TSTP Solution File: GRP173-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP173-1 : 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 : n011.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 05:53:53 EDT 2024

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   79
% Syntax   : Number of formulae    :  213 (  37 unt;   0 def)
%            Number of atoms       :  495 ( 150 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  505 ( 223   ~; 221   |;   0   &)
%                                         (  61 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   63 (  61 usr;  62 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  303 ( 303   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2049,plain,
    $false,
    inference(avatar_sat_refutation,[],[f23,f28,f32,f36,f40,f45,f49,f53,f57,f61,f65,f83,f88,f92,f96,f140,f144,f148,f152,f238,f242,f273,f291,f296,f311,f315,f357,f373,f377,f381,f390,f394,f398,f402,f407,f411,f415,f419,f423,f467,f1089,f1119,f1123,f1127,f1293,f1297,f1301,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1376,f1380,f1384,f2048]) ).

fof(f2048,plain,
    ( spl0_1
    | ~ spl0_2
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1347,f1303,f25,f20]) ).

fof(f20,plain,
    ( spl0_1
  <=> identity = a ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f25,plain,
    ( spl0_2
  <=> identity = least_upper_bound(identity,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1303,plain,
    ( spl0_48
  <=> a = least_upper_bound(identity,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1347,plain,
    ( identity = a
    | ~ spl0_2
    | ~ spl0_48 ),
    inference(superposition,[],[f1305,f27]) ).

fof(f27,plain,
    ( identity = least_upper_bound(identity,a)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f25]) ).

fof(f1305,plain,
    ( a = least_upper_bound(identity,a)
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f1303]) ).

fof(f1384,plain,
    ( spl0_61
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f229,f150,f59,f1382]) ).

fof(f1382,plain,
    ( spl0_61
  <=> ! [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_61])]) ).

fof(f59,plain,
    ( spl0_10
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f150,plain,
    ( spl0_19
  <=> ! [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_19])]) ).

fof(f229,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(greatest_lower_bound(X0,X2),X1))
    | ~ spl0_10
    | ~ spl0_19 ),
    inference(superposition,[],[f60,f151]) ).

fof(f151,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X1,X2),X0) = greatest_lower_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f60,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f1380,plain,
    ( spl0_60
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f224,f150,f51,f1378]) ).

fof(f1378,plain,
    ( spl0_60
  <=> ! [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_60])]) ).

fof(f51,plain,
    ( spl0_8
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f224,plain,
    ( ! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X2),X1) = greatest_lower_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(superposition,[],[f151,f52]) ).

fof(f52,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f1376,plain,
    ( spl0_59
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f210,f146,f63,f1374]) ).

fof(f1374,plain,
    ( spl0_59
  <=> ! [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_59])]) ).

fof(f63,plain,
    ( spl0_11
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f146,plain,
    ( spl0_18
  <=> ! [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_18])]) ).

fof(f210,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(least_upper_bound(X0,X2),X1))
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(superposition,[],[f64,f147]) ).

fof(f147,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X1,X2),X0) = least_upper_bound(multiply(X1,X0),multiply(X2,X0))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f64,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f1346,plain,
    ( spl0_58
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f205,f146,f55,f1344]) ).

fof(f1344,plain,
    ( spl0_58
  <=> ! [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_58])]) ).

fof(f55,plain,
    ( spl0_9
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f205,plain,
    ( ! [X2,X0,X1] : multiply(least_upper_bound(X0,X2),X1) = least_upper_bound(multiply(X2,X1),multiply(X0,X1))
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(superposition,[],[f147,f56]) ).

fof(f56,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f1342,plain,
    ( spl0_57
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f194,f142,f51,f47,f1340]) ).

fof(f1340,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f47,plain,
    ( spl0_7
  <=> ! [X0] : identity = multiply(inverse(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f142,plain,
    ( spl0_17
  <=> ! [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_17])]) ).

fof(f194,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0))
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_17 ),
    inference(forward_demodulation,[],[f180,f52]) ).

fof(f180,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(superposition,[],[f143,f48]) ).

fof(f48,plain,
    ( ! [X0] : identity = multiply(inverse(X0),X0)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f143,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f142]) ).

fof(f1338,plain,
    ( spl0_56
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f187,f142,f59,f1336]) ).

fof(f1336,plain,
    ( spl0_56
  <=> ! [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_56])]) ).

