~ spl0_86
    | ~ spl0_104 ),
    inference(forward_demodulation,[],[f6584,f4704]) ).

fof(f4704,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f4702]) ).

fof(f6584,plain,
    ( greatest_lower_bound(c,b) = greatest_lower_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_6
    | ~ spl0_104 ),
    inference(superposition,[],[f5369,f45]) ).

fof(f5369,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f5368]) ).

fof(f11515,plain,
    ( spl0_170
    | ~ spl0_9
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f791,f530,f57,f11513]) ).

fof(f11513,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

fof(f791,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,least_upper_bound(X0,X1)) = least_upper_bound(X1,least_upper_bound(X0,X2))
    | ~ spl0_9
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f58]) ).

fof(f11511,plain,
    ( spl0_169
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f789,f530,f114,f11509]) ).

fof(f11509,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

fof(f789,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2))
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f115]) ).

fof(f11507,plain,
    ( spl0_168
    | ~ spl0_23
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f777,f530,f267,f11505]) ).

fof(f11505,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

fof(f777,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X1,X0),least_upper_bound(X0,X2))
    | ~ spl0_23
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f268]) ).

fof(f11503,plain,
    ( spl0_167
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f776,f530,f61,f11501]) ).

fof(f11501,plain,
    ( spl0_167
  <=> ! [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_167])]) ).

fof(f776,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(greatest_lower_bound(X0,X1),least_upper_bound(X0,X2))
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f62]) ).

fof(f11499,plain,
    ( spl0_166
    | ~ spl0_24
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f696,f526,f271,f11497]) ).

fof(f11497,plain,
    ( spl0_166
  <=> ! [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_166])]) ).

fof(f696,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2))
    | ~ spl0_24
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f272]) ).

fof(f11495,plain,
    ( spl0_165
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f695,f526,f65,f11493]) ).

fof(f11493,plain,
    ( spl0_165
  <=> ! [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_165])]) ).

fof(f695,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X2,X0)
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f66]) ).

fof(f11491,plain,
    ( spl0_164
    | ~ spl0_8
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f683,f526,f53,f11489]) ).

fof(f11489,plain,
    ( spl0_164
  <=> ! [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_164])]) ).

fof(f683,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X0)
    | ~ spl0_8
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f54]) ).

fof(f11487,plain,
    ( spl0_163
    | ~ spl0_24
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f668,f526,f271,f11485]) ).

fof(f11485,plain,
    ( spl0_163
  <=> ! [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_163])]) ).

fof(f668,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X2,X0))
    | ~ spl0_24
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f272]) ).

fof(f11483,plain,
    ( spl0_162
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f667,f526,f65,f11481]) ).

fof(f11481,plain,
    ( spl0_162
  <=> ! [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_162])]) ).

fof(f667,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,X0) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X2,X0))
    | ~ spl0_11
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f66]) ).

fof(f11479,plain,
    ( spl0_161
    | ~ spl0_8
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f632,f517,f53,f11477]) ).

fof(f11477,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

fof(f632,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(X2,least_upper_bound(X0,X1)))
    | ~ spl0_8
    | ~ spl0_36 ),
    inference(superposition,[],[f518,f54]) ).

fof(f11475,plain,
    ( spl0_160
    | ~ spl0_13
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f6357,f5360,f83,f11472]) ).

fof(f11472,plain,
    ( spl0_160
  <=> b = least_upper_bound(greatest_lower_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f83,plain,
    ( spl0_13
  <=> b = least_upper_bound(b,greatest_lower_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f6357,plain,
    ( b = least_upper_bound(greatest_lower_bound(a,c),b)
    | ~ spl0_13
    | ~ spl0_102 ),
    inference(superposition,[],[f5361,f85]) ).

fof(f85,plain,
    ( b = least_upper_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f11470,plain,
    ( spl0_159
    | ~ spl0_8
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f584,f513,f53,f11468]) ).

fof(f11468,plain,
    ( spl0_159
  <=> ! [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_159])]) ).

fof(f584,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2))
    | ~ spl0_8
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f54]) ).

fof(f11466,plain,
    ( spl0_158
    | ~ spl0_16
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f582,f513,f110,f11464]) ).

fof(f11464,plain,
    ( spl0_158
  <=> ! [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_158])]) ).

fof(f582,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2))
    | ~ spl0_16
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f111]) ).

fof(f11462,plain,
    ( spl0_157
    | ~ spl0_24
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f571,f513,f271,f11460]) ).

fof(f11460,plain,
    ( spl0_157
  <=> ! [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_157])]) ).

fof(f571,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X1,X0),greatest_lower_bound(X0,X2))
    | ~ spl0_24
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f272]) ).

fof(f11458,plain,
    ( spl0_156
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f570,f513,f65,f11456]) ).

fof(f11456,plain,
    ( spl0_156
  <=> ! [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_156])]) ).

fof(f570,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(least_upper_bound(X0,X1),greatest_lower_bound(X0,X2))
    | ~ spl0_11
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f66]) ).

fof(f11454,plain,
    ( spl0_155
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f301,f271,f110,f11452]) ).

fof(f11452,plain,
    ( spl0_155
  <=> ! [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_155])]) ).

fof(f301,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,X2) = greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X1,X0),X2))
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(superposition,[],[f111,f272]) ).

fof(f11450,plain,
    ( spl0_154
    | ~ spl0_17
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f285,f267,f114,f11448]) ).

fof(f11448,plain,
    ( spl0_154
  <=> ! [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_154])]) ).

fof(f285,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,X2) = least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2))
    | ~ spl0_17
    | ~ spl0_23 ),
    inference(superposition,[],[f115,f268]) ).

fof(f10945,plain,
    ( spl0_153
    | ~ spl0_19
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f6239,f5352,f166,f10942]) ).

fof(f10942,plain,
    ( spl0_153
  <=> b = greatest_lower_bound(least_upper_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f166,plain,
    ( spl0_19
  <=> b = greatest_lower_bound(b,least_upper_bound(a,c)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f6239,plain,
    ( b = greatest_lower_bound(least_upper_bound(a,c),b)
    | ~ spl0_19
    | ~ spl0_100 ),
    inference(superposition,[],[f5353,f168]) ).

fof(f168,plain,
    ( b = greatest_lower_bound(b,least_upper_bound(a,c))
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f166]) ).

fof(f9168,plain,
    ( spl0_152
    | ~ spl0_13
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1792,f1493,f83,f9166]) ).

fof(f9166,plain,
    ( spl0_152
  <=> ! [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_152])]) ).

fof(f1792,plain,
    ( ! [X0] : b = least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(b,X0)))
    | ~ spl0_13
    | ~ spl0_55 ),
    inference(superposition,[],[f1494,f85]) ).

fof(f9164,plain,
    ( spl0_151
    | ~ spl0_19
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f1609,f1485,f166,f9162]) ).

fof(f9162,plain,
    ( spl0_151
  <=> ! [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_151])]) ).

fof(f1609,plain,
    ( ! [X0] : b = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),least_upper_bound(b,X0)))
    | ~ spl0_19
    | ~ spl0_53 ),
    inference(superposition,[],[f1486,f168]) ).

fof(f9160,plain,
    ( spl0_150
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f918,f543,f83,f9158]) ).

