TSTP Solution File: SWV879-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV879-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:37:01 EDT 2024

% Result   : Unsatisfiable 21.63s 3.50s
% Output   : Refutation 21.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      : 1759
% Syntax   : Number of formulae    : 3638 ( 854 unt;   0 def)
%            Number of atoms       : 9782 (1379 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 11110 (4966   ~;5071   |;   0   &)
%                                         (1073 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  : 1106 (1104 usr;1074 prp; 0-4 aty)
%            Number of functors    :   50 (  50 usr;   9 con; 0-5 aty)
%            Number of variables   : 7295 (7295   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f34088,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1508,f1516,f1585,f1602,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1674,f1678,f1682,f1689,f1693,f1697,f1701,f1705,f1709,f1713,f1717,f1721,f1726,f1797,f1877,f1881,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1926,f1930,f1934,f1938,f1942,f1946,f1950,f1954,f1958,f1962,f1966,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2009,f2014,f2018,f2022,f2026,f2030,f2034,f2178,f2242,f2264,f2268,f2272,f2276,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2331,f2335,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2562,f2566,f2570,f2574,f2578,f2582,f2586,f2590,f2610,f2933,f2937,f2941,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2982,f2986,f2994,f2998,f3002,f3006,f3010,f3014,f3018,f3022,f3026,f3030,f3035,f3039,f3043,f3047,f3051,f3055,f3059,f3063,f3067,f3071,f3075,f3080,f3084,f3088,f3093,f3099,f3107,f3241,f3750,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4354,f4358,f4362,f4366,f4370,f4488,f5102,f5443,f5961,f5965,f5970,f5974,f5978,f5982,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6573,f6636,f6640,f6644,f6648,f6677,f6681,f6685,f6689,f6693,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6729,f6733,f6737,f6741,f7118,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7338,f7342,f7491,f8012,f8016,f8025,f8029,f8033,f8037,f8041,f8045,f8049,f8053,f8057,f8061,f8065,f8069,f8073,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8122,f8127,f8131,f8135,f8139,f8143,f8147,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8214,f8996,f9364,f9368,f9391,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9435,f9439,f9443,f9447,f9451,f9455,f9459,f9463,f9467,f9471,f9477,f9481,f9485,f9489,f9493,f9497,f9659,f10130,f10273,f10277,f10281,f10285,f10289,f10293,f10333,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10365,f10373,f10618,f10622,f10626,f10630,f10634,f10638,f10642,f10647,f10651,f10655,f10659,f10663,f10667,f10671,f10675,f10679,f10683,f10687,f10698,f10702,f10706,f10837,f11179,f11183,f11187,f11191,f11195,f11199,f11203,f11208,f11212,f11216,f11220,f11224,f11228,f11232,f11236,f11732,f11753,f11757,f11761,f11765,f11769,f11773,f11777,f11781,f11785,f11801,f11805,f11809,f11813,f11817,f11989,f12363,f12408,f12412,f12416,f12420,f12424,f12428,f12432,f12436,f12440,f12444,f12448,f12452,f12456,f12460,f12464,f12468,f12472,f12476,f12480,f12484,f12488,f12493,f12497,f12501,f12505,f12509,f12513,f12517,f12521,f12525,f12529,f12533,f12541,f12545,f12549,f12553,f12658,f12965,f13205,f13210,f13214,f13218,f13222,f13226,f13230,f13234,f13238,f13374,f13538,f13542,f13546,f13550,f13554,f13558,f13562,f13566,f14093,f14124,f14128,f14132,f14136,f14140,f14144,f14148,f14152,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14542,f14546,f14550,f14554,f14558,f14562,f14569,f15566,f15570,f15574,f15578,f15582,f15644,f15648,f15652,f15656,f15660,f15664,f15668,f15672,f15676,f15680,f15687,f15762,f15854,f15858,f15862,f15870,f15874,f15878,f15882,f15886,f15890,f15894,f15898,f15902,f15906,f15914,f15918,f15922,f15926,f17545,f17549,f17553,f17557,f17561,f17565,f17569,f17573,f17577,f17581,f17585,f17677,f18437,f18482,f18505,f18509,f18514,f18518,f18606,f18695,f18823,f18827,f18831,f18835,f18839,f18843,f18999,f19005,f19009,f19013,f19017,f19036,f19318,f19322,f19326,f19330,f19335,f20074,f20079,f20083,f20087,f20236,f20240,f20359,f20363,f20406,f20410,f20508,f20552,f20579,f20698,f20702,f20768,f20774,f21169,f21173,f21177,f21182,f21186,f21190,f21194,f21198,f21352,f21356,f21360,f21364,f21368,f21372,f21376,f21447,f21676,f21684,f21689,f21729,f21773,f21777,f21790,f21794,f21802,f21806,f22069,f22073,f22266,f22315,f22319,f22323,f22327,f22506,f22510,f22514,f22518,f22523,f22565,f22573,f22577,f22605,f22609,f22613,f22617,f22621,f22625,f22630,f22634,f22638,f22645,f22649,f22653,f22657,f23017,f23163,f23167,f23171,f23175,f23229,f23233,f23237,f23241,f23245,f23250,f23254,f23258,f23263,f23268,f23272,f23277,f23282,f23287,f23292,f23296,f23300,f23304,f23308,f23312,f23368,f23710,f23846,f23852,f23856,f23860,f23864,f23868,f23872,f23876,f23880,f23884,f23888,f23892,f23896,f23900,f23904,f23908,f23916,f23920,f23924,f23930,f24044,f24048,f24806,f24849,f24892,f24896,f24900,f24904,f24908,f24951,f24998,f25012,f25035,f25039,f25059,f25083,f25087,f25091,f25095,f25123,f25147,f25151,f25372,f25415,f25419,f25423,f25427,f25488,f25549,f25553,f25557,f25561,f25599,f25638,f25667,f25875,f25956,f25960,f25964,f25968,f25972,f25976,f25980,f25984,f25988,f25992,f25996,f26000,f26004,f26008,f26012,f26016,f26020,f26024,f26028,f26032,f26053,f26057,f26061,f26065,f26069,f26073,f26077,f26081,f26085,f26089,f26152,f26156,f26160,f26164,f26168,f26172,f26176,f26180,f26184,f26188,f26193,f26197,f26201,f26205,f26209,f26213,f26242,f26246,f26250,f26254,f26260,f26264,f26268,f26272,f26276,f26280,f26284,f26288,f26292,f26296,f26300,f26304,f26308,f26312,f26316,f26320,f26324,f26328,f26332,f26336,f26340,f26389,f26393,f26397,f26401,f26511,f26631,f26742,f26746,f26750,f26754,f26806,f26858,f26862,f26866,f26870,f26874,f26878,f26882,f26886,f27134,f28272,f28850,f29423,f30896,f31045,f31049,f31053,f31057,f31061,f31065,f31069,f31076,f31080,f31084,f31088,f31092,f31096,f31144,f31148,f31152,f31156,f31160,f31164,f31168,f31172,f31176,f31180,f31184,f31188,f31192,f31196,f31200,f31204,f31295,f31299,f31387,f31391,f31395,f31399,f31536,f31540,f31628,f31632,f31636,f31640,f31644,f31648,f31652,f31658,f31662,f31666,f31670,f31707,f31711,f31715,f31719,f31726,f32113,f32902,f33488,f33809,f33813,f33817,f33821,f33825,f33889,f33893,f33897,f33901,f33905,f33909,f33913,f33918,f33981,f33987,f34058,f34062,f34066,f34070,f34074,f34078,f34082,f34086,f34087]) ).

fof(f34087,plain,
    ( spl0_39
    | ~ spl0_201
    | ~ spl0_1049 ),
    inference(avatar_split_clause,[],[f33846,f32900,f2311,f1194]) ).

fof(f1194,plain,
    ( spl0_39
  <=> hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f2311,plain,
    ( spl0_201
  <=> ! [X52,X44] :
        ( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
        | hBOOL(hAPP(hAPP(v_P,X44),X52)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f32900,plain,
    ( spl0_1049
  <=> ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f33846,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a)))
    | ~ spl0_201
    | ~ spl0_1049 ),
    inference(resolution,[],[f32901,f2312]) ).

fof(f2312,plain,
    ( ! [X44,X52] :
        ( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
        | hBOOL(hAPP(hAPP(v_P,X44),X52)) )
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f2311]) ).

fof(f32901,plain,
    ( ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool))
    | ~ spl0_1049 ),
    inference(avatar_component_clause,[],[f32900]) ).

fof(f34086,plain,
    ( spl0_1073
    | ~ spl0_126
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2907,f2568,f1632,f34084]) ).

fof(f34084,plain,
    ( spl0_1073
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f1632,plain,
    ( spl0_126
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_lessequals(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f2568,plain,
    ( spl0_231
  <=> ! [X6,X0,X1] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2907,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_126
    | ~ spl0_231 ),
    inference(resolution,[],[f2569,f1633]) ).

fof(f1633,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f1632]) ).

fof(f2569,plain,
    ( ! [X0,X1,X6] :
        ( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2568]) ).

fof(f34082,plain,
    ( spl0_1072
    | ~ spl0_127
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2906,f2568,f1636,f34080]) ).

fof(f34080,plain,
    ( spl0_1072
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f1636,plain,
    ( spl0_127
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f2906,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(c_Complete__Lattice_OSup__class_OSup(X1,X2),X0,X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_127
    | ~ spl0_231 ),
    inference(resolution,[],[f2569,f1637]) ).

fof(f1637,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1636]) ).

fof(f34078,plain,
    ( spl0_1071
    | ~ spl0_126
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2891,f2564,f1632,f34076]) ).

fof(f34076,plain,
    ( spl0_1071
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f2564,plain,
    ( spl0_230
  <=> ! [X6,X0,X1] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2891,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_126
    | ~ spl0_230 ),
    inference(resolution,[],[f2565,f1633]) ).

fof(f2565,plain,
    ( ! [X0,X1,X6] :
        ( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
    | ~ spl0_230 ),
    inference(avatar_component_clause,[],[f2564]) ).

fof(f34074,plain,
    ( spl0_1070
    | ~ spl0_127
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f2890,f2564,f1636,f34072]) ).

fof(f34072,plain,
    ( spl0_1070
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f2890,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2)
        | ~ c_HOL_Oord__class_Oless(X0,c_Complete__Lattice_OInf__class_OInf(X1,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_127
    | ~ spl0_230 ),
    inference(resolution,[],[f2565,f1637]) ).

fof(f34070,plain,
    ( spl0_1069
    | ~ spl0_98
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2800,f2502,f1438,f34068]) ).

fof(f34068,plain,
    ( spl0_1069
  <=> ! [X0,X1] :
        ( c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f1438,plain,
    ( spl0_98
  <=> ! [X13,X4] :
        ( c_lessequals(X4,X13,tc_nat)
        | c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f2502,plain,
    ( spl0_216
  <=> ! [X13,X4] :
        ( c_Suc(X13) = X4
        | c_lessequals(X4,X13,tc_nat)
        | ~ c_lessequals(X4,c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2800,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | c_lessequals(c_Suc(X1),X0,tc_nat) )
    | ~ spl0_98
    | ~ spl0_216 ),
    inference(resolution,[],[f2503,f1439]) ).

fof(f1439,plain,
    ( ! [X4,X13] :
        ( c_lessequals(c_Suc(X13),X4,tc_nat)
        | c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f1438]) ).

fof(f2503,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(X4,c_Suc(X13),tc_nat)
        | c_lessequals(X4,X13,tc_nat)
        | c_Suc(X13) = X4 )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2502]) ).

fof(f34066,plain,
    ( spl0_1068
    | ~ spl0_93
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2779,f2498,f1418,f34064]) ).

fof(f34064,plain,
    ( spl0_1068
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f1418,plain,
    ( spl0_93
  <=> ! [X13,X4] :
        ( c_lessequals(X4,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f2498,plain,
    ( spl0_215
  <=> ! [X13,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | c_Suc(X4) = X13
        | c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f2779,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_lessequals(c_Suc(X0),X1,tc_nat) )
    | ~ spl0_93
    | ~ spl0_215 ),
    inference(resolution,[],[f2499,f1419]) ).

fof(f1419,plain,
    ( ! [X4,X13] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
        | c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f1418]) ).

fof(f2499,plain,
    ( ! [X4,X13] :
        ( c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat)
        | c_Suc(X4) = X13
        | ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f2498]) ).

fof(f34062,plain,
    ( spl0_1067
    | ~ spl0_99
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2778,f2498,f1442,f34060]) ).

fof(f34060,plain,
    ( spl0_1067
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f1442,plain,
    ( spl0_99
  <=> ! [X13,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f2778,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_99
    | ~ spl0_215 ),
    inference(resolution,[],[f2499,f1443]) ).

fof(f1443,plain,
    ( ! [X4,X13] :
        ( ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f1442]) ).

fof(f34058,plain,
    ( spl0_1066
    | ~ spl0_134
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f2661,f2478,f1664,f34056]) ).

fof(f34056,plain,
    ( spl0_1066
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f1664,plain,
    ( spl0_134
  <=> ! [X13,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f2478,plain,
    ( spl0_210
  <=> ! [X29,X27,X28] :
        ( ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f2661,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_134
    | ~ spl0_210 ),
    inference(resolution,[],[f2479,f1665]) ).