fof(f187,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = least_upper_bound(multiply(X0,X1),multiply(X0,greatest_lower_bound(X1,X2)))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(superposition,[],[f60,f143]) ).

fof(f1334,plain,
    ( spl0_55
    | ~ spl0_8
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f183,f142,f51,f1332]) ).

fof(f1332,plain,
    ( spl0_55
  <=> ! [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_55])]) ).

fof(f183,plain,
    ( ! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_8
    | ~ spl0_17 ),
    inference(superposition,[],[f143,f52]) ).

fof(f1330,plain,
    ( spl0_54
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f177,f142,f47,f1328]) ).

fof(f1328,plain,
    ( spl0_54
  <=> ! [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_54])]) ).

fof(f177,plain,
    ( ! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(superposition,[],[f143,f48]) ).

fof(f1326,plain,
    ( spl0_53
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f171,f138,f55,f47,f1324]) ).

fof(f1324,plain,
    ( spl0_53
  <=> ! [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_53])]) ).

fof(f138,plain,
    ( spl0_16
  <=> ! [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_16])]) ).

fof(f171,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),least_upper_bound(X1,X0))
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(forward_demodulation,[],[f157,f56]) ).

fof(f157,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity)
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(superposition,[],[f139,f48]) ).

fof(f139,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2))
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f138]) ).

fof(f1322,plain,
    ( spl0_52
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f164,f138,f63,f1320]) ).

fof(f1320,plain,
    ( spl0_52
  <=> ! [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_52])]) ).

fof(f164,plain,
    ( ! [X2,X0,X1] : multiply(X0,X1) = greatest_lower_bound(multiply(X0,X1),multiply(X0,least_upper_bound(X1,X2)))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(superposition,[],[f64,f139]) ).

fof(f1318,plain,
    ( spl0_51
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f160,f138,f55,f1316]) ).

fof(f1316,plain,
    ( spl0_51
  <=> ! [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_51])]) ).

fof(f160,plain,
    ( ! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1))
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(superposition,[],[f139,f56]) ).

fof(f1314,plain,
    ( spl0_50
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f154,f138,f47,f1312]) ).

fof(f1312,plain,
    ( spl0_50
  <=> ! [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_50])]) ).

fof(f154,plain,
    ( ! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1))
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(superposition,[],[f139,f48]) ).

fof(f1310,plain,
    ( spl0_49
    | ~ spl0_11
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f131,f94,f63,f1308]) ).

fof(f1308,plain,
    ( spl0_49
  <=> ! [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_49])]) ).

fof(f94,plain,
    ( spl0_15
  <=> ! [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_15])]) ).

fof(f131,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_15 ),
    inference(superposition,[],[f64,f95]) ).

fof(f95,plain,
    ( ! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f1306,plain,
    ( spl0_48
    | ~ spl0_3
    | ~ spl0_6
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f1196,f1117,f42,f30,f1303]) ).

fof(f30,plain,
    ( spl0_3
  <=> ! [X0] : multiply(identity,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f42,plain,
    ( spl0_6
  <=> identity = least_upper_bound(identity,inverse(a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1117,plain,
    ( spl0_42
  <=> ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1196,plain,
    ( a = least_upper_bound(identity,a)
    | ~ spl0_3
    | ~ spl0_6
    | ~ spl0_42 ),
    inference(forward_demodulation,[],[f1175,f31]) ).

fof(f31,plain,
    ( ! [X0] : multiply(identity,X0) = X0
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f30]) ).

fof(f1175,plain,
    ( multiply(identity,a) = least_upper_bound(identity,multiply(identity,a))
    | ~ spl0_6
    | ~ spl0_42 ),
    inference(superposition,[],[f1118,f44]) ).

fof(f44,plain,
    ( identity = least_upper_bound(identity,inverse(a))
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f1118,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f1117]) ).

fof(f1301,plain,
    ( spl0_47
    | ~ spl0_10
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f129,f94,f59,f1299]) ).

fof(f1299,plain,
    ( spl0_47
  <=> ! [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_47])]) ).

fof(f129,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_15 ),
    inference(superposition,[],[f95,f60]) ).

fof(f1297,plain,
    ( spl0_46
    | ~ spl0_10
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f113,f90,f59,f1295]) ).