fof(f9158,plain,
    ( spl0_150
  <=> ! [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_150])]) ).

fof(f918,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(X0,b)
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f85]) ).

fof(f9156,plain,
    ( spl0_149
    | ~ spl0_7
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f917,f543,f48,f9154]) ).

fof(f9154,plain,
    ( spl0_149
  <=> ! [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_149])]) ).

fof(f917,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(X0,least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f50]) ).

fof(f9152,plain,
    ( spl0_148
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f890,f543,f83,f9150]) ).

fof(f9150,plain,
    ( spl0_148
  <=> ! [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_148])]) ).

fof(f890,plain,
    ( ! [X0] : least_upper_bound(X0,b) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(X0,b))
    | ~ spl0_13
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f85]) ).

fof(f9148,plain,
    ( spl0_147
    | ~ spl0_7
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f889,f543,f48,f9146]) ).

fof(f9146,plain,
    ( spl0_147
  <=> ! [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_147])]) ).

fof(f889,plain,
    ( ! [X0] : least_upper_bound(X0,least_upper_bound(a,c)) = least_upper_bound(c,least_upper_bound(X0,b))
    | ~ spl0_7
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f50]) ).

fof(f9144,plain,
    ( spl0_146
    | ~ spl0_5
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f6036,f5348,f39,f9142]) ).

fof(f9142,plain,
    ( spl0_146
  <=> ! [X0] : identity = multiply(X0,inverse(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f39,plain,
    ( spl0_5
  <=> ! [X0] : identity = multiply(inverse(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f6036,plain,
    ( ! [X0] : identity = multiply(X0,inverse(X0))
    | ~ spl0_5
    | ~ spl0_99 ),
    inference(superposition,[],[f5349,f40]) ).

fof(f40,plain,
    ( ! [X0] : identity = multiply(inverse(X0),X0)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f9140,plain,
    ( spl0_145
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_34
    | ~ spl0_39
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f813,f543,f530,f467,f57,f48,f9138]) ).

fof(f9138,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f813,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(a,least_upper_bound(X0,c))
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_34
    | ~ spl0_39
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f812,f484]) ).

fof(f484,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(X0,c)) = least_upper_bound(a,least_upper_bound(X0,c))
    | ~ spl0_9
    | ~ spl0_34 ),
    inference(superposition,[],[f468,f58]) ).

fof(f812,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(b,least_upper_bound(X0,c))
    | ~ spl0_7
    | ~ spl0_39
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f786,f544]) ).

fof(f786,plain,
    ( ! [X0] : least_upper_bound(least_upper_bound(a,c),X0) = least_upper_bound(c,least_upper_bound(b,X0))
    | ~ spl0_7
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f50]) ).

fof(f9136,plain,
    ( spl0_144
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f787,f530,f83,f9134]) ).

fof(f9134,plain,
    ( spl0_144
  <=> ! [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_144])]) ).

fof(f787,plain,
    ( ! [X0] : least_upper_bound(b,X0) = least_upper_bound(greatest_lower_bound(a,c),least_upper_bound(b,X0))
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(superposition,[],[f531,f85]) ).

fof(f9132,plain,
    ( spl0_143
    | ~ spl0_19
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f705,f526,f166,f9130]) ).

fof(f9130,plain,
    ( spl0_143
  <=> ! [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_143])]) ).

fof(f705,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(X0,b)
    | ~ spl0_19
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f168]) ).

fof(f9128,plain,
    ( spl0_142
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f704,f526,f43,f9126]) ).

fof(f9126,plain,
    ( spl0_142
  <=> ! [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_142])]) ).

fof(f704,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(X0,greatest_lower_bound(a,c))
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f45]) ).

fof(f9124,plain,
    ( spl0_141
    | ~ spl0_19
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f677,f526,f166,f9122]) ).

fof(f9122,plain,
    ( spl0_141
  <=> ! [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_141])]) ).

fof(f677,plain,
    ( ! [X0] : greatest_lower_bound(X0,b) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(X0,b))
    | ~ spl0_19
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f168]) ).

fof(f9120,plain,
    ( spl0_140
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f676,f526,f43,f9118]) ).

fof(f9118,plain,
    ( spl0_140
  <=> ! [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_140])]) ).

fof(f676,plain,
    ( ! [X0] : greatest_lower_bound(X0,greatest_lower_bound(a,c)) = greatest_lower_bound(c,greatest_lower_bound(X0,b))
    | ~ spl0_6
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f45]) ).

fof(f9116,plain,
    ( spl0_139
    | ~ spl0_6
    | ~ spl0_8
    | ~ spl0_33
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f605,f526,f513,f463,f53,f43,f9114]) ).

fof(f9114,plain,
    ( spl0_139
  <=> ! [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_139])]) ).

fof(f605,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(a,greatest_lower_bound(X0,c))
    | ~ spl0_6
    | ~ spl0_8
    | ~ spl0_33
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f604,f471]) ).

fof(f471,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(X0,c)) = greatest_lower_bound(a,greatest_lower_bound(X0,c))
    | ~ spl0_8
    | ~ spl0_33 ),
    inference(superposition,[],[f464,f54]) ).

fof(f604,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(b,greatest_lower_bound(X0,c))
    | ~ spl0_6
    | ~ spl0_35
    | ~ spl0_38 ),
    inference(forward_demodulation,[],[f579,f527]) ).

fof(f579,plain,
    ( ! [X0] : greatest_lower_bound(greatest_lower_bound(a,c),X0) = greatest_lower_bound(c,greatest_lower_bound(b,X0))
    | ~ spl0_6
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f45]) ).

fof(f9112,plain,
    ( spl0_138
    | ~ spl0_19
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f580,f513,f166,f9110]) ).

fof(f9110,plain,
    ( spl0_138
  <=> ! [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_138])]) ).

fof(f580,plain,
    ( ! [X0] : greatest_lower_bound(b,X0) = greatest_lower_bound(least_upper_bound(a,c),greatest_lower_bound(b,X0))
    | ~ spl0_19
    | ~ spl0_35 ),
    inference(superposition,[],[f514,f168]) ).

fof(f9108,plain,
    ( spl0_137
    | ~ spl0_9
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f484,f467,f57,f9106]) ).

fof(f9106,plain,
    ( spl0_137
  <=> ! [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_137])]) ).

fof(f9104,plain,
    ( spl0_136
    | ~ spl0_8
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f471,f463,f53,f9102]) ).

fof(f9102,plain,
    ( spl0_136
  <=> ! [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_136])]) ).

fof(f9055,plain,
    ( spl0_135
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f264,f166,f110,f9053]) ).

fof(f9053,plain,
    ( spl0_135
  <=> ! [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_135])]) ).

fof(f264,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,c),X0)) = greatest_lower_bound(b,X0)
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(superposition,[],[f111,f168]) ).

fof(f9051,plain,
    ( spl0_134
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f262,f114,f83,f9049]) ).

fof(f9049,plain,
    ( spl0_134
  <=> ! [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_134])]) ).

fof(f262,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(greatest_lower_bound(a,c),X0)) = least_upper_bound(b,X0)
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f85]) ).

fof(f9046,plain,
    ( spl0_133
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1239,f563,f53,f39,f9044]) ).