fof(f1665,plain,
    ( ! [X4,X13] :
        ( c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1664]) ).

fof(f2479,plain,
    ( ! [X28,X29,X27] :
        ( ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) )
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f2478]) ).

fof(f33987,plain,
    ( ~ spl0_20
    | spl0_1065
    | ~ spl0_116
    | ~ spl0_166
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2372,f2270,f1940,f1513,f33985,f1098]) ).

fof(f1098,plain,
    ( spl0_20
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f33985,plain,
    ( spl0_1065
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f1513,plain,
    ( spl0_116
  <=> c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1940,plain,
    ( spl0_166
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f2270,plain,
    ( spl0_191
  <=> ! [X29,X27,X28] :
        ( ~ c_lessequals(X27,X29,tc_nat)
        | ~ c_lessequals(X29,X28,tc_nat)
        | c_lessequals(X27,X28,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f2372,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X2),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_116
    | ~ spl0_166
    | ~ spl0_191 ),
    inference(forward_demodulation,[],[f2356,f1515]) ).

fof(f1515,plain,
    ( c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat)
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1513]) ).

fof(f2356,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2),tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_166
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1941]) ).

fof(f1941,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
        | ~ class_Lattices_Olattice(X0) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1940]) ).

fof(f2271,plain,
    ( ! [X28,X29,X27] :
        ( ~ c_lessequals(X29,X28,tc_nat)
        | ~ c_lessequals(X27,X29,tc_nat)
        | c_lessequals(X27,X28,tc_nat) )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f2270]) ).

fof(f33981,plain,
    ( ~ spl0_20
    | spl0_1064
    | ~ spl0_156
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2365,f2270,f1900,f33979,f1098]) ).

fof(f33979,plain,
    ( spl0_1064
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f1900,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f2365,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_156
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1901]) ).

fof(f1901,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0)
        | ~ class_Lattices_Olattice(X0) )
    | ~ spl0_156 ),
    inference(avatar_component_clause,[],[f1900]) ).

fof(f33918,plain,
    ( spl0_1063
    | ~ spl0_242
    | ~ spl0_1062 ),
    inference(avatar_split_clause,[],[f33914,f33911,f2943,f33916]) ).

fof(f33916,plain,
    ( spl0_1063
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f2943,plain,
    ( spl0_242
  <=> c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f33911,plain,
    ( spl0_1062
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f33914,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_242
    | ~ spl0_1062 ),
    inference(forward_demodulation,[],[f33912,f2945]) ).

fof(f2945,plain,
    ( c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat)
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f2943]) ).

fof(f33912,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_1062 ),
    inference(avatar_component_clause,[],[f33911]) ).

fof(f33913,plain,
    ( ~ spl0_20
    | spl0_1062
    | ~ spl0_155
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2363,f2270,f1896,f33911,f1098]) ).

fof(f1896,plain,
    ( spl0_155
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f2363,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X2),tc_nat)
        | c_lessequals(X0,X1,tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_155
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1897]) ).

fof(f1897,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0)
        | ~ class_Lattices_Olattice(X0) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1896]) ).

fof(f33909,plain,
    ( spl0_1061
    | ~ spl0_64
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2249,f2020,f1295,f33907]) ).

fof(f33907,plain,
    ( spl0_1061
  <=> ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f1295,plain,
    ( spl0_64
  <=> ! [X55,X56] :
        ( ~ class_Orderings_Obot(X56)
        | class_Orderings_Obot(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f2020,plain,
    ( spl0_183
  <=> ! [X20] :
        ( ~ class_Orderings_Obot(X20)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f2249,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,X1)) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(X0,X1))),v_x)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_64
    | ~ spl0_183 ),
    inference(resolution,[],[f2021,f1296]) ).

fof(f1296,plain,
    ( ! [X56,X55] :
        ( class_Orderings_Obot(tc_fun(X55,X56))
        | ~ class_Orderings_Obot(X56) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1295]) ).

fof(f2021,plain,
    ( ! [X20] :
        ( ~ class_Orderings_Obot(X20)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f2020]) ).

fof(f33905,plain,
    ( spl0_1060
    | ~ spl0_63
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f2244,f1994,f1291,f33903]) ).

fof(f33903,plain,
    ( spl0_1060
  <=> ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
        | ~ class_Orderings_Otop(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f1291,plain,
    ( spl0_63
  <=> ! [X55,X56] :
        ( ~ class_Orderings_Otop(X56)
        | class_Orderings_Otop(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1994,plain,
    ( spl0_177
  <=> ! [X20] :
        ( ~ class_Orderings_Otop(X20)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f2244,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(tc_fun(X0,X1)) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_fun(X0,X1))),v_x)
        | ~ class_Orderings_Otop(X1) )
    | ~ spl0_63
    | ~ spl0_177 ),
    inference(resolution,[],[f1995,f1292]) ).

fof(f1292,plain,
    ( ! [X56,X55] :
        ( class_Orderings_Otop(tc_fun(X55,X56))
        | ~ class_Orderings_Otop(X56) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f1995,plain,
    ( ! [X20] :
        ( ~ class_Orderings_Otop(X20)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1994]) ).

fof(f33901,plain,
    ( spl0_1059
    | ~ spl0_59
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2230,f1964,f1275,f33899]) ).

fof(f33899,plain,
    ( spl0_1059
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
        | ~ class_Lattices_Obounded__lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f1275,plain,
    ( spl0_59
  <=> ! [X55,X56] :
        ( ~ class_Lattices_Obounded__lattice(X56)
        | class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1964,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f2230,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))) = X2
        | ~ class_Lattices_Obounded__lattice(X1) )
    | ~ spl0_59
    | ~ spl0_172 ),
    inference(resolution,[],[f1965,f1276]) ).

fof(f1276,plain,
    ( ! [X56,X55] :
        ( class_Lattices_Obounded__lattice(tc_fun(X55,X56))
        | ~ class_Lattices_Obounded__lattice(X56) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f1275]) ).

fof(f1965,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1964]) ).

fof(f33897,plain,
    ( spl0_1058
    | ~ spl0_59
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2228,f1960,f1275,f33895]) ).

fof(f33895,plain,
    ( spl0_1058
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
        | ~ class_Lattices_Obounded__lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f1960,plain,
    ( spl0_171
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f2228,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),c_Orderings_Obot__class_Obot(tc_fun(X0,X1))),X2) = X2
        | ~ class_Lattices_Obounded__lattice(X1) )
    | ~ spl0_59
    | ~ spl0_171 ),
    inference(resolution,[],[f1961,f1276]) ).

fof(f1961,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1960]) ).

fof(f33893,plain,
    ( spl0_1057
    | ~ spl0_129
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f2154,f1928,f1644,f33891]) ).

fof(f33891,plain,
    ( spl0_1057
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f1644,plain,
    ( spl0_129
  <=> ! [X13,X4] :
        ( ~ c_lessequals(X13,X4,tc_nat)
        | c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1928,plain,
    ( spl0_163
  <=> ! [X13,X4] :
        ( X4 = X13
        | ~ c_lessequals(X4,X13,tc_nat)
        | c_HOL_Oord__class_Oless(X4,X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f2154,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_129
    | ~ spl0_163 ),
    inference(resolution,[],[f1929,f1645]) ).

fof(f1645,plain,
    ( ! [X4,X13] :
        ( c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat)
        | ~ c_lessequals(X13,X4,tc_nat) )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1644]) ).

fof(f1929,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(X4,X13,tc_nat)
        | X4 = X13
        | c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1928]) ).

fof(f33889,plain,
    ( spl0_1056
    | ~ spl0_133
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f2068,f1892,f1660,f33887]) ).

fof(f33887,plain,
    ( spl0_1056
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f1660,plain,
    ( spl0_133
  <=> ! [X13,X4] :
        ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1892,plain,
    ( spl0_154
  <=> ! [X2,X1] :
        ( X1 = X2
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f2068,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_133
    | ~ spl0_154 ),
    inference(resolution,[],[f1893,f1661]) ).

fof(f1661,plain,
    ( ! [X4,X13] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat)
        | c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1660]) ).

fof(f1893,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1892]) ).

fof(f33825,plain,
    ( spl0_1055
    | ~ spl0_129
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f2053,f1888,f1644,f33823]) ).

fof(f33823,plain,
    ( spl0_1055
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f1888,plain,
    ( spl0_153
  <=> ! [X13,X4] :
        ( X4 = X13
        | ~ c_lessequals(X4,X13,tc_nat)
        | ~ c_lessequals(X13,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f2053,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | ~ c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_129
    | ~ spl0_153 ),
    inference(resolution,[],[f1889,f1645]) ).

fof(f1889,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(X13,X4,tc_nat)
        | ~ c_lessequals(X4,X13,tc_nat)
        | X4 = X13 )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1888]) ).

fof(f33821,plain,
    ( spl0_1054
    | ~ spl0_59
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f2038,f1879,f1275,f33819]) ).

fof(f33819,plain,
    ( spl0_1054
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
        | ~ class_Lattices_Obounded__lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f1879,plain,
    ( spl0_151
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f2038,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))) = X2
        | ~ class_Lattices_Obounded__lattice(X1) )
    | ~ spl0_59
    | ~ spl0_151 ),
    inference(resolution,[],[f1880,f1276]) ).

fof(f1880,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 )
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1879]) ).

fof(f33817,plain,
    ( spl0_1053
    | ~ spl0_59
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f2036,f1875,f1275,f33815]) ).

fof(f33815,plain,
    ( spl0_1053
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
        | ~ class_Lattices_Obounded__lattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f1875,plain,
    ( spl0_150
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f2036,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X0,X1))),X2) = X2
        | ~ class_Lattices_Obounded__lattice(X1) )
    | ~ spl0_59
    | ~ spl0_150 ),
    inference(resolution,[],[f1876,f1276]) ).

fof(f1876,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1875]) ).

fof(f33813,plain,
    ( spl0_1052
    | ~ spl0_57
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f1555,f1422,f1267,f33811]) ).

fof(f33811,plain,
    ( spl0_1052
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
        | c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omin(tc_fun(X0,X1))
        | ~ class_Lattices_Olattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f1267,plain,
    ( spl0_57
  <=> ! [X55,X56] :
        ( ~ class_Lattices_Olattice(X56)
        | class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1422,plain,
    ( spl0_94
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1555,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
        | c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omin(tc_fun(X0,X1))
        | ~ class_Lattices_Olattice(X1) )
    | ~ spl0_57
    | ~ spl0_94 ),
    inference(resolution,[],[f1423,f1268]) ).

fof(f1268,plain,
    ( ! [X56,X55] :
        ( class_Lattices_Olower__semilattice(tc_fun(X55,X56))
        | ~ class_Lattices_Olattice(X56) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1267]) ).

fof(f1423,plain,
    ( ! [X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f1422]) ).

fof(f33809,plain,
    ( spl0_1051
    | ~ spl0_56
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f1511,f1382,f1263,f33807]) ).

fof(f33807,plain,
    ( spl0_1051
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
        | c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omax(tc_fun(X0,X1))
        | ~ class_Lattices_Olattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f1263,plain,
    ( spl0_56
  <=> ! [X55,X56] :
        ( ~ class_Lattices_Olattice(X56)
        | class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1382,plain,
    ( spl0_84
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f1511,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_fun(X0,X1))
        | c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)) = c_Orderings_Oord__class_Omax(tc_fun(X0,X1))
        | ~ class_Lattices_Olattice(X1) )
    | ~ spl0_56
    | ~ spl0_84 ),
    inference(resolution,[],[f1383,f1264]) ).

fof(f1264,plain,
    ( ! [X56,X55] :
        ( class_Lattices_Oupper__semilattice(tc_fun(X55,X56))
        | ~ class_Lattices_Olattice(X56) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f1263]) ).

fof(f1383,plain,
    ( ! [X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f1382]) ).

fof(f33488,plain,
    ( spl0_1050
    | ~ spl0_959
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f30823,f26868,f26298,f33486]) ).

fof(f33486,plain,
    ( spl0_1050
  <=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_G,X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f26298,plain,
    ( spl0_959
  <=> ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f26868,plain,
    ( spl0_984
  <=> ! [X4,X0,X3,X2,X1] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f30823,plain,
    ( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_G,X0,X2)
    | ~ spl0_959
    | ~ spl0_984 ),
    inference(superposition,[],[f26869,f26299]) ).

fof(f26299,plain,
    ( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0)
    | ~ spl0_959 ),
    inference(avatar_component_clause,[],[f26298]) ).

fof(f26869,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ spl0_984 ),
    inference(avatar_component_clause,[],[f26868]) ).

fof(f32902,plain,
    ( spl0_1049
    | ~ spl0_883
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f26382,f26298,f25145,f32900]) ).

fof(f25145,plain,
    ( spl0_883
  <=> ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f26382,plain,
    ( ! [X0] : c_lessequals(c_fequal(hAPP(v_mgt__call,v_x),X0),v_G,tc_fun(X0,tc_bool))
    | ~ spl0_883
    | ~ spl0_959 ),
    inference(superposition,[],[f25146,f26299]) ).