fof(f1295,plain,
    ( spl0_46
  <=> ! [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_46])]) ).

fof(f90,plain,
    ( spl0_14
  <=> ! [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_14])]) ).

fof(f113,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_14 ),
    inference(superposition,[],[f60,f91]) ).

fof(f91,plain,
    ( ! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f1293,plain,
    ( spl0_45
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f111,f90,f63,f1291]) ).

fof(f1291,plain,
    ( spl0_45
  <=> ! [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_45])]) ).

fof(f111,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_14 ),
    inference(superposition,[],[f91,f64]) ).

fof(f1127,plain,
    ( spl0_44
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f232,f150,f51,f47,f1125]) ).

fof(f1125,plain,
    ( spl0_44
  <=> ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f232,plain,
    ( ! [X0,X1] : greatest_lower_bound(identity,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(forward_demodulation,[],[f220,f52]) ).

fof(f220,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,inverse(X0)),X0) = greatest_lower_bound(multiply(X1,X0),identity)
    | ~ spl0_7
    | ~ spl0_19 ),
    inference(superposition,[],[f151,f48]) ).

fof(f1123,plain,
    ( spl0_43
    | ~ spl0_7
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f217,f150,f47,f1121]) ).

fof(f1121,plain,
    ( spl0_43
  <=> ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f217,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0))
    | ~ spl0_7
    | ~ spl0_19 ),
    inference(superposition,[],[f151,f48]) ).

fof(f1119,plain,
    ( spl0_42
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f213,f146,f55,f47,f1117]) ).

fof(f213,plain,
    ( ! [X0,X1] : least_upper_bound(identity,multiply(X1,X0)) = multiply(least_upper_bound(X1,inverse(X0)),X0)
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(forward_demodulation,[],[f201,f56]) ).

fof(f201,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,inverse(X0)),X0) = least_upper_bound(multiply(X1,X0),identity)
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(superposition,[],[f147,f48]) ).

fof(f1089,plain,
    ( spl0_41
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f198,f146,f47,f1087]) ).

fof(f1087,plain,
    ( spl0_41
  <=> ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f198,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0))
    | ~ spl0_7
    | ~ spl0_18 ),
    inference(superposition,[],[f147,f48]) ).

fof(f467,plain,
    ( spl0_40
    | ~ spl0_3
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f274,f271,f30,f465]) ).

fof(f465,plain,
    ( spl0_40
  <=> ! [X0] : multiply(inverse(identity),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f271,plain,
    ( spl0_22
  <=> ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f274,plain,
    ( ! [X0] : multiply(inverse(identity),X0) = X0
    | ~ spl0_3
    | ~ spl0_22 ),
    inference(superposition,[],[f272,f31]) ).

fof(f272,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f423,plain,
    ( spl0_39
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f219,f150,f30,f421]) ).

fof(f421,plain,
    ( spl0_39
  <=> ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f219,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0)
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(superposition,[],[f151,f31]) ).

fof(f419,plain,
    ( spl0_38
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f216,f150,f30,f417]) ).

fof(f417,plain,
    ( spl0_38
  <=> ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f216,plain,
    ( ! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0))
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(superposition,[],[f151,f31]) ).

fof(f415,plain,
    ( spl0_37
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f200,f146,f30,f413]) ).

fof(f413,plain,
    ( spl0_37
  <=> ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f200,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(X1,identity),X0) = least_upper_bound(multiply(X1,X0),X0)
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(superposition,[],[f147,f31]) ).

fof(f411,plain,
    ( spl0_36
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f197,f146,f30,f409]) ).

fof(f409,plain,
    ( spl0_36
  <=> ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f197,plain,
    ( ! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0))
    | ~ spl0_3
    | ~ spl0_18 ),
    inference(superposition,[],[f147,f31]) ).

fof(f407,plain,
    ( spl0_35
    | ~ spl0_9
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f127,f94,f55,f405]) ).

fof(f405,plain,
    ( spl0_35
  <=> ! [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_35])]) ).

fof(f127,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_15 ),
    inference(superposition,[],[f95,f56]) ).

fof(f402,plain,
    ( spl0_34
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f126,f94,f34,f400]) ).

fof(f400,plain,
    ( spl0_34
  <=> ! [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_34])]) ).

fof(f34,plain,
    ( spl0_4
  <=> ! [X0] : least_upper_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f126,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X1)))
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(superposition,[],[f95,f35]) ).