fof(f9044,plain,
    ( spl0_133
  <=> ! [X0] : greatest_lower_bound(identity,X0) = multiply(greatest_lower_bound(identity,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1239,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(greatest_lower_bound(identity,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1195,f54]) ).

fof(f1195,plain,
    ( ! [X0] : greatest_lower_bound(identity,X0) = multiply(greatest_lower_bound(inverse(X0),identity),X0)
    | ~ spl0_5
    | ~ spl0_47 ),
    inference(superposition,[],[f564,f40]) ).

fof(f8887,plain,
    ( spl0_132
    | ~ spl0_14
    | ~ spl0_69
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f8883,f8880,f1964,f88,f8885]) ).

fof(f8885,plain,
    ( spl0_132
  <=> ! [X0] : greatest_lower_bound(X0,identity) = multiply(inverse(least_upper_bound(identity,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f8880,plain,
    ( spl0_131
  <=> ! [X0] : greatest_lower_bound(X0,identity) = multiply(greatest_lower_bound(identity,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f8883,plain,
    ( ! [X0] : greatest_lower_bound(X0,identity) = multiply(inverse(least_upper_bound(identity,X0)),X0)
    | ~ spl0_14
    | ~ spl0_69
    | ~ spl0_131 ),
    inference(forward_demodulation,[],[f8881,f2816]) ).

fof(f2816,plain,
    ( ! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0))
    | ~ spl0_14
    | ~ spl0_69 ),
    inference(superposition,[],[f89,f1966]) ).

fof(f8881,plain,
    ( ! [X0] : greatest_lower_bound(X0,identity) = multiply(greatest_lower_bound(identity,inverse(X0)),X0)
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f8880]) ).

fof(f8882,plain,
    ( spl0_131
    | ~ spl0_5
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1136,f559,f39,f8880]) ).

fof(f1136,plain,
    ( ! [X0] : greatest_lower_bound(X0,identity) = multiply(greatest_lower_bound(identity,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_46 ),
    inference(superposition,[],[f560,f40]) ).

fof(f8877,plain,
    ( spl0_130
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1084,f551,f57,f39,f8875]) ).

fof(f8875,plain,
    ( spl0_130
  <=> ! [X0] : least_upper_bound(identity,X0) = multiply(least_upper_bound(identity,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1084,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(least_upper_bound(identity,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_44 ),
    inference(forward_demodulation,[],[f1044,f58]) ).

fof(f1044,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = multiply(least_upper_bound(inverse(X0),identity),X0)
    | ~ spl0_5
    | ~ spl0_44 ),
    inference(superposition,[],[f552,f40]) ).

fof(f8716,plain,
    ( spl0_129
    | ~ spl0_12
    | ~ spl0_69
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f8712,f8709,f1964,f79,f8714]) ).

fof(f8714,plain,
    ( spl0_129
  <=> ! [X0] : least_upper_bound(X0,identity) = multiply(inverse(greatest_lower_bound(identity,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f8709,plain,
    ( spl0_128
  <=> ! [X0] : least_upper_bound(X0,identity) = multiply(least_upper_bound(identity,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f8712,plain,
    ( ! [X0] : least_upper_bound(X0,identity) = multiply(inverse(greatest_lower_bound(identity,X0)),X0)
    | ~ spl0_12
    | ~ spl0_69
    | ~ spl0_128 ),
    inference(forward_demodulation,[],[f8710,f2814]) ).

fof(f2814,plain,
    ( ! [X0] : least_upper_bound(identity,inverse(X0)) = inverse(greatest_lower_bound(identity,X0))
    | ~ spl0_12
    | ~ spl0_69 ),
    inference(superposition,[],[f80,f1966]) ).

fof(f8710,plain,
    ( ! [X0] : least_upper_bound(X0,identity) = multiply(least_upper_bound(identity,inverse(X0)),X0)
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f8709]) ).

fof(f8711,plain,
    ( spl0_128
    | ~ spl0_5
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f998,f547,f39,f8709]) ).

fof(f998,plain,
    ( ! [X0] : least_upper_bound(X0,identity) = multiply(least_upper_bound(identity,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f40]) ).

fof(f8707,plain,
    ( spl0_127
    | ~ spl0_45
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f8011,f7278,f555,f8705]) ).

fof(f555,plain,
    ( spl0_45
  <=> ! [X0] : multiply(inverse(inverse(X0)),identity) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f7278,plain,
    ( spl0_118
  <=> ! [X0] : multiply(X0,identity) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f8011,plain,
    ( ! [X0] : inverse(inverse(X0)) = X0
    | ~ spl0_45
    | ~ spl0_118 ),
    inference(superposition,[],[f7279,f556]) ).

fof(f556,plain,
    ( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f555]) ).

fof(f7279,plain,
    ( ! [X0] : multiply(X0,identity) = X0
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f7278]) ).

fof(f8155,plain,
    ( spl0_126
    | ~ spl0_5
    | ~ spl0_25
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f2339,f1517,f375,f305,f39,f8153]) ).

fof(f8153,plain,
    ( spl0_126
  <=> ! [X0,X1] : identity = greatest_lower_bound(identity,multiply(X0,inverse(greatest_lower_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f2339,plain,
    ( ! [X0,X1] : identity = greatest_lower_bound(identity,multiply(X0,inverse(greatest_lower_bound(X0,X1))))
    | ~ spl0_5
    | ~ spl0_25
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f2338,f40]) ).

fof(f2338,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(X0)) = greatest_lower_bound(identity,multiply(X0,inverse(greatest_lower_bound(X0,X1))))
    | ~ spl0_25
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(forward_demodulation,[],[f2298,f311]) ).

fof(f311,plain,
    ( ! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1)
    | ~ spl0_25 ),
    inference(superposition,[],[f306,f306]) ).

fof(f2298,plain,
    ( ! [X0,X1] : multiply(inverse(inverse(X0)),inverse(X0)) = greatest_lower_bound(identity,multiply(inverse(inverse(X0)),inverse(greatest_lower_bound(X0,X1))))
    | ~ spl0_29
    | ~ spl0_61 ),
    inference(superposition,[],[f1518,f376]) ).

fof(f8150,plain,
    ( spl0_125
    | ~ spl0_5
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f2022,f1501,f83,f39,f8147]) ).

fof(f8147,plain,
    ( spl0_125
  <=> identity = least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f2022,plain,
    ( identity = least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c)))
    | ~ spl0_5
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1989,f40]) ).

fof(f1989,plain,
    ( least_upper_bound(identity,multiply(inverse(b),greatest_lower_bound(a,c))) = multiply(inverse(b),b)
    | ~ spl0_13
    | ~ spl0_57 ),
    inference(superposition,[],[f1502,f85]) ).

fof(f8145,plain,
    ( spl0_124
    | ~ spl0_5
    | ~ spl0_25
    | ~ spl0_32
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f2020,f1501,f387,f305,f39,f8143]) ).

fof(f8143,plain,
    ( spl0_124
  <=> ! [X0,X1] : identity = least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f2020,plain,
    ( ! [X0,X1] : identity = least_upper_bound(identity,multiply(X0,inverse(least_upper_bound(X0,X1))))
    | ~ spl0_5
    | ~ spl0_25
    | ~ spl0_32
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f2019,f311]) ).