fof(f25146,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool))
    | ~ spl0_883 ),
    inference(avatar_component_clause,[],[f25145]) ).

fof(f32113,plain,
    ( spl0_1048
    | ~ spl0_875
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f26381,f26298,f25033,f32111]) ).

fof(f32111,plain,
    ( spl0_1048
  <=> ! [X0,X1] : hBOOL(c_in(hAPP(v_mgt__call,v_x),c_Set_Oinsert(X1,v_G,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f25033,plain,
    ( spl0_875
  <=> ! [X0,X3,X2,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f26381,plain,
    ( ! [X0,X1] : hBOOL(c_in(hAPP(v_mgt__call,v_x),c_Set_Oinsert(X1,v_G,X0),X0))
    | ~ spl0_875
    | ~ spl0_959 ),
    inference(superposition,[],[f25034,f26299]) ).

fof(f25034,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3))
    | ~ spl0_875 ),
    inference(avatar_component_clause,[],[f25033]) ).

fof(f31726,plain,
    ( spl0_1047
    | ~ spl0_173
    | ~ spl0_262
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f11642,f11222,f3028,f1978,f31724]) ).

fof(f31724,plain,
    ( spl0_1047
  <=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f1978,plain,
    ( spl0_173
  <=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f3028,plain,
    ( spl0_262
  <=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f11222,plain,
    ( spl0_565
  <=> ! [X0,X14,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f11642,plain,
    ( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool))
    | ~ spl0_173
    | ~ spl0_262
    | ~ spl0_565 ),
    inference(forward_demodulation,[],[f11619,f3029]) ).

fof(f3029,plain,
    ( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f3028]) ).

fof(f11619,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X2,X0,X1),tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_fequal(X2,X1),tc_fun(X1,tc_bool))
    | ~ spl0_173
    | ~ spl0_565 ),
    inference(superposition,[],[f11223,f1979]) ).

fof(f1979,plain,
    ( ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool))
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1978]) ).

fof(f11223,plain,
    ( ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool))
    | ~ spl0_565 ),
    inference(avatar_component_clause,[],[f11222]) ).

fof(f31719,plain,
    ( spl0_1046
    | ~ spl0_124
    | ~ spl0_519 ),
    inference(avatar_split_clause,[],[f10380,f10283,f1624,f31717]) ).

fof(f31717,plain,
    ( spl0_1046
  <=> ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
        | c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X0,tc_bool)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f1624,plain,
    ( spl0_124
  <=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f10283,plain,
    ( spl0_519
  <=> ! [X6,X0,X8] :
        ( c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f10380,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
        | c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X0,tc_bool)) = X1 )
    | ~ spl0_124
    | ~ spl0_519 ),
    inference(superposition,[],[f10284,f1625]) ).

fof(f1625,plain,
    ( ! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1624]) ).

fof(f10284,plain,
    ( ! [X0,X8,X6] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
        | c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6 )
    | ~ spl0_519 ),
    inference(avatar_component_clause,[],[f10283]) ).

fof(f31715,plain,
    ( spl0_1045
    | ~ spl0_82
    | ~ spl0_477 ),
    inference(avatar_split_clause,[],[f9266,f8165,f1369,f31713]) ).

fof(f31713,plain,
    ( spl0_1045
  <=> ! [X4,X0,X3,X2,X1] : hBOOL(c_in(hAPP(X0,X1),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f1369,plain,
    ( spl0_82
  <=> ! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f8165,plain,
    ( spl0_477
  <=> ! [X20,X0,X14,X25,X8] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f9266,plain,
    ( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(hAPP(X0,X1),c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),X4))
    | ~ spl0_82
    | ~ spl0_477 ),
    inference(superposition,[],[f1370,f8166]) ).

fof(f8166,plain,
    ( ! [X0,X8,X14,X25,X20] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0)
    | ~ spl0_477 ),
    inference(avatar_component_clause,[],[f8165]) ).

fof(f1370,plain,
    ( ! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0))
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f1369]) ).

fof(f31711,plain,
    ( spl0_1044
    | ~ spl0_186
    | ~ spl0_432 ),
    inference(avatar_split_clause,[],[f7784,f7315,f2032,f31709]) ).

fof(f31709,plain,
    ( spl0_1044
  <=> ! [X2,X0,X1] :
        ( c_fequal(X0,X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f2032,plain,
    ( spl0_186
  <=> ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f7315,plain,
    ( spl0_432
  <=> ! [X16,X0,X14] :
        ( X14 = X16
        | c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f7784,plain,
    ( ! [X2,X0,X1] :
        ( c_fequal(X0,X1) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
        | X0 = X2 )
    | ~ spl0_186
    | ~ spl0_432 ),
    inference(superposition,[],[f7316,f2033]) ).

fof(f2033,plain,
    ( ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0)
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f2032]) ).

fof(f7316,plain,
    ( ! [X0,X16,X14] :
        ( c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
        | X14 = X16 )
    | ~ spl0_432 ),
    inference(avatar_component_clause,[],[f7315]) ).

fof(f31707,plain,
    ( spl0_1042
    | spl0_1043
    | ~ spl0_79
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f7693,f7295,f1357,f31705,f31702]) ).

fof(f31702,plain,
    ( spl0_1042
  <=> ! [X5,X0,X6,X2,X1] : ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f31705,plain,
    ( spl0_1043
  <=> ! [X4,X3] : X3 = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f1357,plain,
    ( spl0_79
  <=> ! [X20,X0,X50,X26] : hAPP(c_COMBK(X26,X0,X20),X50) = X26 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f7295,plain,
    ( spl0_427
  <=> ! [X20,X0,X25,X2,X1] :
        ( X1 = X2
        | hAPP(X25,X1) != hAPP(X25,X2)
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f7693,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( X3 = X4
        | ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
    | ~ spl0_79
    | ~ spl0_427 ),
    inference(trivial_inequality_removal,[],[f7692]) ).

fof(f7692,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( X0 != X0
        | X3 = X4
        | ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
    | ~ spl0_79
    | ~ spl0_427 ),
    inference(forward_demodulation,[],[f7663,f1358]) ).

fof(f1358,plain,
    ( ! [X50,X0,X26,X20] : hAPP(c_COMBK(X26,X0,X20),X50) = X26
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f1357]) ).

fof(f7663,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( hAPP(c_COMBK(X0,X1,X2),X4) != X0
        | X3 = X4
        | ~ c_Fun_Oinj__on(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X6) )
    | ~ spl0_79
    | ~ spl0_427 ),
    inference(superposition,[],[f7296,f1358]) ).

fof(f7296,plain,
    ( ! [X2,X0,X1,X25,X20] :
        ( hAPP(X25,X1) != hAPP(X25,X2)
        | X1 = X2
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) )
    | ~ spl0_427 ),
    inference(avatar_component_clause,[],[f7295]) ).

fof(f31670,plain,
    ( ~ spl0_19
    | spl0_1041
    | ~ spl0_44
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f7099,f6711,f1215,f31668,f1093]) ).

fof(f1093,plain,
    ( spl0_19
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f31668,plain,
    ( spl0_1041
  <=> ! [X0] :
        ( ~ c_Finite__Set_Ofinite(X0,tc_nat)
        | ~ hBOOL(c_in(c_Suc(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),X0)),X0,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f1215,plain,
    ( spl0_44
  <=> ! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f6711,plain,
    ( spl0_402
  <=> ! [X6,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f7099,plain,
    ( ! [X0] :
        ( ~ c_Finite__Set_Ofinite(X0,tc_nat)
        | ~ hBOOL(c_in(c_Suc(hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),X0)),X0,tc_nat))
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_44
    | ~ spl0_402 ),
    inference(resolution,[],[f6712,f1216]) ).

fof(f1216,plain,
    ( ! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f1215]) ).

fof(f6712,plain,
    ( ! [X0,X1,X6] :
        ( c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_402 ),
    inference(avatar_component_clause,[],[f6711]) ).

fof(f31666,plain,
    ( spl0_1040
    | ~ spl0_358
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f6493,f6026,f4368,f31664]) ).

fof(f31664,plain,
    ( spl0_1040
  <=> ! [X2,X0,X1] :
        ( c_Set_Oinsert(X1,X2,X0) != X2
        | c_lessequals(c_fequal(X1,X0),X2,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f4368,plain,
    ( spl0_358
  <=> ! [X6,X0,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f6026,plain,
    ( spl0_377
  <=> ! [X6,X0,X8] :
        ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f6493,plain,
    ( ! [X2,X0,X1] :
        ( c_Set_Oinsert(X1,X2,X0) != X2
        | c_lessequals(c_fequal(X1,X0),X2,tc_fun(X0,tc_bool)) )
    | ~ spl0_358
    | ~ spl0_377 ),
    inference(superposition,[],[f6027,f4369]) ).

fof(f4369,plain,
    ( ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6)
    | ~ spl0_358 ),
    inference(avatar_component_clause,[],[f4368]) ).

fof(f6027,plain,
    ( ! [X0,X8,X6] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8
        | c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
    | ~ spl0_377 ),
    inference(avatar_component_clause,[],[f6026]) ).

fof(f31662,plain,
    ( spl0_1039
    | ~ spl0_52
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6259,f5988,f1247,f31660]) ).

fof(f31660,plain,
    ( spl0_1039
  <=> ! [X2,X0,X1,X3] :
        ( ~ class_HOL_Oord(X0)
        | c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
        | ~ class_Orderings_Oorder(tc_fun(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f1247,plain,
    ( spl0_52
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f5988,plain,
    ( spl0_369
  <=> ! [X20,X0,X25,X21,X1] :
        ( ~ class_HOL_Oord(X20)
        | ~ c_lessequals(X25,X21,tc_fun(X0,X20))
        | c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f6259,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_HOL_Oord(X0)
        | c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
        | ~ class_Orderings_Oorder(tc_fun(X3,X0)) )
    | ~ spl0_52
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1248]) ).

fof(f1248,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1247]) ).

fof(f5989,plain,
    ( ! [X21,X0,X1,X25,X20] :
        ( ~ c_lessequals(X25,X21,tc_fun(X0,X20))
        | ~ class_HOL_Oord(X20)
        | c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) )
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f5988]) ).

fof(f31658,plain,
    ( spl0_1038
    | ~ spl0_53
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6258,f5988,f1251,f31656]) ).

fof(f31656,plain,
    ( spl0_1038
  <=> ! [X2,X0,X1,X3] :
        ( ~ class_HOL_Oord(X0)
        | c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
        | ~ class_Orderings_Opreorder(tc_fun(X3,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f1251,plain,
    ( spl0_53
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f6258,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_HOL_Oord(X0)
        | c_lessequals(hAPP(X1,X2),hAPP(X1,X2),X0)
        | ~ class_Orderings_Opreorder(tc_fun(X3,X0)) )
    | ~ spl0_53
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1252]) ).

fof(f1252,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f1251]) ).

fof(f31652,plain,
    ( spl0_1037
    | ~ spl0_109
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f5422,f4276,f1482,f31650]) ).

fof(f31650,plain,
    ( spl0_1037
  <=> ! [X2,X0,X1,X3] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f1482,plain,
    ( spl0_109
  <=> ! [X0,X1,X51] :
        ( ~ hBOOL(hAPP(X51,X1))
        | hBOOL(c_in(X1,X51,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f4276,plain,
    ( spl0_336
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X8,X0))
        | ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f5422,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X0)) )
    | ~ spl0_109
    | ~ spl0_336 ),
    inference(resolution,[],[f4277,f1483]) ).

fof(f1483,plain,
    ( ! [X51,X0,X1] :
        ( hBOOL(c_in(X1,X51,X0))
        | ~ hBOOL(hAPP(X51,X1)) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1482]) ).

fof(f4277,plain,
    ( ! [X0,X8,X6,X15] :
        ( ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0))
        | ~ hBOOL(c_in(X15,X8,X0)) )
    | ~ spl0_336 ),
    inference(avatar_component_clause,[],[f4276]) ).

fof(f31648,plain,
    ( spl0_1036
    | ~ spl0_109
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f5417,f4272,f1482,f31646]) ).

fof(f31646,plain,
    ( spl0_1036
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(c_in(X0,X1,X2))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f4272,plain,
    ( spl0_335
  <=> ! [X15,X0,X6,X8] :
        ( hBOOL(c_in(X15,X6,X0))
        | ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f5417,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(c_in(X0,X1,X2))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X0)) )
    | ~ spl0_109
    | ~ spl0_335 ),
    inference(resolution,[],[f4273,f1483]) ).

fof(f4273,plain,
    ( ! [X0,X8,X6,X15] :
        ( ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0))
        | hBOOL(c_in(X15,X6,X0)) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f4272]) ).

fof(f31644,plain,
    ( spl0_1035
    | ~ spl0_68
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f5017,f4178,f1311,f31642]) ).

fof(f31642,plain,
    ( spl0_1035
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f1311,plain,
    ( spl0_68
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Obot(X0)
        | c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f4178,plain,
    ( spl0_312
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X16,X14,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f5017,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_312 ),
    inference(resolution,[],[f4179,f1312]) ).

fof(f1312,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1311]) ).