fof(f35,plain,
    ( ! [X0] : least_upper_bound(X0,X0) = X0
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f34]) ).

fof(f398,plain,
    ( spl0_33
    | ~ spl0_10
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f124,f94,f59,f396]) ).

fof(f396,plain,
    ( spl0_33
  <=> ! [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_33])]) ).

fof(f124,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_15 ),
    inference(superposition,[],[f95,f60]) ).

fof(f394,plain,
    ( spl0_32
    | ~ spl0_9
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f122,f94,f55,f392]) ).

fof(f392,plain,
    ( spl0_32
  <=> ! [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_32])]) ).

fof(f122,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_15 ),
    inference(superposition,[],[f95,f56]) ).

fof(f390,plain,
    ( spl0_31
    | ~ spl0_8
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f109,f90,f51,f388]) ).

fof(f388,plain,
    ( spl0_31
  <=> ! [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_31])]) ).

fof(f109,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_14 ),
    inference(superposition,[],[f91,f52]) ).

fof(f381,plain,
    ( spl0_30
    | ~ spl0_5
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f108,f90,f38,f379]) ).

fof(f379,plain,
    ( spl0_30
  <=> ! [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_30])]) ).

fof(f38,plain,
    ( spl0_5
  <=> ! [X0] : greatest_lower_bound(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f108,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1)))
    | ~ spl0_5
    | ~ spl0_14 ),
    inference(superposition,[],[f91,f39]) ).

fof(f39,plain,
    ( ! [X0] : greatest_lower_bound(X0,X0) = X0
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f377,plain,
    ( spl0_29
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f106,f90,f63,f375]) ).

fof(f375,plain,
    ( spl0_29
  <=> ! [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_29])]) ).

fof(f106,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_14 ),
    inference(superposition,[],[f91,f64]) ).

fof(f373,plain,
    ( spl0_28
    | ~ spl0_8
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f104,f90,f51,f371]) ).

fof(f371,plain,
    ( spl0_28
  <=> ! [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_28])]) ).

fof(f104,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_14 ),
    inference(superposition,[],[f91,f52]) ).

fof(f357,plain,
    ( spl0_27
    | ~ spl0_6
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f120,f94,f42,f355]) ).

fof(f355,plain,
    ( spl0_27
  <=> ! [X0] : least_upper_bound(identity,X0) = least_upper_bound(identity,least_upper_bound(inverse(a),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f120,plain,
    ( ! [X0] : least_upper_bound(identity,X0) = least_upper_bound(identity,least_upper_bound(inverse(a),X0))
    | ~ spl0_6
    | ~ spl0_15 ),
    inference(superposition,[],[f95,f44]) ).

fof(f315,plain,
    ( spl0_26
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f121,f94,f34,f313]) ).

fof(f313,plain,
    ( spl0_26
  <=> ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f121,plain,
    ( ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1))
    | ~ spl0_4
    | ~ spl0_15 ),
    inference(superposition,[],[f95,f35]) ).

fof(f311,plain,
    ( spl0_25
    | ~ spl0_5
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f103,f90,f38,f309]) ).

fof(f309,plain,
    ( spl0_25
  <=> ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f103,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X0,greatest_lower_bound(X0,X1))
    | ~ spl0_5
    | ~ spl0_14 ),
    inference(superposition,[],[f91,f39]) ).

fof(f296,plain,
    ( spl0_24
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f175,f85,f63,f293]) ).

fof(f293,plain,
    ( spl0_24
  <=> a = greatest_lower_bound(a,identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f85,plain,
    ( spl0_13
  <=> identity = least_upper_bound(a,identity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f175,plain,
    ( a = greatest_lower_bound(a,identity)
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(superposition,[],[f64,f87]) ).

fof(f87,plain,
    ( identity = least_upper_bound(a,identity)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f291,plain,
    ( spl0_23
    | ~ spl0_2
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f119,f94,f25,f289]) ).

fof(f289,plain,
    ( spl0_23
  <=> ! [X0] : least_upper_bound(identity,least_upper_bound(a,X0)) = least_upper_bound(identity,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f119,plain,
    ( ! [X0] : least_upper_bound(identity,least_upper_bound(a,X0)) = least_upper_bound(identity,X0)
    | ~ spl0_2
    | ~ spl0_15 ),
    inference(superposition,[],[f95,f27]) ).