fof(f2019,plain,
    ( ! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1))))
    | ~ spl0_5
    | ~ spl0_32
    | ~ spl0_57 ),
    inference(forward_demodulation,[],[f1984,f40]) ).

fof(f1984,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(inverse(X0)),inverse(least_upper_bound(X0,X1)))) = multiply(inverse(inverse(X0)),inverse(X0))
    | ~ spl0_32
    | ~ spl0_57 ),
    inference(superposition,[],[f1502,f388]) ).

fof(f8140,plain,
    ( spl0_123
    | ~ spl0_5
    | ~ spl0_32
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1324,f1280,f387,f39,f8138]) ).

fof(f8138,plain,
    ( spl0_123
  <=> ! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1324,plain,
    ( ! [X0,X1] : identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0))
    | ~ spl0_5
    | ~ spl0_32
    | ~ spl0_48 ),
    inference(forward_demodulation,[],[f1297,f40]) ).

fof(f1297,plain,
    ( ! [X0,X1] : multiply(inverse(X0),X0) = least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,X1)),X0))
    | ~ spl0_32
    | ~ spl0_48 ),
    inference(superposition,[],[f1281,f388]) ).

fof(f8010,plain,
    ( spl0_122
    | ~ spl0_7
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f450,f387,f48,f8007]) ).

fof(f8007,plain,
    ( spl0_122
  <=> inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f450,plain,
    ( inverse(b) = least_upper_bound(inverse(b),inverse(least_upper_bound(a,c)))
    | ~ spl0_7
    | ~ spl0_32 ),
    inference(superposition,[],[f388,f50]) ).

fof(f8005,plain,
    ( spl0_121
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f413,f375,f43,f8002]) ).

fof(f8002,plain,
    ( spl0_121
  <=> inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,c))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f413,plain,
    ( inverse(b) = greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(a,c)))
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(superposition,[],[f376,f45]) ).

fof(f8000,plain,
    ( spl0_120
    | ~ spl0_12
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f295,f271,f79,f7998]) ).

fof(f7998,plain,
    ( spl0_120
  <=> ! [X0,X1] : inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f295,plain,
    ( ! [X0,X1] : inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_12
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f80]) ).

fof(f7996,plain,
    ( spl0_119
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f280,f267,f88,f7994]) ).

fof(f280,plain,
    ( ! [X0,X1] : inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_14
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f89]) ).

fof(f7280,plain,
    ( spl0_118
    | ~ spl0_45
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f6037,f5348,f555,f7278]) ).

fof(f6037,plain,
    ( ! [X0] : multiply(X0,identity) = X0
    | ~ spl0_45
    | ~ spl0_99 ),
    inference(superposition,[],[f5349,f556]) ).

fof(f5422,plain,
    ( spl0_117
    | ~ spl0_2
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f2433,f1521,f27,f5420]) ).

fof(f5420,plain,
    ( spl0_117
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(identity,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f27,plain,
    ( spl0_2
  <=> ! [X0] : multiply(identity,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f2433,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = multiply(identity,greatest_lower_bound(X0,X1))
    | ~ spl0_2
    | ~ spl0_62 ),
    inference(forward_demodulation,[],[f2371,f28]) ).

fof(f28,plain,
    ( ! [X0] : multiply(identity,X0) = X0
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f2371,plain,
    ( ! [X0,X1] : multiply(identity,greatest_lower_bound(X0,X1)) = greatest_lower_bound(multiply(identity,X1),X0)
    | ~ spl0_2
    | ~ spl0_62 ),
    inference(superposition,[],[f1522,f28]) ).

fof(f5418,plain,
    ( spl0_116
    | ~ spl0_2
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f2106,f1505,f27,f5416]) ).

fof(f5416,plain,
    ( spl0_116
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = multiply(identity,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f2106,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = multiply(identity,least_upper_bound(X0,X1))
    | ~ spl0_2
    | ~ spl0_58 ),
    inference(forward_demodulation,[],[f2048,f28]) ).

fof(f2048,plain,
    ( ! [X0,X1] : multiply(identity,least_upper_bound(X0,X1)) = least_upper_bound(multiply(identity,X1),X0)
    | ~ spl0_2
    | ~ spl0_58 ),
    inference(superposition,[],[f1506,f28]) ).

fof(f5414,plain,
    ( spl0_115
    | ~ spl0_2
    | ~ spl0_8
    | ~ spl0_11
    | ~ spl0_43
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f1244,f563,f547,f65,f53,f27,f5412]) ).

fof(f5412,plain,
    ( spl0_115
  <=> ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1244,plain,
    ( ! [X0,X1] : greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1) = X1
    | ~ spl0_2
    | ~ spl0_8
    | ~ spl0_11
    | ~ spl0_43
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1243,f28]) ).

fof(f1243,plain,
    ( ! [X0,X1] : multiply(identity,X1) = greatest_lower_bound(least_upper_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_8
    | ~ spl0_11
    | ~ spl0_43
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1242,f66]) ).

fof(f1242,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_8
    | ~ spl0_43
    | ~ spl0_47 ),
    inference(forward_demodulation,[],[f1197,f54]) ).

fof(f1197,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_43
    | ~ spl0_47 ),
    inference(superposition,[],[f564,f548]) ).

fof(f5410,plain,
    ( spl0_114
    | ~ spl0_2
    | ~ spl0_9
    | ~ spl0_10
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1187,f559,f551,f61,f57,f27,f5408]) ).

fof(f5408,plain,
    ( spl0_114
  <=> ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1187,plain,
    ( ! [X0,X1] : least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1) = X1
    | ~ spl0_2
    | ~ spl0_9
    | ~ spl0_10
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f1186,f28]) ).

fof(f1186,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(greatest_lower_bound(X1,multiply(X0,X1)),X1)
    | ~ spl0_9
    | ~ spl0_10
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f1185,f62]) ).

fof(f1185,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_9
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f1157,f58]) ).

fof(f1157,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_44
    | ~ spl0_46 ),
    inference(superposition,[],[f552,f560]) ).

fof(f5406,plain,
    ( spl0_113
    | ~ spl0_24
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f1072,f551,f271,f5404]) ).

fof(f5404,plain,
    ( spl0_113
  <=> ! [X0,X1] : greatest_lower_bound(X1,multiply(least_upper_bound(X0,identity),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1072,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,multiply(least_upper_bound(X0,identity),X1)) = X1
    | ~ spl0_24
    | ~ spl0_44 ),
    inference(superposition,[],[f272,f552]) ).

fof(f5402,plain,
    ( spl0_112
    | ~ spl0_32
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f2824,f1964,f387,f5400]) ).

fof(f5400,plain,
    ( spl0_112
  <=> ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2824,plain,
    ( ! [X0] : identity = least_upper_bound(identity,inverse(least_upper_bound(identity,X0)))
    | ~ spl0_32
    | ~ spl0_69 ),
    inference(superposition,[],[f388,f1966]) ).

fof(f5398,plain,
    ( spl0_111
    | ~ spl0_2
    | ~ spl0_23
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1031,f547,f267,f27,f5396]) ).