fof(f4179,plain,
    ( ! [X0,X16,X14] :
        ( ~ c_lessequals(X16,X14,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f4178]) ).

fof(f31640,plain,
    ( spl0_1034
    | ~ spl0_70
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f5000,f4178,f1319,f31638]) ).

fof(f31638,plain,
    ( spl0_1034
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f1319,plain,
    ( spl0_70
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Otop(X0)
        | c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f5000,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_312 ),
    inference(resolution,[],[f4179,f1320]) ).

fof(f1320,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f1319]) ).

fof(f31636,plain,
    ( spl0_1033
    | ~ spl0_68
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f4970,f4170,f1311,f31634]) ).

fof(f31634,plain,
    ( spl0_1033
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f4170,plain,
    ( spl0_310
  <=> ! [X0,X28,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X3,X28,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f4970,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_310 ),
    inference(resolution,[],[f4171,f1312]) ).

fof(f4171,plain,
    ( ! [X3,X28,X0] :
        ( ~ c_lessequals(X3,X28,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) )
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f4170]) ).

fof(f31632,plain,
    ( spl0_1032
    | ~ spl0_70
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f4953,f4170,f1319,f31630]) ).

fof(f31630,plain,
    ( spl0_1032
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f4953,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_310 ),
    inference(resolution,[],[f4171,f1320]) ).

fof(f31628,plain,
    ( spl0_1031
    | ~ spl0_112
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4046,f3086,f1494,f31626]) ).

fof(f31626,plain,
    ( spl0_1031
  <=> ! [X2,X4,X0,X3,X1] : hBOOL(c_in(X2,c_Set_Oimage(c_Finite__Set_Ofold1(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f1494,plain,
    ( spl0_112
  <=> ! [X25,X0,X14] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f3086,plain,
    ( spl0_276
  <=> ! [X20,X0,X25,X1] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f4046,plain,
    ( ! [X2,X3,X0,X1,X4] : hBOOL(c_in(X2,c_Set_Oimage(c_Finite__Set_Ofold1(X0,X1),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4))
    | ~ spl0_112
    | ~ spl0_276 ),
    inference(superposition,[],[f3087,f1495]) ).

fof(f1495,plain,
    ( ! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f1494]) ).

fof(f3087,plain,
    ( ! [X0,X1,X25,X20] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0))
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f3086]) ).

fof(f31540,plain,
    ( ~ spl0_14
    | spl0_1030
    | ~ spl0_77
    | ~ spl0_116
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f3879,f3053,f1513,f1349,f31538,f1068]) ).

fof(f1068,plain,
    ( spl0_14
  <=> class_Lattices_Oupper__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f31538,plain,
    ( spl0_1030
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X1
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f1349,plain,
    ( spl0_77
  <=> ! [X13,X4] :
        ( c_lessequals(X4,X13,tc_nat)
        | c_lessequals(X13,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f3053,plain,
    ( spl0_268
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f3879,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X1
        | ~ class_Lattices_Oupper__semilattice(tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_77
    | ~ spl0_116
    | ~ spl0_268 ),
    inference(forward_demodulation,[],[f3840,f1515]) ).

fof(f3840,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(tc_nat)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = X1
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_77
    | ~ spl0_268 ),
    inference(resolution,[],[f3054,f1350]) ).

fof(f1350,plain,
    ( ! [X4,X13] :
        ( c_lessequals(X4,X13,tc_nat)
        | c_lessequals(X13,X4,tc_nat) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1349]) ).

fof(f3054,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f3053]) ).

fof(f31536,plain,
    ( spl0_1029
    | ~ spl0_70
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f3853,f3053,f1319,f31534]) ).

fof(f31534,plain,
    ( spl0_1029
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f3853,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0))
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_268 ),
    inference(resolution,[],[f3054,f1320]) ).

fof(f31399,plain,
    ( ~ spl0_14
    | spl0_1028
    | ~ spl0_77
    | ~ spl0_116
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f3818,f3045,f1513,f1349,f31397,f1068]) ).

fof(f31397,plain,
    ( spl0_1028
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X0
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f3045,plain,
    ( spl0_266
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X2,X1,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f3818,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = X0
        | ~ class_Lattices_Oupper__semilattice(tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_77
    | ~ spl0_116
    | ~ spl0_266 ),
    inference(forward_demodulation,[],[f3779,f1515]) ).

fof(f3779,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(tc_nat)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1) = X0
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_77
    | ~ spl0_266 ),
    inference(resolution,[],[f3046,f1350]) ).

fof(f3046,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f3045]) ).

fof(f31395,plain,
    ( spl0_1027
    | ~ spl0_70
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f3792,f3045,f1319,f31393]) ).

fof(f31393,plain,
    ( spl0_1027
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f3792,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_266 ),
    inference(resolution,[],[f3046,f1320]) ).

fof(f31391,plain,
    ( spl0_1026
    | ~ spl0_201
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f3752,f3041,f2311,f31389]) ).

fof(f31389,plain,
    ( spl0_1026
  <=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_Set_Oimage(X1,c_Set_Ovimage(X1,X0,X2,t_a),X2,t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f3041,plain,
    ( spl0_265
  <=> ! [X20,X0,X6,X25] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f3752,plain,
    ( ! [X2,X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_Set_Oimage(X1,c_Set_Ovimage(X1,X0,X2,t_a),X2,t_a)))
    | ~ spl0_201
    | ~ spl0_265 ),
    inference(resolution,[],[f3042,f2312]) ).

fof(f3042,plain,
    ( ! [X0,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool))
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f3041]) ).

fof(f31387,plain,
    ( spl0_1025
    | ~ spl0_200
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f3751,f3041,f2307,f31385]) ).

fof(f31385,plain,
    ( spl0_1025
  <=> ! [X0,X3,X2,X1] :
        ( c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,X1,X2,X3),X2,X3),X3)
        | ~ c_Finite__Set_Ofinite(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f2307,plain,
    ( spl0_200
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Finite__Set_Ofinite(X6,X0)
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f3751,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,X1,X2,X3),X2,X3),X3)
        | ~ c_Finite__Set_Ofinite(X1,X3) )
    | ~ spl0_200
    | ~ spl0_265 ),
    inference(resolution,[],[f3042,f2308]) ).

fof(f2308,plain,
    ( ! [X0,X8,X6] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0) )
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f2307]) ).

fof(f31299,plain,
    ( ~ spl0_15
    | spl0_1024
    | ~ spl0_77
    | ~ spl0_242
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f3669,f3008,f2943,f1349,f31297,f1073]) ).

fof(f1073,plain,
    ( spl0_15
  <=> class_Lattices_Olower__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f31297,plain,
    ( spl0_1024
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X1
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f3008,plain,
    ( spl0_257
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X2,X1,X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f3669,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X1
        | ~ class_Lattices_Olower__semilattice(tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_77
    | ~ spl0_242
    | ~ spl0_257 ),
    inference(forward_demodulation,[],[f3632,f2945]) ).

fof(f3632,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(tc_nat)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = X1
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_77
    | ~ spl0_257 ),
    inference(resolution,[],[f3009,f1350]) ).

fof(f3009,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 )
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f3008]) ).

fof(f31295,plain,
    ( spl0_1023
    | ~ spl0_68
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f3660,f3008,f1311,f31293]) ).

fof(f31293,plain,
    ( spl0_1023
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f3660,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0))
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_257 ),
    inference(resolution,[],[f3009,f1312]) ).

fof(f31204,plain,
    ( ~ spl0_15
    | spl0_1022
    | ~ spl0_77
    | ~ spl0_242
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f3611,f3000,f2943,f1349,f31202,f1073]) ).

fof(f31202,plain,
    ( spl0_1022
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X0
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f3000,plain,
    ( spl0_255
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f3611,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = X0
        | ~ class_Lattices_Olower__semilattice(tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_77
    | ~ spl0_242
    | ~ spl0_255 ),
    inference(forward_demodulation,[],[f3574,f2945]) ).

fof(f3574,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(tc_nat)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = X0
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_77
    | ~ spl0_255 ),
    inference(resolution,[],[f3001,f1350]) ).

fof(f3001,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 )
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f3000]) ).

fof(f31200,plain,
    ( spl0_1021
    | ~ spl0_865
    | ~ spl0_984 ),
    inference(avatar_split_clause,[],[f30824,f26868,f24804,f31198]) ).

fof(f31198,plain,
    ( spl0_1021
  <=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_U,X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f24804,plain,
    ( spl0_865
  <=> ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f30824,plain,
    ( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X1,v_U,X0,X2)
    | ~ spl0_865
    | ~ spl0_984 ),
    inference(superposition,[],[f26869,f24805]) ).

fof(f24805,plain,
    ( ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0)
    | ~ spl0_865 ),
    inference(avatar_component_clause,[],[f24804]) ).

fof(f31196,plain,
    ( spl0_1020
    | ~ spl0_68
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f3602,f3000,f1311,f31194]) ).

fof(f31194,plain,
    ( spl0_1020
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f3602,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_255 ),
    inference(resolution,[],[f3001,f1312]) ).

fof(f31192,plain,
    ( spl0_1019
    | ~ spl0_140
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f3536,f2992,f1691,f31190]) ).

fof(f31190,plain,
    ( spl0_1019
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_lessequals(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f1691,plain,
    ( spl0_140
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X2,X0)
        | c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f2992,plain,
    ( spl0_253
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X2,X1,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f3536,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_lessequals(X1,X2,X0) )
    | ~ spl0_140
    | ~ spl0_253 ),
    inference(duplicate_literal_removal,[],[f3497]) ).

fof(f3497,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_140
    | ~ spl0_253 ),
    inference(resolution,[],[f2993,f1692]) ).

fof(f1692,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,X1,X0)
        | c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1691]) ).

fof(f2993,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 )
    | ~ spl0_253 ),
    inference(avatar_component_clause,[],[f2992]) ).

fof(f31188,plain,
    ( spl0_1018
    | ~ spl0_125
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f3534,f2992,f1628,f31186]) ).

fof(f31186,plain,
    ( spl0_1018
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f1628,plain,
    ( spl0_125
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f3534,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X1,X2,X0) )
    | ~ spl0_125
    | ~ spl0_253 ),
    inference(duplicate_literal_removal,[],[f3499]) ).

fof(f3499,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_125
    | ~ spl0_253 ),
    inference(resolution,[],[f2993,f1629]) ).

fof(f1629,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1628]) ).

fof(f31184,plain,
    ( spl0_1017
    | ~ spl0_68
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f3523,f2992,f1311,f31182]) ).

fof(f31182,plain,
    ( spl0_1017
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Obot__class_Obot(X0))
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f3523,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Obot__class_Obot(X0))
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_253 ),
    inference(resolution,[],[f2993,f1312]) ).

fof(f31180,plain,
    ( spl0_1016
    | ~ spl0_140
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3488,f2980,f1691,f31178]) ).

fof(f31178,plain,
    ( spl0_1016
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f2980,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f3488,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_lessequals(X2,X1,X0) )
    | ~ spl0_140
    | ~ spl0_251 ),
    inference(duplicate_literal_removal,[],[f3449]) ).

fof(f3449,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_140
    | ~ spl0_251 ),
    inference(resolution,[],[f2981,f1692]) ).

fof(f2981,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 )
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f2980]) ).

fof(f31176,plain,
    ( spl0_1015
    | ~ spl0_125
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3486,f2980,f1628,f31174]) ).

fof(f31174,plain,
    ( spl0_1015
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f3486,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X2,X1,X0) )
    | ~ spl0_125
    | ~ spl0_251 ),
    inference(duplicate_literal_removal,[],[f3451]) ).

fof(f3451,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_125
    | ~ spl0_251 ),
    inference(resolution,[],[f2981,f1629]) ).

fof(f31172,plain,
    ( spl0_1014
    | ~ spl0_68
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3475,f2980,f1311,f31170]) ).

fof(f31170,plain,
    ( spl0_1014
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Obot__class_Obot(X0)),X1)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f3475,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Obot__class_Obot(X0)),X1)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_251 ),
    inference(resolution,[],[f2981,f1312]) ).

fof(f31168,plain,
    ( spl0_1013
    | ~ spl0_140
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f3440,f2976,f1691,f31166]) ).

fof(f31166,plain,
    ( spl0_1013
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_lessequals(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f2976,plain,
    ( spl0_250
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X2,X1,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f3440,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_lessequals(X1,X2,X0) )
    | ~ spl0_140
    | ~ spl0_250 ),
    inference(duplicate_literal_removal,[],[f3401]) ).

fof(f3401,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_140
    | ~ spl0_250 ),
    inference(resolution,[],[f2977,f1692]) ).

fof(f2977,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 )
    | ~ spl0_250 ),
    inference(avatar_component_clause,[],[f2976]) ).

fof(f31164,plain,
    ( spl0_1012
    | ~ spl0_125
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f3438,f2976,f1628,f31162]) ).

fof(f31162,plain,
    ( spl0_1012
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f3438,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X1,X2,X0) )
    | ~ spl0_125
    | ~ spl0_250 ),
    inference(duplicate_literal_removal,[],[f3403]) ).

fof(f3403,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_125
    | ~ spl0_250 ),
    inference(resolution,[],[f2977,f1629]) ).