fof(f273,plain,
    ( spl0_22
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f100,f81,f47,f30,f271]) ).

fof(f81,plain,
    ( spl0_12
  <=> ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f100,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_12 ),
    inference(forward_demodulation,[],[f98,f31]) ).

fof(f98,plain,
    ( ! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1)
    | ~ spl0_7
    | ~ spl0_12 ),
    inference(superposition,[],[f82,f48]) ).

fof(f82,plain,
    ( ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f242,plain,
    ( spl0_21
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f76,f63,f55,f240]) ).

fof(f240,plain,
    ( spl0_21
  <=> ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f76,plain,
    ( ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(superposition,[],[f64,f56]) ).

fof(f238,plain,
    ( spl0_20
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f71,f59,f51,f236]) ).

fof(f236,plain,
    ( spl0_20
  <=> ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f71,plain,
    ( ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(superposition,[],[f60,f52]) ).

fof(f152,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f15,f150]) ).

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/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).

fof(f148,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f14,f146]) ).

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/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).

fof(f144,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f13,f142]) ).

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/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).

fof(f140,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f12,f138]) ).

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/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).

fof(f96,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f7,f94]) ).

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/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).

fof(f92,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f6,f90]) ).

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/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).

fof(f88,plain,
    ( spl0_13
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f66,f55,f25,f85]) ).

fof(f66,plain,
    ( identity = least_upper_bound(a,identity)
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(superposition,[],[f56,f27]) ).

fof(f83,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f3,f81]) ).

fof(f3,axiom,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).

fof(f65,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f11,f63]) ).

fof(f11,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).

fof(f61,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f10,f59]) ).

fof(f10,axiom,
    ! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).

fof(f57,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f5,f55]) ).

fof(f5,axiom,
    ! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).

fof(f53,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f4,f51]) ).

fof(f4,axiom,
    ! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).

fof(f49,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f2,f47]) ).

fof(f2,axiom,
    ! [X0] : identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

fof(f45,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f17,f42]) ).

fof(f17,axiom,
    identity = least_upper_bound(identity,inverse(a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05a_2) ).

fof(f40,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f9,f38]) ).

fof(f9,axiom,
    ! [X0] : greatest_lower_bound(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).

fof(f36,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f8,f34]) ).

fof(f8,axiom,
    ! [X0] : least_upper_bound(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_lub) ).

fof(f32,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f1,f30]) ).

fof(f1,axiom,
    ! [X0] : multiply(identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

fof(f28,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f16,f25]) ).

fof(f16,axiom,
    identity = least_upper_bound(identity,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p05a_1) ).

fof(f23,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f18,f20]) ).

fof(f18,axiom,
    identity != a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p05a) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : GRP173-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri May  3 20:44:23 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.19/0.35  % (30806)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36  % (30810)WARNING: value z3 for option sas not known
% 0.19/0.36  % (30812)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)
% 0.19/0.36  % (30814)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)
% 0.19/0.36  % (30813)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)
% 0.19/0.36  % (30810)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)
% 0.19/0.36  % (30811)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36  % (30807)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.36  TRYING [1]
% 0.19/0.36  % (30809)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.36  TRYING [2]
% 0.19/0.37  TRYING [3]
% 0.19/0.37  TRYING [1]
% 0.19/0.37  TRYING [2]
% 0.19/0.38  TRYING [3]
% 0.19/0.38  TRYING [4]
% 0.19/0.42  TRYING [1]
% 0.19/0.42  TRYING [2]
% 0.19/0.43  TRYING [3]
% 0.19/0.43  % (30812)First to succeed.
% 0.19/0.44  % (30812)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30806"
% 0.19/0.44  % (30812)Refutation found. Thanks to Tanya!
% 0.19/0.44  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.44  % (30812)------------------------------
% 0.19/0.44  % (30812)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.44  % (30812)Termination reason: Refutation
% 0.19/0.44  
% 0.19/0.44  % (30812)Memory used [KB]: 2222
% 0.19/0.44  % (30812)Time elapsed: 0.077 s
% 0.19/0.44  % (30812)Instructions burned: 166 (million)
% 0.19/0.44  % (30806)Success in time 0.078 s
%------------------------------------------------------------------------------