fof(f5396,plain,
    ( spl0_111
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1031,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1)) = X1
    | ~ spl0_2
    | ~ spl0_23
    | ~ spl0_43 ),
    inference(forward_demodulation,[],[f992,f28]) ).

fof(f992,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(X1,multiply(greatest_lower_bound(X0,identity),X1))
    | ~ spl0_23
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f268]) ).

fof(f5394,plain,
    ( spl0_110
    | ~ spl0_2
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1030,f547,f61,f27,f5392]) ).

fof(f5392,plain,
    ( spl0_110
  <=> ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1030,plain,
    ( ! [X0,X1] : least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1)) = X1
    | ~ spl0_2
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(forward_demodulation,[],[f991,f28]) ).

fof(f991,plain,
    ( ! [X0,X1] : multiply(identity,X1) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X0),X1))
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f62]) ).

fof(f5390,plain,
    ( spl0_109
    | ~ spl0_11
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1016,f547,f65,f5388]) ).

fof(f5388,plain,
    ( spl0_109
  <=> ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1016,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,multiply(least_upper_bound(identity,X1),X0)) = X0
    | ~ spl0_11
    | ~ spl0_43 ),
    inference(superposition,[],[f66,f548]) ).

fof(f5386,plain,
    ( spl0_108
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f920,f543,f327,f5384]) ).

fof(f5384,plain,
    ( spl0_108
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f920,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,X0))
    | ~ spl0_27
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f328]) ).

fof(f5382,plain,
    ( spl0_107
    | ~ spl0_3
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f901,f543,f31,f5380]) ).

fof(f901,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_3
    | ~ spl0_42 ),
    inference(superposition,[],[f544,f32]) ).

fof(f5378,plain,
    ( spl0_106
    | ~ spl0_10
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f719,f526,f61,f5376]) ).

fof(f5376,plain,
    ( spl0_106
  <=> ! [X2,X0,X1] : least_upper_bound(X0,greatest_lower_bound(X2,greatest_lower_bound(X0,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f719,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,greatest_lower_bound(X2,greatest_lower_bound(X0,X1))) = X0
    | ~ spl0_10
    | ~ spl0_38 ),
    inference(superposition,[],[f62,f527]) ).

fof(f5374,plain,
    ( spl0_105
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f707,f526,f323,f5372]) ).

fof(f5372,plain,
    ( spl0_105
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f707,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,X0))
    | ~ spl0_26
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f324]) ).

fof(f5370,plain,
    ( spl0_104
    | ~ spl0_4
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f688,f526,f35,f5368]) ).

fof(f688,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_38 ),
    inference(superposition,[],[f527,f36]) ).

fof(f5366,plain,
    ( spl0_103
    | ~ spl0_11
    | ~ spl0_24
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f652,f517,f271,f65,f5364]) ).

fof(f5364,plain,
    ( spl0_103
  <=> ! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X2,least_upper_bound(X0,X1))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f652,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X2,least_upper_bound(X0,X1))) = X0
    | ~ spl0_11
    | ~ spl0_24
    | ~ spl0_36 ),
    inference(forward_demodulation,[],[f636,f66]) ).

fof(f636,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_24
    | ~ spl0_36 ),
    inference(superposition,[],[f518,f272]) ).

fof(f5362,plain,
    ( spl0_102
    | ~ spl0_9
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f351,f327,f57,f5360]) ).

fof(f5358,plain,
    ( spl0_101
    | ~ spl0_29
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f2821,f1964,f375,f5356]) ).

fof(f5356,plain,
    ( spl0_101
  <=> ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f2821,plain,
    ( ! [X0] : identity = greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X0)))
    | ~ spl0_29
    | ~ spl0_69 ),
    inference(superposition,[],[f376,f1966]) ).

fof(f5354,plain,
    ( spl0_100
    | ~ spl0_8
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f331,f323,f53,f5352]) ).

fof(f5350,plain,
    ( spl0_99
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f311,f305,f5348]) ).

fof(f5346,plain,
    ( spl0_98
    | ~ spl0_23
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f300,f271,f267,f5344]) ).

fof(f5344,plain,
    ( spl0_98
  <=> ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(least_upper_bound(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f300,plain,
    ( ! [X0,X1] : least_upper_bound(X1,X0) = least_upper_bound(least_upper_bound(X1,X0),X0)
    | ~ spl0_23
    | ~ spl0_24 ),
    inference(superposition,[],[f268,f272]) ).

fof(f5342,plain,
    ( spl0_97
    | ~ spl0_17
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f296,f271,f114,f5340]) ).

fof(f5340,plain,
    ( spl0_97
  <=> ! [X2,X0,X1] : greatest_lower_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f296,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X2,least_upper_bound(X0,least_upper_bound(X1,X2))) = X2
    | ~ spl0_17
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f115]) ).

fof(f5338,plain,
    ( spl0_96
    | ~ spl0_23
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f292,f271,f267,f5336]) ).

fof(f5336,plain,
    ( spl0_96
  <=> ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(greatest_lower_bound(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f292,plain,
    ( ! [X0,X1] : greatest_lower_bound(X1,X0) = greatest_lower_bound(greatest_lower_bound(X1,X0),X0)
    | ~ spl0_23
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f268]) ).

fof(f5334,plain,
    ( spl0_95
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f291,f271,f61,f5332]) ).

fof(f5332,plain,
    ( spl0_95
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(greatest_lower_bound(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f291,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(greatest_lower_bound(X0,X1),X0)
    | ~ spl0_10
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f62]) ).

fof(f5330,plain,
    ( spl0_94
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f281,f267,f110,f5328]) ).

fof(f5328,plain,
    ( spl0_94
  <=> ! [X2,X0,X1] : least_upper_bound(X2,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f281,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X2,greatest_lower_bound(X0,greatest_lower_bound(X1,X2))) = X2
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f111]) ).

fof(f5326,plain,
    ( spl0_93
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f277,f267,f65,f5324]) ).

fof(f5324,plain,
    ( spl0_93
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f277,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0)
    | ~ spl0_11
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f66]) ).

fof(f4732,plain,
    ( spl0_92
    | ~ spl0_11
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f489,f467,f65,f4730]) ).

fof(f4730,plain,
    ( spl0_92
  <=> ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f489,plain,
    ( ! [X0] : b = greatest_lower_bound(b,least_upper_bound(a,least_upper_bound(c,X0)))
    | ~ spl0_11
    | ~ spl0_34 ),
    inference(superposition,[],[f66,f468]) ).

fof(f4728,plain,
    ( spl0_91
    | ~ spl0_10
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f476,f463,f61,f4726]) ).

fof(f4726,plain,
    ( spl0_91
  <=> ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f476,plain,
    ( ! [X0] : b = least_upper_bound(b,greatest_lower_bound(a,greatest_lower_bound(c,X0)))
    | ~ spl0_10
    | ~ spl0_33 ),
    inference(superposition,[],[f62,f464]) ).

fof(f4724,plain,
    ( spl0_90
    | ~ spl0_14
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f421,f383,f88,f4722]) ).

fof(f4722,plain,
    ( spl0_90
  <=> ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f421,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = inverse(least_upper_bound(X1,X0))
    | ~ spl0_14
    | ~ spl0_31 ),
    inference(superposition,[],[f384,f89]) ).