fof(f31160,plain,
    ( spl0_1011
    | ~ spl0_70
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f3412,f2976,f1319,f31158]) ).

fof(f31158,plain,
    ( spl0_1011
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Otop__class_Otop(X0)),X1)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f3412,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Otop__class_Otop(X0)),X1)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_250 ),
    inference(resolution,[],[f2977,f1320]) ).

fof(f31156,plain,
    ( spl0_1010
    | ~ spl0_865
    | ~ spl0_983 ),
    inference(avatar_split_clause,[],[f30716,f26864,f24804,f31154]) ).

fof(f31154,plain,
    ( spl0_1010
  <=> ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X1,v_U,X0,X2),hAPP(X1,v_x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f26864,plain,
    ( spl0_983
  <=> ! [X2,X4,X0,X3,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f30716,plain,
    ( ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X1,v_U,X0,X2),hAPP(X1,v_x)))
    | ~ spl0_865
    | ~ spl0_983 ),
    inference(superposition,[],[f26865,f24805]) ).

fof(f26865,plain,
    ( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1)))
    | ~ spl0_983 ),
    inference(avatar_component_clause,[],[f26864]) ).

fof(f31152,plain,
    ( spl0_1009
    | ~ spl0_140
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3392,f2968,f1691,f31150]) ).

fof(f31150,plain,
    ( spl0_1009
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f2968,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f3392,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_lessequals(X2,X1,X0) )
    | ~ spl0_140
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f3353]) ).

fof(f3353,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_140
    | ~ spl0_248 ),
    inference(resolution,[],[f2969,f1692]) ).

fof(f2969,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 )
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f2968]) ).

fof(f31148,plain,
    ( spl0_1008
    | ~ spl0_125
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3390,f2968,f1628,f31146]) ).

fof(f31146,plain,
    ( spl0_1008
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f3390,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X2,X1,X0) )
    | ~ spl0_125
    | ~ spl0_248 ),
    inference(duplicate_literal_removal,[],[f3355]) ).

fof(f3355,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_125
    | ~ spl0_248 ),
    inference(resolution,[],[f2969,f1629]) ).

fof(f31144,plain,
    ( spl0_1007
    | ~ spl0_70
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3364,f2968,f1319,f31142]) ).

fof(f31142,plain,
    ( spl0_1007
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Otop__class_Otop(X0))
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f3364,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Otop__class_Otop(X0))
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_248 ),
    inference(resolution,[],[f2969,f1320]) ).

fof(f31096,plain,
    ( ~ spl0_21
    | spl0_1006
    | ~ spl0_77
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3160,f2939,f1349,f31094,f1103]) ).

fof(f1103,plain,
    ( spl0_21
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f31094,plain,
    ( spl0_1006
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f2939,plain,
    ( spl0_241
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_lessequals(X19,X2,X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f3160,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_77
    | ~ spl0_241 ),
    inference(resolution,[],[f2940,f1350]) ).

fof(f2940,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X19,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0) )
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f2939]) ).

fof(f31092,plain,
    ( spl0_1005
    | ~ spl0_68
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3141,f2931,f1311,f31090]) ).

fof(f31090,plain,
    ( spl0_1005
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | c_lessequals(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f2931,plain,
    ( spl0_239
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f3141,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | c_lessequals(X1,c_Orderings_Obot__class_Obot(X0),X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_239 ),
    inference(resolution,[],[f2932,f1312]) ).

fof(f2932,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_lessequals(X2,X1,X0) )
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f2931]) ).

fof(f31088,plain,
    ( spl0_1004
    | ~ spl0_70
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3126,f2931,f1319,f31086]) ).

fof(f31086,plain,
    ( spl0_1004
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(X0),X0)
        | c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f3126,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,c_Orderings_Otop__class_Otop(X0),X0)
        | c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_239 ),
    inference(resolution,[],[f2932,f1320]) ).

fof(f31084,plain,
    ( spl0_1003
    | ~ spl0_79
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2929,f2584,f1357,f31082]) ).

fof(f31082,plain,
    ( spl0_1003
  <=> ! [X3,X4,X0,X5,X2,X1] : hBOOL(c_in(X3,c_Set_Ovimage(c_COMBK(X0,X1,X2),c_fequal(X0,X4),X5,X4),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f2584,plain,
    ( spl0_235
  <=> ! [X53,X0,X14,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f2929,plain,
    ( ! [X2,X3,X0,X1,X4,X5] : hBOOL(c_in(X3,c_Set_Ovimage(c_COMBK(X0,X1,X2),c_fequal(X0,X4),X5,X4),X5))
    | ~ spl0_79
    | ~ spl0_235 ),
    inference(superposition,[],[f2585,f1358]) ).

fof(f2585,plain,
    ( ! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53))
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2584]) ).

fof(f31080,plain,
    ( spl0_1002
    | ~ spl0_129
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2799,f2502,f1644,f31078]) ).

fof(f31078,plain,
    ( spl0_1002
  <=> ! [X0,X1] :
        ( c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f2799,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_Suc(X1) = c_Suc(X0)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_129
    | ~ spl0_216 ),
    inference(resolution,[],[f2503,f1645]) ).

fof(f31076,plain,
    ( spl0_1001
    | ~ spl0_133
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2763,f2498,f1660,f31074]) ).

fof(f31074,plain,
    ( spl0_1001
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f2763,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(X0)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_133
    | ~ spl0_215 ),
    inference(resolution,[],[f2499,f1661]) ).

fof(f31069,plain,
    ( spl0_1000
    | ~ spl0_89
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f2659,f2478,f1402,f31067]) ).

fof(f31067,plain,
    ( spl0_1000
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f1402,plain,
    ( spl0_89
  <=> ! [X13,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f2659,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_89
    | ~ spl0_210 ),
    inference(resolution,[],[f2479,f1403]) ).

fof(f1403,plain,
    ( ! [X4,X13] :
        ( c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f1402]) ).

fof(f31065,plain,
    ( spl0_999
    | ~ spl0_92
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f2658,f2478,f1414,f31063]) ).

fof(f31063,plain,
    ( spl0_999
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f1414,plain,
    ( spl0_92
  <=> ! [X13,X4] :
        ( ~ c_lessequals(X4,X13,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f2658,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_92
    | ~ spl0_210 ),
    inference(resolution,[],[f2479,f1415]) ).

fof(f1415,plain,
    ( ! [X4,X13] :
        ( c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat)
        | ~ c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f1414]) ).

fof(f31061,plain,
    ( spl0_998
    | ~ spl0_100
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f2657,f2478,f1446,f31059]) ).

fof(f31059,plain,
    ( spl0_998
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f1446,plain,
    ( spl0_100
  <=> ! [X13,X4] :
        ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f2657,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_100
    | ~ spl0_210 ),
    inference(resolution,[],[f2479,f1447]) ).

fof(f1447,plain,
    ( ! [X4,X13] :
        ( c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat)
        | c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f1446]) ).

fof(f31057,plain,
    ( spl0_997
    | ~ spl0_129
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2371,f2270,f1644,f31055]) ).

fof(f31055,plain,
    ( spl0_997
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f2371,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_129
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1645]) ).

fof(f31053,plain,
    ( spl0_996
    | ~ spl0_62
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1871,f1711,f1287,f31051]) ).

fof(f31051,plain,
    ( spl0_996
  <=> ! [X2,X0,X1] :
        ( c_fequal(X0,tc_fun(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_fun(X1,X2))
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f1287,plain,
    ( spl0_62
  <=> ! [X55,X56] :
        ( ~ class_Orderings_Oorder(X56)
        | class_Orderings_Oorder(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1711,plain,
    ( spl0_145
  <=> ! [X0,X14] :
        ( c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1871,plain,
    ( ! [X2,X0,X1] :
        ( c_fequal(X0,tc_fun(X1,X2)) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_fun(X1,X2))
        | ~ class_Orderings_Oorder(X2) )
    | ~ spl0_62
    | ~ spl0_145 ),
    inference(resolution,[],[f1712,f1288]) ).

fof(f1288,plain,
    ( ! [X56,X55] :
        ( class_Orderings_Oorder(tc_fun(X55,X56))
        | ~ class_Orderings_Oorder(X56) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1287]) ).

fof(f1712,plain,
    ( ! [X0,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1711]) ).

fof(f31049,plain,
    ( spl0_995
    | ~ spl0_112
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1834,f1680,f1494,f31047]) ).

fof(f31047,plain,
    ( spl0_995
  <=> ! [X4,X0,X3,X2,X1] : c_Finite__Set_Ofold1(X0,X1) = c_Fun_Ofun__upd(c_Finite__Set_Ofold1(X0,X1),c_fequal(X2,X1),X2,X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f1680,plain,
    ( spl0_138
  <=> ! [X20,X0,X25,X1] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1834,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Finite__Set_Ofold1(X0,X1) = c_Fun_Ofun__upd(c_Finite__Set_Ofold1(X0,X1),c_fequal(X2,X1),X2,X3,X4)
    | ~ spl0_112
    | ~ spl0_138 ),
    inference(superposition,[],[f1681,f1495]) ).

fof(f1681,plain,
    ( ! [X0,X1,X25,X20] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1680]) ).

fof(f31045,plain,
    ( spl0_994
    | ~ spl0_79
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1833,f1680,f1357,f31043]) ).

fof(f31043,plain,
    ( spl0_994
  <=> ! [X2,X4,X0,X5,X3,X1] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f1833,plain,
    ( ! [X2,X3,X0,X1,X4,X5] : c_COMBK(X0,X1,X2) = c_Fun_Ofun__upd(c_COMBK(X0,X1,X2),X3,X0,X4,X5)
    | ~ spl0_79
    | ~ spl0_138 ),
    inference(superposition,[],[f1681,f1358]) ).

fof(f30896,plain,
    ( spl0_993
    | ~ spl0_3
    | ~ spl0_981 ),
    inference(avatar_split_clause,[],[f30690,f26856,f1013,f30893]) ).

fof(f30893,plain,
    ( spl0_993
  <=> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f1013,plain,
    ( spl0_3
  <=> v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f26856,plain,
    ( spl0_981
  <=> ! [X0,X3,X2,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f30690,plain,
    ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),v_G,t_a,tc_Com_Opname)
    | ~ spl0_3
    | ~ spl0_981 ),
    inference(superposition,[],[f26857,f1015]) ).

fof(f1015,plain,
    ( v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f1013]) ).

fof(f26857,plain,
    ( ! [X2,X3,X0,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2)
    | ~ spl0_981 ),
    inference(avatar_component_clause,[],[f26856]) ).

fof(f29423,plain,
    ( ~ spl0_37
    | spl0_992
    | ~ spl0_254
    | ~ spl0_908 ),
    inference(avatar_split_clause,[],[f26111,f25990,f2996,f29421,f1183]) ).

fof(f1183,plain,
    ( spl0_37
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f29421,plain,
    ( spl0_992
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f2996,plain,
    ( spl0_254
  <=> ! [X20,X0,X25,X21] :
        ( ~ class_HOL_Oord(X20)
        | ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
        | ~ c_lessequals(X21,X25,tc_fun(X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f25990,plain,
    ( spl0_908
  <=> ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f26111,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,X0),tc_fun(X0,tc_bool))
        | ~ class_HOL_Oord(tc_bool) )
    | ~ spl0_254
    | ~ spl0_908 ),
    inference(resolution,[],[f25991,f2997]) ).

fof(f2997,plain,
    ( ! [X21,X0,X25,X20] :
        ( ~ c_lessequals(X21,X25,tc_fun(X0,X20))
        | ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
        | ~ class_HOL_Oord(X20) )
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f2996]) ).

fof(f25991,plain,
    ( ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool))
    | ~ spl0_908 ),
    inference(avatar_component_clause,[],[f25990]) ).

fof(f28850,plain,
    ( spl0_991
    | ~ spl0_272
    | ~ spl0_908 ),
    inference(avatar_split_clause,[],[f26091,f25990,f3069,f28848]) ).

fof(f28848,plain,
    ( spl0_991
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_fequal(v_x,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f3069,plain,
    ( spl0_272
  <=> ! [X0,X50,X1,X26] :
        ( ~ hBOOL(hAPP(X26,X1))
        | hBOOL(hAPP(X50,X1))
        | ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f26091,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_fequal(v_x,X1),X0)) )
    | ~ spl0_272
    | ~ spl0_908 ),
    inference(resolution,[],[f25991,f3070]) ).

fof(f3070,plain,
    ( ! [X50,X0,X1,X26] :
        ( ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool))
        | hBOOL(hAPP(X50,X1))
        | ~ hBOOL(hAPP(X26,X1)) )
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f3069]) ).

fof(f28272,plain,
    ( spl0_990
    | ~ spl0_861
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f26379,f26298,f23922,f28270]) ).

fof(f28270,plain,
    ( spl0_990
  <=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_G,X0),hAPP(v_mgt__call,v_x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f23922,plain,
    ( spl0_861
  <=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f26379,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_G,X0),hAPP(v_mgt__call,v_x)))
    | ~ spl0_861
    | ~ spl0_959 ),
    inference(superposition,[],[f23923,f26299]) ).