fof(f4720,plain,
    ( spl0_89
    | ~ spl0_12
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f390,f371,f79,f4718]) ).

fof(f390,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0))
    | ~ spl0_12
    | ~ spl0_28 ),
    inference(superposition,[],[f372,f80]) ).

fof(f4714,plain,
    ( spl0_88
    | ~ spl0_4
    | ~ spl0_30
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f1176,f559,f379,f35,f4712]) ).

fof(f4712,plain,
    ( spl0_88
  <=> ! [X0] : multiply(greatest_lower_bound(identity,inverse(identity)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f379,plain,
    ( spl0_30
  <=> ! [X0] : multiply(inverse(identity),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f1176,plain,
    ( ! [X0] : multiply(greatest_lower_bound(identity,inverse(identity)),X0) = X0
    | ~ spl0_4
    | ~ spl0_30
    | ~ spl0_46 ),
    inference(forward_demodulation,[],[f1137,f36]) ).

fof(f1137,plain,
    ( ! [X0] : greatest_lower_bound(X0,X0) = multiply(greatest_lower_bound(identity,inverse(identity)),X0)
    | ~ spl0_30
    | ~ spl0_46 ),
    inference(superposition,[],[f560,f380]) ).

fof(f380,plain,
    ( ! [X0] : multiply(inverse(identity),X0) = X0
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f4710,plain,
    ( spl0_87
    | ~ spl0_7
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f360,f327,f48,f4707]) ).

fof(f360,plain,
    ( least_upper_bound(a,c) = least_upper_bound(b,least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_27 ),
    inference(superposition,[],[f328,f50]) ).

fof(f4705,plain,
    ( spl0_86
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f340,f323,f43,f4702]) ).

fof(f340,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(superposition,[],[f324,f45]) ).

fof(f4700,plain,
    ( spl0_85
    | ~ spl0_13
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f298,f271,f83,f4697]) ).

fof(f4697,plain,
    ( spl0_85
  <=> greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f298,plain,
    ( greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,c),b)
    | ~ spl0_13
    | ~ spl0_24 ),
    inference(superposition,[],[f272,f85]) ).

fof(f4695,plain,
    ( spl0_84
    | ~ spl0_19
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f283,f267,f166,f4692]) ).

fof(f4692,plain,
    ( spl0_84
  <=> least_upper_bound(a,c) = least_upper_bound(least_upper_bound(a,c),b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f283,plain,
    ( least_upper_bound(a,c) = least_upper_bound(least_upper_bound(a,c),b)
    | ~ spl0_19
    | ~ spl0_23 ),
    inference(superposition,[],[f268,f168]) ).

fof(f4332,plain,
    ( spl0_83
    | ~ spl0_15
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f219,f171,f106,f4330]) ).

fof(f4330,plain,
    ( spl0_83
  <=> ! [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_83])]) ).

fof(f219,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_15
    | ~ spl0_20 ),
    inference(forward_demodulation,[],[f218,f107]) ).

fof(f218,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_15
    | ~ spl0_20 ),
    inference(forward_demodulation,[],[f205,f107]) ).

fof(f205,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_15
    | ~ spl0_20 ),
    inference(superposition,[],[f172,f107]) ).

fof(f4328,plain,
    ( spl0_82
    | ~ spl0_15
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f198,f162,f106,f4326]) ).

fof(f4326,plain,
    ( spl0_82
  <=> ! [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_82])]) ).

fof(f198,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_15
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f197,f107]) ).

fof(f197,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_15
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f184,f107]) ).

fof(f184,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_15
    | ~ spl0_18 ),
    inference(superposition,[],[f163,f107]) ).

fof(f4057,plain,
    ( spl0_81
    | ~ spl0_25
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f1120,f555,f305,f4055]) ).

fof(f4055,plain,
    ( spl0_81
  <=> ! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1120,plain,
    ( ! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0)
    | ~ spl0_25
    | ~ spl0_45 ),
    inference(superposition,[],[f306,f556]) ).

fof(f3220,plain,
    ( spl0_80
    | ~ spl0_16
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f255,f179,f110,f3218]) ).

fof(f3218,plain,
    ( spl0_80
  <=> ! [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_80])]) ).

fof(f255,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_16
    | ~ spl0_22 ),
    inference(superposition,[],[f111,f180]) ).

fof(f3216,plain,
    ( spl0_79
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f248,f179,f106,f3214]) ).

fof(f3214,plain,
    ( spl0_79
  <=> ! [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_79])]) ).

fof(f248,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_15
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f107]) ).

fof(f3212,plain,
    ( spl0_78
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f245,f179,f106,f3210]) ).

fof(f3210,plain,
    ( spl0_78
  <=> ! [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_78])]) ).

fof(f245,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_15
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f107]) ).

fof(f3208,plain,
    ( spl0_77
    | ~ spl0_17
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f236,f175,f114,f3206]) ).

fof(f3206,plain,
    ( spl0_77
  <=> ! [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_77])]) ).

fof(f236,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_17
    | ~ spl0_21 ),
    inference(superposition,[],[f115,f176]) ).

fof(f3202,plain,
    ( spl0_76
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f1034,f547,f379,f31,f3200]) ).

fof(f3200,plain,
    ( spl0_76
  <=> ! [X0] : multiply(least_upper_bound(identity,inverse(identity)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1034,plain,
    ( ! [X0] : multiply(least_upper_bound(identity,inverse(identity)),X0) = X0
    | ~ spl0_3
    | ~ spl0_30
    | ~ spl0_43 ),
    inference(forward_demodulation,[],[f999,f32]) ).

fof(f999,plain,
    ( ! [X0] : least_upper_bound(X0,X0) = multiply(least_upper_bound(identity,inverse(identity)),X0)
    | ~ spl0_30
    | ~ spl0_43 ),
    inference(superposition,[],[f548,f380]) ).

fof(f3198,plain,
    ( spl0_75
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f229,f175,f106,f3196]) ).

fof(f3196,plain,
    ( spl0_75
  <=> ! [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_75])]) ).

fof(f229,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_15
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f107]) ).

fof(f3194,plain,
    ( spl0_74
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f226,f175,f106,f3192]) ).

fof(f3192,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f226,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_15
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f107]) ).

fof(f3190,plain,
    ( spl0_73
    | ~ spl0_16
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f213,f171,f110,f3188]) ).

fof(f3188,plain,
    ( spl0_73
  <=> ! [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_73])]) ).

fof(f213,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_16
    | ~ spl0_20 ),
    inference(superposition,[],[f111,f172]) ).

fof(f3186,plain,
    ( spl0_72
    | ~ spl0_17
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f192,f162,f114,f3184]) ).

fof(f3184,plain,
    ( spl0_72
  <=> ! [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_72])]) ).

fof(f192,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_17
    | ~ spl0_18 ),
    inference(superposition,[],[f115,f163]) ).

fof(f3038,plain,
    ( spl0_71
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f146,f114,f79,f3036]) ).

fof(f146,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_12
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f80]) ).

fof(f3034,plain,
    ( spl0_70
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f127,f110,f88,f3032]) ).

fof(f127,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_14
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f89]) ).

fof(f1967,plain,
    ( spl0_69
    | ~ spl0_5
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1524,f1481,f39,f1964]) ).

fof(f1481,plain,
    ( spl0_52
  <=> ! [X0] : multiply(inverse(inverse(identity)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1524,plain,
    ( identity = inverse(identity)
    | ~ spl0_5
    | ~ spl0_52 ),
    inference(superposition,[],[f1482,f40]) ).

fof(f1482,plain,
    ( ! [X0] : multiply(inverse(inverse(identity)),X0) = X0
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1481]) ).

fof(f1588,plain,
    ( spl0_68
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f256,f179,f61,f1586]) ).

fof(f256,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(superposition,[],[f62,f180]) ).

fof(f1584,plain,
    ( spl0_67
    | ~ spl0_8
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f251,f179,f53,f1582]) ).

fof(f251,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_8
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f54]) ).

fof(f1580,plain,
    ( spl0_66
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f237,f175,f65,f1578]) ).

fof(f237,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_11
    | ~ spl0_21 ),
    inference(superposition,[],[f66,f176]) ).

fof(f1576,plain,
    ( spl0_65
    | ~ spl0_9
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f232,f175,f57,f1574]) ).

fof(f232,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_9
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f58]) ).

fof(f1572,plain,
    ( spl0_64
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f221,f171,f53,f39,f1570]) ).

fof(f221,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0))
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_20 ),
    inference(forward_demodulation,[],[f207,f54]) ).

fof(f207,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(superposition,[],[f172,f40]) ).

fof(f1568,plain,
    ( spl0_63
    | ~ spl0_10
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f214,f171,f61,f1566]) ).

fof(f214,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_10
    | ~ spl0_20 ),
    inference(superposition,[],[f62,f172]) ).

fof(f1523,plain,
    ( spl0_62
    | ~ spl0_8
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f210,f171,f53,f1521]) ).

fof(f210,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_8
    | ~ spl0_20 ),
    inference(superposition,[],[f172,f54]) ).

fof(f1519,plain,
    ( spl0_61
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f204,f171,f39,f1517]) ).

fof(f204,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_5
    | ~ spl0_20 ),
    inference(superposition,[],[f172,f40]) ).

fof(f1515,plain,
    ( spl0_60
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f200,f162,f57,f39,f1513]) ).

fof(f200,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0))
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f186,f58]) ).

fof(f186,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(superposition,[],[f163,f40]) ).

fof(f1511,plain,
    ( spl0_59
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f193,f162,f65,f1509]) ).

fof(f193,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(superposition,[],[f66,f163]) ).

fof(f1507,plain,
    ( spl0_58
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f189,f162,f57,f1505]) ).

fof(f189,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(superposition,[],[f163,f58]) ).

fof(f1503,plain,
    ( spl0_57
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f183,f162,f39,f1501]) ).

fof(f183,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(superposition,[],[f163,f40]) ).

fof(f1499,plain,
    ( spl0_56
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f154,f114,f65,f1497]) ).

fof(f154,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_11
    | ~ spl0_17 ),
    inference(superposition,[],[f66,f115]) ).

fof(f1495,plain,
    ( spl0_55
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f152,f114,f61,f1493]) ).

fof(f152,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_10
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f62]) ).

fof(f1491,plain,
    ( spl0_54
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f135,f110,f61,f1489]) ).

fof(f135,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_10
    | ~ spl0_16 ),
    inference(superposition,[],[f62,f111]) ).

fof(f1487,plain,
    ( spl0_53
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f133,f110,f65,f1485]) ).

fof(f133,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_11
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f66]) ).

fof(f1483,plain,
    ( spl0_52
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f506,f379,f305,f1481]) ).

fof(f506,plain,
    ( ! [X0] : multiply(inverse(inverse(identity)),X0) = X0
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(superposition,[],[f306,f380]) ).

fof(f1294,plain,
    ( spl0_51
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f259,f179,f53,f39,f1292]) ).

fof(f1292,plain,
    ( spl0_51
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f259,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_8
    | ~ spl0_22 ),
    inference(forward_demodulation,[],[f247,f54]) ).

fof(f247,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,inverse(X0)),X0) = greatest_lower_bound(multiply(X1,X0),identity)
    | ~ spl0_5
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f40]) ).

fof(f1290,plain,
    ( spl0_50
    | ~ spl0_5
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f244,f179,f39,f1288]) ).

fof(f244,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
    | ~ spl0_5
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f40]) ).

fof(f1286,plain,
    ( spl0_49
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f240,f175,f57,f39,f1284]) ).

fof(f240,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_5
    | ~ spl0_9
    | ~ spl0_21 ),
    inference(forward_demodulation,[],[f228,f58]) ).

fof(f228,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,inverse(X0)),X0) = least_upper_bound(multiply(X1,X0),identity)
    | ~ spl0_5
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f40]) ).

fof(f1282,plain,
    ( spl0_48
    | ~ spl0_5
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f225,f175,f39,f1280]) ).

fof(f225,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
    | ~ spl0_5
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f40]) ).

fof(f565,plain,
    ( spl0_47
    | ~ spl0_2
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f246,f179,f27,f563]) ).

fof(f246,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
    | ~ spl0_2
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f28]) ).

fof(f561,plain,
    ( spl0_46
    | ~ spl0_2
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f243,f179,f27,f559]) ).

fof(f243,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
    | ~ spl0_2
    | ~ spl0_22 ),
    inference(superposition,[],[f180,f28]) ).

fof(f557,plain,
    ( spl0_45
    | ~ spl0_5
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f309,f305,f39,f555]) ).

fof(f309,plain,
    ( ! [X0] : multiply(inverse(inverse(X0)),identity) = X0
    | ~ spl0_5
    | ~ spl0_25 ),
    inference(superposition,[],[f306,f40]) ).

fof(f553,plain,
    ( spl0_44
    | ~ spl0_2
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f227,f175,f27,f551]) ).

fof(f227,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
    | ~ spl0_2
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f28]) ).

fof(f549,plain,
    ( spl0_43
    | ~ spl0_2
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f224,f175,f27,f547]) ).

fof(f224,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
    | ~ spl0_2
    | ~ spl0_21 ),
    inference(superposition,[],[f176,f28]) ).

fof(f545,plain,
    ( spl0_42
    | ~ spl0_9
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f150,f114,f57,f543]) ).

fof(f150,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1))
    | ~ spl0_9
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f58]) ).

fof(f540,plain,
    ( spl0_41
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f149,f114,f31,f538]) ).

fof(f538,plain,
    ( spl0_41
  <=> ! [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_41])]) ).

fof(f149,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1)))
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f32]) ).

fof(f536,plain,
    ( spl0_40
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f145,f114,f61,f534]) ).

fof(f145,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2)
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f62]) ).

fof(f532,plain,
    ( spl0_39
    | ~ spl0_9
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f143,f114,f57,f530]) ).

fof(f143,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X1,X0),X2)
    | ~ spl0_9
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f58]) ).

fof(f528,plain,
    ( spl0_38
    | ~ spl0_8
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f131,f110,f53,f526]) ).

fof(f131,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1))
    | ~ spl0_8
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f54]) ).

fof(f523,plain,
    ( spl0_37
    | ~ spl0_4
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f130,f110,f35,f521]) ).