fof(f23923,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
    | ~ spl0_861 ),
    inference(avatar_component_clause,[],[f23922]) ).

fof(f27134,plain,
    ( spl0_989
    | ~ spl0_82
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f26342,f26298,f1369,f27132]) ).

fof(f27132,plain,
    ( spl0_989
  <=> ! [X0] : hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f26342,plain,
    ( ! [X0] : hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,X0))
    | ~ spl0_82
    | ~ spl0_959 ),
    inference(superposition,[],[f1370,f26299]) ).

fof(f26886,plain,
    ( spl0_988
    | ~ spl0_173
    | ~ spl0_186
    | ~ spl0_225
    | ~ spl0_400
    | ~ spl0_637 ),
    inference(avatar_split_clause,[],[f13866,f13548,f6703,f2538,f2032,f1978,f26884]) ).

fof(f26884,plain,
    ( spl0_988
  <=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f2538,plain,
    ( spl0_225
  <=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f6703,plain,
    ( spl0_400
  <=> ! [X20,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f13548,plain,
    ( spl0_637
  <=> ! [X20,X0,X14,X6,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f13866,plain,
    ( ! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool))
    | ~ spl0_173
    | ~ spl0_186
    | ~ spl0_225
    | ~ spl0_400
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f13865,f2539]) ).

fof(f2539,plain,
    ( ! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2538]) ).

fof(f13865,plain,
    ( ! [X2,X3,X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X0)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
    | ~ spl0_173
    | ~ spl0_186
    | ~ spl0_400
    | ~ spl0_637 ),
    inference(forward_demodulation,[],[f13766,f6986]) ).

fof(f6986,plain,
    ( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1,X0,tc_fun(X2,tc_bool))
    | ~ spl0_173
    | ~ spl0_400 ),
    inference(superposition,[],[f6704,f1979]) ).

fof(f6704,plain,
    ( ! [X0,X8,X6,X20] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
    | ~ spl0_400 ),
    inference(avatar_component_clause,[],[f6703]) ).

fof(f13766,plain,
    ( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(X2,X0)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_fequal(X0,X1),X2,X1,tc_fun(X3,tc_bool))
    | ~ spl0_186
    | ~ spl0_637 ),
    inference(superposition,[],[f13549,f2033]) ).

fof(f13549,plain,
    ( ! [X0,X8,X6,X14,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)))
    | ~ spl0_637 ),
    inference(avatar_component_clause,[],[f13548]) ).

fof(f26882,plain,
    ( spl0_987
    | ~ spl0_54
    | ~ spl0_186
    | ~ spl0_262
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f10593,f10355,f3028,f2032,f1255,f26880]) ).

fof(f26880,plain,
    ( spl0_987
  <=> ! [X0,X1] : c_Finite__Set_Ocard(c_fequal(X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f1255,plain,
    ( spl0_54
  <=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f10355,plain,
    ( spl0_528
  <=> ! [X6,X0,X1] :
        ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
        | ~ c_Finite__Set_Ofinite(X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f10593,plain,
    ( ! [X0,X1] : c_Finite__Set_Ocard(c_fequal(X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
    | ~ spl0_54
    | ~ spl0_186
    | ~ spl0_262
    | ~ spl0_528 ),
    inference(forward_demodulation,[],[f10592,f2033]) ).

fof(f10592,plain,
    ( ! [X0,X1] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
    | ~ spl0_54
    | ~ spl0_262
    | ~ spl0_528 ),
    inference(forward_demodulation,[],[f10581,f3029]) ).

fof(f10581,plain,
    ( ! [X0,X1] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1))
    | ~ spl0_54
    | ~ spl0_528 ),
    inference(resolution,[],[f10356,f1256]) ).

fof(f1256,plain,
    ( ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f1255]) ).

fof(f10356,plain,
    ( ! [X0,X1,X6] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)) )
    | ~ spl0_528 ),
    inference(avatar_component_clause,[],[f10355]) ).

fof(f26878,plain,
    ( spl0_986
    | ~ spl0_416
    | ~ spl0_519 ),
    inference(avatar_split_clause,[],[f10389,f10283,f7246,f26876]) ).

fof(f26876,plain,
    ( spl0_986
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f7246,plain,
    ( spl0_416
  <=> ! [X6,X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f10389,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1
    | ~ spl0_416
    | ~ spl0_519 ),
    inference(trivial_inequality_removal,[],[f10384]) ).

fof(f10384,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X1 )
    | ~ spl0_416
    | ~ spl0_519 ),
    inference(superposition,[],[f10284,f7247]) ).

fof(f7247,plain,
    ( ! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)))
    | ~ spl0_416 ),
    inference(avatar_component_clause,[],[f7246]) ).

fof(f26874,plain,
    ( spl0_985
    | ~ spl0_186
    | ~ spl0_233
    | ~ spl0_477 ),
    inference(avatar_split_clause,[],[f9288,f8165,f2576,f2032,f26872]) ).

fof(f26872,plain,
    ( spl0_985
  <=> ! [X0,X3,X2,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_fequal(hAPP(X2,X0),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f2576,plain,
    ( spl0_233
  <=> ! [X20,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f9288,plain,
    ( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_fequal(hAPP(X2,X0),X3)
    | ~ spl0_186
    | ~ spl0_233
    | ~ spl0_477 ),
    inference(forward_demodulation,[],[f9287,f2033]) ).

fof(f9287,plain,
    ( ! [X2,X3,X0,X1] : c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3) = c_Set_Oinsert(hAPP(X2,X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
    | ~ spl0_186
    | ~ spl0_233
    | ~ spl0_477 ),
    inference(forward_demodulation,[],[f9222,f2577]) ).

fof(f2577,plain,
    ( ! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0)
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2576]) ).

fof(f9222,plain,
    ( ! [X2,X3,X0,X1] : c_Set_Oinsert(hAPP(X2,X0),c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,X3),X3) = c_Set_Oimage(X2,c_fequal(X0,X1),X1,X3)
    | ~ spl0_186
    | ~ spl0_477 ),
    inference(superposition,[],[f8166,f2033]) ).

fof(f26870,plain,
    ( spl0_984
    | ~ spl0_106
    | ~ spl0_477 ),
    inference(avatar_split_clause,[],[f9268,f8165,f1470,f26868]) ).

fof(f1470,plain,
    ( spl0_106
  <=> ! [X6,X0,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f9268,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
    | ~ spl0_106
    | ~ spl0_477 ),
    inference(superposition,[],[f1471,f8166]) ).

fof(f1471,plain,
    ( ! [X0,X6,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0)
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1470]) ).

fof(f26866,plain,
    ( spl0_983
    | ~ spl0_72
    | ~ spl0_477 ),
    inference(avatar_split_clause,[],[f9265,f8165,f1327,f26864]) ).

fof(f1327,plain,
    ( spl0_72
  <=> ! [X6,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f9265,plain,
    ( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4),hAPP(X0,X1)))
    | ~ spl0_72
    | ~ spl0_477 ),
    inference(superposition,[],[f1328,f8166]) ).

fof(f1328,plain,
    ( ! [X0,X1,X6] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1))
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f1327]) ).

fof(f26862,plain,
    ( spl0_982
    | ~ spl0_174
    | ~ spl0_186
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f9180,f8153,f2032,f1982,f26860]) ).

fof(f26860,plain,
    ( spl0_982
  <=> ! [X2,X0,X1] :
        ( c_Finite__Set_Ofinite(X2,X1)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f1982,plain,
    ( spl0_174
  <=> ! [X6,X0] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f8153,plain,
    ( spl0_474
  <=> ! [X0,X14,X6,X8] :
        ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f9180,plain,
    ( ! [X2,X0,X1] :
        ( c_Finite__Set_Ofinite(X2,X1)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1) )
    | ~ spl0_174
    | ~ spl0_186
    | ~ spl0_474 ),
    inference(forward_demodulation,[],[f9170,f1983]) ).

fof(f1983,plain,
    ( ! [X0,X6] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f1982]) ).

fof(f9170,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_fequal(X0,X1),tc_fun(X1,tc_bool)),X1)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X1) )
    | ~ spl0_186
    | ~ spl0_474 ),
    inference(superposition,[],[f8154,f2033]) ).

fof(f8154,plain,
    ( ! [X0,X8,X6,X14] :
        ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) )
    | ~ spl0_474 ),
    inference(avatar_component_clause,[],[f8153]) ).

fof(f26858,plain,
    ( spl0_981
    | ~ spl0_51
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f9020,f8125,f1243,f26856]) ).

fof(f1243,plain,
    ( spl0_51
  <=> ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f8125,plain,
    ( spl0_467
  <=> ! [X20,X0,X6,X25,X8] :
        ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20)
        | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f9020,plain,
    ( ! [X2,X3,X0,X1] : c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X0,X1,X2,X3),c_Set_Oimage(X1,X0,X2,X3),X3,X2)
    | ~ spl0_51
    | ~ spl0_467 ),
    inference(resolution,[],[f8126,f1244]) ).

fof(f1244,plain,
    ( ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool))
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f1243]) ).

fof(f8126,plain,
    ( ! [X0,X8,X6,X25,X20] :
        ( ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool))
        | c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20) )
    | ~ spl0_467 ),
    inference(avatar_component_clause,[],[f8125]) ).

fof(f26806,plain,
    ( ~ spl0_19
    | spl0_980
    | ~ spl0_21
    | ~ spl0_42
    | ~ spl0_145
    | ~ spl0_437 ),
    inference(avatar_split_clause,[],[f8008,f7340,f1711,f1207,f1103,f26804,f1093]) ).

fof(f26804,plain,
    ( spl0_980
  <=> ! [X0] : c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f1207,plain,
    ( spl0_42
  <=> ! [X13] : c_lessequals(X13,X13,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f7340,plain,
    ( spl0_437
  <=> ! [X5,X0,X3] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f8008,plain,
    ( ! [X0] :
        ( c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_21
    | ~ spl0_42
    | ~ spl0_145
    | ~ spl0_437 ),
    inference(forward_demodulation,[],[f7933,f1869]) ).

fof(f1869,plain,
    ( ! [X0] : c_fequal(X0,tc_nat) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat)
    | ~ spl0_21
    | ~ spl0_145 ),
    inference(resolution,[],[f1712,f1105]) ).

fof(f1105,plain,
    ( class_Orderings_Oorder(tc_nat)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f1103]) ).

fof(f7933,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Olinorder(tc_nat)
        | c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OgreaterThanAtMost(X0,X0,tc_nat),tc_nat) )
    | ~ spl0_42
    | ~ spl0_437 ),
    inference(resolution,[],[f7341,f1208]) ).

fof(f1208,plain,
    ( ! [X13] : c_lessequals(X13,X13,tc_nat)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f1207]) ).

fof(f7341,plain,
    ( ! [X3,X0,X5] :
        ( ~ c_lessequals(X3,X5,X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0) )
    | ~ spl0_437 ),
    inference(avatar_component_clause,[],[f7340]) ).

fof(f26754,plain,
    ( ~ spl0_19
    | spl0_979
    | ~ spl0_21
    | ~ spl0_42
    | ~ spl0_145
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f7932,f7336,f1711,f1207,f1103,f26752,f1093]) ).

fof(f26752,plain,
    ( spl0_979
  <=> ! [X0] : c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f7336,plain,
    ( spl0_436
  <=> ! [X5,X0,X3] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f7932,plain,
    ( ! [X0] :
        ( c_fequal(X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_21
    | ~ spl0_42
    | ~ spl0_145
    | ~ spl0_436 ),
    inference(forward_demodulation,[],[f7857,f1869]) ).

fof(f7857,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Olinorder(tc_nat)
        | c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) )
    | ~ spl0_42
    | ~ spl0_436 ),
    inference(resolution,[],[f7337,f1208]) ).

fof(f7337,plain,
    ( ! [X3,X0,X5] :
        ( ~ c_lessequals(X3,X5,X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0) )
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f7336]) ).

fof(f26750,plain,
    ( spl0_978
    | ~ spl0_80
    | ~ spl0_233
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f6542,f6034,f2576,f1361,f26748]) ).

fof(f26748,plain,
    ( spl0_978
  <=> ! [X2,X0] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f1361,plain,
    ( spl0_80
  <=> ! [X20,X0,X25] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f6034,plain,
    ( spl0_379
  <=> ! [X20,X0,X6,X25] :
        ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f6542,plain,
    ( ! [X2,X0] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | ~ spl0_80
    | ~ spl0_233
    | ~ spl0_379 ),
    inference(forward_demodulation,[],[f6539,f2577]) ).

fof(f6539,plain,
    ( ! [X2,X0,X1] : c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Finite__Set_Ocard(c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X2),X2)
    | ~ spl0_80
    | ~ spl0_379 ),
    inference(resolution,[],[f6035,f1362]) ).

fof(f1362,plain,
    ( ! [X0,X25,X20] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20)
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f1361]) ).

fof(f6035,plain,
    ( ! [X0,X6,X25,X20] :
        ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) )
    | ~ spl0_379 ),
    inference(avatar_component_clause,[],[f6034]) ).

fof(f26746,plain,
    ( spl0_977
    | ~ spl0_106
    | ~ spl0_959 ),
    inference(avatar_split_clause,[],[f26344,f26298,f1470,f26744]) ).