fof(f521,plain,
    ( spl0_37
  <=> ! [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_37])]) ).

fof(f130,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1)))
    | ~ spl0_4
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f36]) ).

fof(f519,plain,
    ( spl0_36
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f126,f110,f65,f517]) ).

fof(f126,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2)
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f66]) ).

fof(f515,plain,
    ( spl0_35
    | ~ spl0_8
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f124,f110,f53,f513]) ).

fof(f124,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X1,X0),X2)
    | ~ spl0_8
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f54]) ).

fof(f469,plain,
    ( spl0_34
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f160,f114,f48,f467]) ).

fof(f160,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(a,least_upper_bound(c,X0))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(forward_demodulation,[],[f148,f115]) ).

fof(f148,plain,
    ( ! [X0] : least_upper_bound(b,least_upper_bound(c,X0)) = least_upper_bound(least_upper_bound(a,c),X0)
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f50]) ).

fof(f465,plain,
    ( spl0_33
    | ~ spl0_6
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f141,f110,f43,f463]) ).

fof(f141,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(a,greatest_lower_bound(c,X0))
    | ~ spl0_6
    | ~ spl0_16 ),
    inference(forward_demodulation,[],[f129,f111]) ).

fof(f129,plain,
    ( ! [X0] : greatest_lower_bound(b,greatest_lower_bound(c,X0)) = greatest_lower_bound(greatest_lower_bound(a,c),X0)
    | ~ spl0_6
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f45]) ).

fof(f389,plain,
    ( spl0_32
    | ~ spl0_10
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f102,f88,f61,f387]) ).

fof(f102,plain,
    ( ! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1)))
    | ~ spl0_10
    | ~ spl0_14 ),
    inference(superposition,[],[f62,f89]) ).

fof(f385,plain,
    ( spl0_31
    | ~ spl0_8
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f99,f88,f53,f383]) ).

fof(f99,plain,
    ( ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X1),inverse(X0))
    | ~ spl0_8
    | ~ spl0_14 ),
    inference(superposition,[],[f89,f54]) ).

fof(f381,plain,
    ( spl0_30
    | ~ spl0_2
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f308,f305,f27,f379]) ).

fof(f308,plain,
    ( ! [X0] : multiply(inverse(identity),X0) = X0
    | ~ spl0_2
    | ~ spl0_25 ),
    inference(superposition,[],[f306,f28]) ).

fof(f377,plain,
    ( spl0_29
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f95,f79,f65,f375]) ).

fof(f95,plain,
    ( ! [X0,X1] : inverse(X0) = greatest_lower_bound(inverse(X0),inverse(greatest_lower_bound(X0,X1)))
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(superposition,[],[f66,f80]) ).

fof(f373,plain,
    ( spl0_28
    | ~ spl0_9
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f92,f79,f57,f371]) ).

fof(f92,plain,
    ( ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0))
    | ~ spl0_9
    | ~ spl0_12 ),
    inference(superposition,[],[f80,f58]) ).

fof(f329,plain,
    ( spl0_27
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f142,f114,f31,f327]) ).

fof(f142,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_3
    | ~ spl0_17 ),
    inference(superposition,[],[f115,f32]) ).

fof(f325,plain,
    ( spl0_26
    | ~ spl0_4
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f123,f110,f35,f323]) ).

fof(f123,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_16 ),
    inference(superposition,[],[f111,f36]) ).

fof(f307,plain,
    ( spl0_25
    | ~ spl0_2
    | ~ spl0_5
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f120,f106,f39,f27,f305]) ).

fof(f120,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_2
    | ~ spl0_5
    | ~ spl0_15 ),
    inference(forward_demodulation,[],[f118,f28]) ).

fof(f118,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1)
    | ~ spl0_5
    | ~ spl0_15 ),
    inference(superposition,[],[f107,f40]) ).

fof(f273,plain,
    ( spl0_24
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f73,f65,f57,f271]) ).

fof(f73,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(superposition,[],[f66,f58]) ).

fof(f269,plain,
    ( spl0_23
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f69,f61,f53,f267]) ).

fof(f69,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(superposition,[],[f62,f54]) ).

fof(f181,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f15,f179]) ).

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(f177,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f14,f175]) ).

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(f173,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f13,f171]) ).

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(f169,plain,
    ( spl0_19
    | ~ spl0_7
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f76,f65,f48,f166]) ).

fof(f76,plain,
    ( b = greatest_lower_bound(b,least_upper_bound(a,c))
    | ~ spl0_7
    | ~ spl0_11 ),
    inference(superposition,[],[f66,f50]) ).

fof(f164,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f12,f162]) ).

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(f116,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f7,f114]) ).

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(f112,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f6,f110]) ).

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(f108,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f3,f106]) ).

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(f90,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f19,f88]) ).

fof(f19,axiom,
    ! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).

fof(f86,plain,
    ( spl0_13
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f71,f61,f43,f83]) ).

fof(f71,plain,
    ( b = least_upper_bound(b,greatest_lower_bound(a,c))
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(superposition,[],[f62,f45]) ).

fof(f81,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f18,f79]) ).

fof(f18,axiom,
    ! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_3) ).

fof(f67,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f11,f65]) ).

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(f63,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f10,f61]) ).

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(f59,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f5,f57]) ).

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(f55,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f4,f53]) ).

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(f51,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f17,f48]) ).

fof(f17,axiom,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).

fof(f46,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f16,f43]) ).

fof(f16,axiom,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).

fof(f41,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f2,f39]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).

fof(f37,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f9,f35]) ).

fof(f9,axiom,
    ! [X0] : greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).

fof(f33,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f8,f31]) ).

fof(f8,axiom,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).

fof(f29,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f1,f27]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).

fof(f25,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f20,f22]) ).

fof(f20,axiom,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP181-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 20:46:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.36  % (683)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (686)WARNING: value z3 for option sas not known
% 0.13/0.37  % (685)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (684)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (687)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (688)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)
% 0.13/0.37  % (686)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)
% 0.13/0.37  % (689)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)
% 0.13/0.37  % (690)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)
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.13/0.38  TRYING [3]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.22/0.40  TRYING [3]
% 0.22/0.40  TRYING [4]
% 0.22/0.45  TRYING [4]
% 0.22/0.47  TRYING [5]
% 1.40/0.54  TRYING [5]
% 1.40/0.60  TRYING [6]
% 3.26/0.81  TRYING [6]
% 4.54/0.99  TRYING [7]
% 7.76/1.45  % (688)First to succeed.
% 7.76/1.46  % (688)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-683"
% 7.76/1.47  % (688)Refutation found. Thanks to Tanya!
% 7.76/1.47  % SZS status Unsatisfiable for theBenchmark
% 7.76/1.47  % SZS output start Proof for theBenchmark
% See solution above
% 7.76/1.47  % (688)------------------------------
% 7.76/1.47  % (688)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.76/1.47  % (688)Termination reason: Refutation
% 7.76/1.47  
% 7.76/1.47  % (688)Memory used [KB]: 22277
% 7.76/1.47  % (688)Time elapsed: 1.090 s
% 7.76/1.47  % (688)Instructions burned: 3107 (million)
% 7.76/1.47  % (683)Success in time 1.099 s
%------------------------------------------------------------------------------