fof(f26744,plain,
    ( spl0_977
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f26344,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != v_G
    | ~ spl0_106
    | ~ spl0_959 ),
    inference(superposition,[],[f1471,f26299]) ).

fof(f26742,plain,
    ( spl0_976
    | ~ spl0_105
    | ~ spl0_378 ),
    inference(avatar_split_clause,[],[f6517,f6030,f1466,f26740]) ).

fof(f26740,plain,
    ( spl0_976
  <=> ! [X0,X3,X2,X1] :
        ( c_Fun_Oinj__on(X0,X1,X2,X3)
        | ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f1466,plain,
    ( spl0_105
  <=> ! [X6,X0] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f6030,plain,
    ( spl0_378
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
        | c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f6517,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Fun_Oinj__on(X0,X1,X2,X3)
        | ~ c_Fun_Oinj__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) )
    | ~ spl0_105
    | ~ spl0_378 ),
    inference(resolution,[],[f6031,f1467]) ).

fof(f1467,plain,
    ( ! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f1466]) ).

fof(f6031,plain,
    ( ! [X0,X8,X6,X25,X20] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_Fun_Oinj__on(X25,X8,X0,X20) )
    | ~ spl0_378 ),
    inference(avatar_component_clause,[],[f6030]) ).

fof(f26631,plain,
    ( spl0_975
    | ~ spl0_37
    | ~ spl0_103
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6293,f5988,f1458,f1183,f26629]) ).

fof(f26629,plain,
    ( spl0_975
  <=> ! [X2,X0,X1] : c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f1458,plain,
    ( spl0_103
  <=> ! [X6,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f6293,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1),hAPP(X2,X1),tc_bool) )
    | ~ spl0_103
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1459]) ).

fof(f1459,plain,
    ( ! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f1458]) ).

fof(f26511,plain,
    ( spl0_974
    | ~ spl0_37
    | ~ spl0_104
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6278,f5988,f1462,f1183,f26509]) ).

fof(f26509,plain,
    ( spl0_974
  <=> ! [X0,X3,X2,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f1462,plain,
    ( spl0_104
  <=> ! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f6278,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(X0,X1),hAPP(c_Set_Oinsert(X2,X0,X3),X1),tc_bool) )
    | ~ spl0_104
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1463]) ).

fof(f1463,plain,
    ( ! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool))
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f1462]) ).

fof(f26401,plain,
    ( spl0_973
    | ~ spl0_37
    | ~ spl0_105
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6276,f5988,f1466,f1183,f26399]) ).

fof(f26399,plain,
    ( spl0_973
  <=> ! [X2,X0,X1] : c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f6276,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(X0,X1),hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1),tc_bool) )
    | ~ spl0_105
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1467]) ).

fof(f26397,plain,
    ( spl0_972
    | ~ spl0_104
    | ~ spl0_363 ),
    inference(avatar_split_clause,[],[f6135,f5963,f1462,f26395]) ).

fof(f26395,plain,
    ( spl0_972
  <=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X1,X2,X0)),X2) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

fof(f5963,plain,
    ( spl0_363
  <=> ! [X6,X0,X8] :
        ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f6135,plain,
    ( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X1,X2,X0)),X2) = X2
    | ~ spl0_104
    | ~ spl0_363 ),
    inference(resolution,[],[f5964,f1463]) ).

fof(f5964,plain,
    ( ! [X0,X8,X6] :
        ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 )
    | ~ spl0_363 ),
    inference(avatar_component_clause,[],[f5963]) ).

fof(f26393,plain,
    ( spl0_971
    | ~ spl0_104
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f6091,f5959,f1462,f26391]) ).

fof(f26391,plain,
    ( spl0_971
  <=> ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Set_Oinsert(X2,X1,X0)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f5959,plain,
    ( spl0_362
  <=> ! [X6,X0,X8] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f6091,plain,
    ( ! [X2,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Set_Oinsert(X2,X1,X0)) = X1
    | ~ spl0_104
    | ~ spl0_362 ),
    inference(resolution,[],[f5960,f1463]) ).

fof(f5960,plain,
    ( ! [X0,X8,X6] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f5959]) ).

fof(f26389,plain,
    ( spl0_970
    | ~ spl0_347
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f5933,f4368,f4320,f26387]) ).

fof(f26387,plain,
    ( spl0_970
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
        | ~ hBOOL(hAPP(c_fequal(X1,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f4320,plain,
    ( spl0_347
  <=> ! [X6,X0,X1,X8] :
        ( ~ hBOOL(hAPP(X6,X1))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f5933,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
        | ~ hBOOL(hAPP(c_fequal(X1,X0),X3)) )
    | ~ spl0_347
    | ~ spl0_358 ),
    inference(superposition,[],[f4321,f4369]) ).

fof(f4321,plain,
    ( ! [X0,X1,X8,X6] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1))
        | ~ hBOOL(hAPP(X6,X1)) )
    | ~ spl0_347 ),
    inference(avatar_component_clause,[],[f4320]) ).

fof(f26340,plain,
    ( spl0_969
    | ~ spl0_186
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f5928,f4364,f2032,f26338]) ).

fof(f26338,plain,
    ( spl0_969
  <=> ! [X2,X0,X1] : c_Set_Oinsert(X2,c_fequal(X0,X1),X1) = c_Set_Oinsert(X0,c_fequal(X2,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f4364,plain,
    ( spl0_357
  <=> ! [X0,X6,X2,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f5928,plain,
    ( ! [X2,X0,X1] : c_Set_Oinsert(X2,c_fequal(X0,X1),X1) = c_Set_Oinsert(X0,c_fequal(X2,X1),X1)
    | ~ spl0_186
    | ~ spl0_357 ),
    inference(forward_demodulation,[],[f5888,f2033]) ).

fof(f5888,plain,
    ( ! [X2,X0,X1] : c_Set_Oinsert(X0,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = c_Set_Oinsert(X2,c_fequal(X0,X1),X1)
    | ~ spl0_186
    | ~ spl0_357 ),
    inference(superposition,[],[f4365,f2033]) ).

fof(f4365,plain,
    ( ! [X2,X0,X1,X6] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0)
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f4364]) ).

fof(f26336,plain,
    ( spl0_968
    | ~ spl0_32
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f5428,f4280,f1158,f26334]) ).

fof(f26334,plain,
    ( spl0_968
  <=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f1158,plain,
    ( spl0_32
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f4280,plain,
    ( spl0_337
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f5428,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X0)
    | ~ spl0_32
    | ~ spl0_337 ),
    inference(resolution,[],[f4281,f1160]) ).

fof(f1160,plain,
    ( class_Lattices_Olattice(tc_bool)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f1158]) ).

fof(f4281,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f4280]) ).

fof(f26332,plain,
    ( spl0_967
    | ~ spl0_48
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f5353,f4256,f1231,f26330]) ).

fof(f26330,plain,
    ( spl0_967
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f1231,plain,
    ( spl0_48
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f4256,plain,
    ( spl0_331
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X16,X0)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f5353,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_48
    | ~ spl0_331 ),
    inference(resolution,[],[f4257,f1232]) ).

fof(f1232,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f1231]) ).

fof(f4257,plain,
    ( ! [X0,X1,X16,X14] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0)
        | ~ c_HOL_Oord__class_Oless(X1,X16,X0)
        | ~ class_Lattices_Oupper__semilattice(X0) )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f4256]) ).

fof(f26328,plain,
    ( spl0_966
    | ~ spl0_48
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f5321,f4252,f1231,f26326]) ).

fof(f26326,plain,
    ( spl0_966
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f4252,plain,
    ( spl0_330
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X14,X0)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f5321,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_48
    | ~ spl0_330 ),
    inference(resolution,[],[f4253,f1232]) ).

fof(f4253,plain,
    ( ! [X0,X1,X16,X14] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0)
        | ~ c_HOL_Oord__class_Oless(X1,X14,X0)
        | ~ class_Lattices_Oupper__semilattice(X0) )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f4252]) ).

fof(f26324,plain,
    ( spl0_965
    | ~ spl0_19
    | ~ spl0_325 ),
    inference(avatar_split_clause,[],[f5307,f4232,f1093,f26322]) ).

fof(f26322,plain,
    ( spl0_965
  <=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f4232,plain,
    ( spl0_325
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f5307,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),X0)
    | ~ spl0_19
    | ~ spl0_325 ),
    inference(resolution,[],[f4233,f1095]) ).

fof(f1095,plain,
    ( class_Orderings_Olinorder(tc_nat)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f1093]) ).

fof(f4233,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) )
    | ~ spl0_325 ),
    inference(avatar_component_clause,[],[f4232]) ).

fof(f26320,plain,
    ( spl0_964
    | ~ spl0_15
    | ~ spl0_242
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f4896,f4162,f2943,f1073,f26318]) ).

fof(f26318,plain,
    ( spl0_964
  <=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f4162,plain,
    ( spl0_308
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f4896,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0)
    | ~ spl0_15
    | ~ spl0_242
    | ~ spl0_308 ),
    inference(forward_demodulation,[],[f4893,f2945]) ).

fof(f4893,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0)
    | ~ spl0_15
    | ~ spl0_308 ),
    inference(resolution,[],[f4163,f1075]) ).

fof(f1075,plain,
    ( class_Lattices_Olower__semilattice(tc_nat)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f1073]) ).

fof(f4163,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) )
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f4162]) ).

fof(f26316,plain,
    ( spl0_963
    | ~ spl0_27
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f4894,f4162,f1133,f26314]) ).

fof(f26314,plain,
    ( spl0_963
  <=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f1133,plain,
    ( spl0_27
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f4894,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X0)
    | ~ spl0_27
    | ~ spl0_308 ),
    inference(resolution,[],[f4163,f1135]) ).

fof(f1135,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f1133]) ).

fof(f26312,plain,
    ( spl0_962
    | ~ spl0_9
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f4811,f4138,f1043,f26310]) ).

fof(f26310,plain,
    ( spl0_962
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f1043,plain,
    ( spl0_9
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f4138,plain,
    ( spl0_302
  <=> ! [X0,X16,X14] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f4811,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)
    | ~ spl0_9
    | ~ spl0_302 ),
    inference(resolution,[],[f4139,f1045]) ).

fof(f1045,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f1043]) ).

fof(f4139,plain,
    ( ! [X0,X16,X14] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f4138]) ).

fof(f26308,plain,
    ( spl0_961
    | ~ spl0_48
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f4723,f4119,f1231,f26306]) ).

fof(f26306,plain,
    ( spl0_961
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2),X1)
        | ~ class_Lattices_Olower__semilattice(X1)
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f4119,plain,
    ( spl0_298
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f4723,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X0),X2),X1)
        | ~ class_Lattices_Olower__semilattice(X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_48
    | ~ spl0_298 ),
    inference(resolution,[],[f4120,f1232]) ).

fof(f4120,plain,
    ( ! [X0,X1,X16,X14] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0)
        | ~ c_HOL_Oord__class_Oless(X14,X1,X0)
        | ~ class_Lattices_Olower__semilattice(X0) )
    | ~ spl0_298 ),
    inference(avatar_component_clause,[],[f4119]) ).

fof(f26304,plain,
    ( spl0_960
    | ~ spl0_48
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f4687,f4115,f1231,f26302]) ).

fof(f26302,plain,
    ( spl0_960
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0),X1)
        | ~ class_Lattices_Olower__semilattice(X1)
        | ~ class_Orderings_Oorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f4115,plain,
    ( spl0_297
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X16,X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f4687,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X0),X1)
        | ~ class_Lattices_Olower__semilattice(X1)
        | ~ class_Orderings_Oorder(X1) )
    | ~ spl0_48
    | ~ spl0_297 ),
    inference(resolution,[],[f4116,f1232]) ).

fof(f4116,plain,
    ( ! [X0,X1,X16,X14] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0)
        | ~ c_HOL_Oord__class_Oless(X16,X1,X0)
        | ~ class_Lattices_Olower__semilattice(X0) )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f4115]) ).

fof(f26300,plain,
    ( spl0_959
    | ~ spl0_746
    | ~ spl0_852 ),
    inference(avatar_split_clause,[],[f24438,f23886,f20403,f26298]) ).

fof(f20403,plain,
    ( spl0_746
  <=> hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f23886,plain,
    ( spl0_852
  <=> ! [X2,X0,X1] :
        ( c_Set_Oinsert(X0,X1,X2) = X1
        | ~ hBOOL(hAPP(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f24438,plain,
    ( ! [X0] : v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,X0)
    | ~ spl0_746
    | ~ spl0_852 ),
    inference(resolution,[],[f23887,f20405]) ).

fof(f20405,plain,
    ( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x)))
    | ~ spl0_746 ),
    inference(avatar_component_clause,[],[f20403]) ).

fof(f23887,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(X1,X0))
        | c_Set_Oinsert(X0,X1,X2) = X1 )
    | ~ spl0_852 ),
    inference(avatar_component_clause,[],[f23886]) ).

fof(f26296,plain,
    ( spl0_958
    | ~ spl0_20
    | ~ spl0_116
    | ~ spl0_242
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f4682,f4111,f2943,f1513,f1098,f26294]) ).

fof(f26294,plain,
    ( spl0_958
  <=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f4111,plain,
    ( spl0_296
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f4682,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_116
    | ~ spl0_242
    | ~ spl0_296 ),
    inference(forward_demodulation,[],[f4681,f2945]) ).

fof(f4681,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_116
    | ~ spl0_296 ),
    inference(forward_demodulation,[],[f4678,f1515]) ).

fof(f4678,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_296 ),
    inference(resolution,[],[f4112,f1100]) ).

fof(f1100,plain,
    ( class_Lattices_Olattice(tc_nat)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f4112,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 )
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f4111]) ).

fof(f26292,plain,
    ( spl0_957
    | ~ spl0_32
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f4679,f4111,f1158,f26290]) ).

fof(f26290,plain,
    ( spl0_957
  <=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f4679,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X1)) = X0
    | ~ spl0_32
    | ~ spl0_296 ),
    inference(resolution,[],[f4112,f1160]) ).

fof(f26288,plain,
    ( spl0_956
    | ~ spl0_20
    | ~ spl0_116
    | ~ spl0_242
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f4677,f4107,f2943,f1513,f1098,f26286]) ).

fof(f26286,plain,
    ( spl0_956
  <=> ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f4107,plain,
    ( spl0_295
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f4677,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_116
    | ~ spl0_242
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f4676,f1515]) ).

fof(f4676,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_242
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f4673,f2945]) ).

fof(f4673,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1)) = X0
    | ~ spl0_20
    | ~ spl0_295 ),
    inference(resolution,[],[f4108,f1100]) ).

fof(f4108,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 )
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f4107]) ).

fof(f26284,plain,
    ( spl0_955
    | ~ spl0_32
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f4674,f4107,f1158,f26282]) ).

fof(f26282,plain,
    ( spl0_955
  <=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f4674,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X1)) = X0
    | ~ spl0_32
    | ~ spl0_295 ),
    inference(resolution,[],[f4108,f1160]) ).

fof(f26280,plain,
    ( spl0_954
    | ~ spl0_13
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f4671,f4099,f1063,f26278]) ).

fof(f26278,plain,
    ( spl0_954
  <=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f1063,plain,
    ( spl0_13
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f4099,plain,
    ( spl0_293
  <=> ! [X0,X16,X14] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f4671,plain,
    ( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)
    | ~ spl0_13
    | ~ spl0_293 ),
    inference(resolution,[],[f4100,f1065]) ).

fof(f1065,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f1063]) ).

fof(f4100,plain,
    ( ! [X0,X16,X14] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f4099]) ).

fof(f26276,plain,
    ( spl0_953
    | ~ spl0_110
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4039,f3086,f1486,f26274]) ).

fof(f26274,plain,
    ( spl0_953
  <=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f1486,plain,
    ( spl0_110
  <=> ! [X0,X1,X51] :
        ( hBOOL(hAPP(X51,X1))
        | ~ hBOOL(c_in(X1,X51,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f4039,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X2),hAPP(X0,X3)))
    | ~ spl0_110
    | ~ spl0_276 ),
    inference(resolution,[],[f3087,f1487]) ).

fof(f1487,plain,
    ( ! [X51,X0,X1] :
        ( ~ hBOOL(c_in(X1,X51,X0))
        | hBOOL(hAPP(X51,X1)) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f1486]) ).

fof(f26272,plain,
    ( spl0_952
    | ~ spl0_165
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f4011,f3069,f1936,f26270]) ).

fof(f26270,plain,
    ( spl0_952
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f1936,plain,
    ( spl0_165
  <=> ! [X6,X0,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f4011,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X0,X2,tc_fun(X3,tc_bool)),X1)) )
    | ~ spl0_165
    | ~ spl0_272 ),
    inference(resolution,[],[f3070,f1937]) ).

fof(f1937,plain,
    ( ! [X0,X8,X6] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool))
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1936]) ).

fof(f26268,plain,
    ( spl0_951
    | ~ spl0_68
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f3972,f3065,f1311,f26266]) ).

fof(f26266,plain,
    ( spl0_951
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,X2,X1)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f3065,plain,
    ( spl0_271
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X2,X0)
        | ~ c_lessequals(X2,X19,X0)
        | c_lessequals(X1,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f3972,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,X2,X1)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_68
    | ~ spl0_271 ),
    inference(resolution,[],[f3066,f1312]) ).

fof(f3066,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X2,X19,X0)
        | ~ c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X19,X0) )
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f3065]) ).

fof(f26264,plain,
    ( spl0_950
    | ~ spl0_70
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f3914,f3061,f1319,f26262]) ).

fof(f26262,plain,
    ( spl0_950
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f3061,plain,
    ( spl0_270
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X2,X1,X0)
        | ~ c_lessequals(X19,X2,X0)
        | c_lessequals(X19,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f3914,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_270 ),
    inference(resolution,[],[f3062,f1320]) ).

fof(f3062,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X19,X2,X0)
        | ~ c_lessequals(X2,X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X19,X1,X0) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f3061]) ).

fof(f26260,plain,
    ( spl0_949
    | ~ spl0_68
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f3868,f3053,f1311,f26258]) ).

fof(f26258,plain,
    ( spl0_949
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f3868,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_268 ),
    inference(resolution,[],[f3054,f1312]) ).

fof(f26254,plain,
    ( spl0_948
    | ~ spl0_68
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f3807,f3045,f1311,f26252]) ).

fof(f26252,plain,
    ( spl0_948
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f3807,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_266 ),
    inference(resolution,[],[f3046,f1312]) ).

fof(f26250,plain,
    ( spl0_947
    | ~ spl0_186
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f3738,f3037,f2032,f26248]) ).

fof(f26248,plain,
    ( spl0_947
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_fequal(X0,X1),X2,tc_fun(X1,tc_bool))
        | hBOOL(c_in(X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f3037,plain,
    ( spl0_264
  <=> ! [X0,X8,X6,X1] :
        ( hBOOL(c_in(X1,X8,X0))
        | ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f3738,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_fequal(X0,X1),X2,tc_fun(X1,tc_bool))
        | hBOOL(c_in(X0,X2,X1)) )
    | ~ spl0_186
    | ~ spl0_264 ),
    inference(superposition,[],[f3038,f2033]) ).

fof(f3038,plain,
    ( ! [X0,X1,X8,X6] :
        ( ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool))
        | hBOOL(c_in(X1,X8,X0)) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f3037]) ).

fof(f26246,plain,
    ( spl0_946
    | ~ spl0_70
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f3645,f3008,f1319,f26244]) ).

fof(f26244,plain,
    ( spl0_946
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f3645,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_257 ),
    inference(resolution,[],[f3009,f1320]) ).

fof(f26242,plain,
    ( spl0_945
    | ~ spl0_70
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f3587,f3000,f1319,f26240]) ).

fof(f26240,plain,
    ( spl0_945
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f3587,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_255 ),
    inference(resolution,[],[f3001,f1320]) ).

fof(f26213,plain,
    ( ~ spl0_37
    | spl0_944
    | ~ spl0_165
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f3567,f2996,f1936,f26211,f1183]) ).

fof(f26211,plain,
    ( spl0_944
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f3567,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
        | ~ class_HOL_Oord(tc_bool) )
    | ~ spl0_165
    | ~ spl0_254 ),
    inference(resolution,[],[f2997,f1937]) ).

fof(f26209,plain,
    ( spl0_943
    | ~ spl0_70
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f3508,f2992,f1319,f26207]) ).

fof(f26207,plain,
    ( spl0_943
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f3508,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_253 ),
    inference(resolution,[],[f2993,f1320]) ).

fof(f26205,plain,
    ( spl0_942
    | ~ spl0_70
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f3460,f2980,f1319,f26203]) ).

fof(f26203,plain,
    ( spl0_942
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f3460,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_251 ),
    inference(resolution,[],[f2981,f1320]) ).

fof(f26201,plain,
    ( spl0_941
    | ~ spl0_68
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f3427,f2976,f1311,f26199]) ).

fof(f26199,plain,
    ( spl0_941
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f3427,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_250 ),
    inference(resolution,[],[f2977,f1312]) ).

fof(f26197,plain,
    ( spl0_940
    | ~ spl0_68
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3379,f2968,f1311,f26195]) ).

fof(f26195,plain,
    ( spl0_940
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f3379,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_248 ),
    inference(resolution,[],[f2969,f1312]) ).

fof(f26193,plain,
    ( spl0_939
    | ~ spl0_201
    | ~ spl0_908 ),
    inference(avatar_split_clause,[],[f26108,f25990,f2311,f26190]) ).

fof(f26190,plain,
    ( spl0_939
  <=> hBOOL(hAPP(hAPP(v_P,v_U),c_fequal(v_x,t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f26108,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_U),c_fequal(v_x,t_a)))
    | ~ spl0_201
    | ~ spl0_908 ),
    inference(resolution,[],[f25991,f2312]) ).

fof(f26188,plain,
    ( spl0_938
    | ~ spl0_70
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3301,f2956,f1319,f26186]) ).

fof(f26186,plain,
    ( spl0_938
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
        | ~ class_Orderings_Otop(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f2956,plain,
    ( spl0_245
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_lessequals(X2,X19,X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f3301,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
        | ~ class_Orderings_Otop(X2) )
    | ~ spl0_70
    | ~ spl0_245 ),
    inference(resolution,[],[f2957,f1320]) ).

fof(f2957,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X2,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2956]) ).

fof(f26184,plain,
    ( spl0_937
    | ~ spl0_68
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3275,f2952,f1311,f26182]) ).

fof(f26182,plain,
    ( spl0_937
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
        | ~ class_Orderings_Obot(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f2952,plain,
    ( spl0_244
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
        | ~ c_lessequals(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f3275,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
        | ~ class_Orderings_Obot(X2) )
    | ~ spl0_68
    | ~ spl0_244 ),
    inference(resolution,[],[f2953,f1312]) ).

fof(f2953,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2952]) ).

fof(f26180,plain,
    ( spl0_936
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3229,f2948,f1311,f26178]) ).

fof(f26178,plain,
    ( spl0_936
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,X2,X1)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f2948,plain,
    ( spl0_243
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
        | ~ c_lessequals(X2,X1,X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f3229,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,X2,X1)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(resolution,[],[f2949,f1312]) ).

fof(f2949,plain,
    ( ! [X2,X0,X1,X19] :
        ( ~ c_lessequals(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f2948]) ).

fof(f26176,plain,
    ( spl0_935
    | ~ spl0_70
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3214,f2948,f1319,f26174]) ).

fof(f26174,plain,
    ( spl0_935
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
        | ~ class_Orderings_Otop(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f3214,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X2),X2)
        | ~ class_Orderings_Otop(X2) )
    | ~ spl0_70
    | ~ spl0_243 ),
    inference(resolution,[],[f2949,f1320]) ).

fof(f26172,plain,
    ( spl0_934
    | ~ spl0_68
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3188,f2939,f1311,f26170]) ).

fof(f26170,plain,
    ( spl0_934
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
        | ~ class_Orderings_Obot(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f3188,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X2),X1,X2)
        | ~ class_Orderings_Obot(X2) )
    | ~ spl0_68
    | ~ spl0_241 ),
    inference(resolution,[],[f2940,f1312]) ).

fof(f26168,plain,
    ( spl0_933
    | ~ spl0_70
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3173,f2939,f1319,f26166]) ).

fof(f26166,plain,
    ( spl0_933
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f3173,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_241 ),
    inference(resolution,[],[f2940,f1320]) ).

fof(f26164,plain,
    ( spl0_932
    | ~ spl0_68
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2880,f2560,f1311,f26162]) ).

fof(f26162,plain,
    ( spl0_932
  <=> ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X1) = X0
        | ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f2560,plain,
    ( spl0_229
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | X1 = X2
        | ~ c_lessequals(X1,X2,X0)
        | ~ c_lessequals(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f2880,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X1) = X0
        | ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_68
    | ~ spl0_229 ),
    inference(resolution,[],[f2561,f1312]) ).

fof(f2561,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,X1,X0)
        | X1 = X2
        | ~ c_lessequals(X1,X2,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f2560]) ).

fof(f26160,plain,
    ( spl0_931
    | ~ spl0_70
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2866,f2560,f1319,f26158]) ).

fof(f26158,plain,
    ( spl0_931
  <=> ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X0) = X1
        | ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f2866,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X0) = X1
        | ~ c_lessequals(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_229 ),
    inference(resolution,[],[f2561,f1320]) ).

fof(f26156,plain,
    ( spl0_930
    | ~ spl0_201
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2817,f2522,f2311,f26154]) ).

fof(f26154,plain,
    ( spl0_930
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f2522,plain,
    ( spl0_221
  <=> ! [X6,X0,X8] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f2817,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X1))
    | ~ spl0_201
    | ~ spl0_221 ),
    inference(resolution,[],[f2523,f2312]) ).

fof(f2523,plain,
    ( ! [X0,X8,X6] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool))
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f2522]) ).

fof(f26152,plain,
    ( spl0_929
    | ~ spl0_201
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2810,f2518,f2311,f26150]) ).

fof(f26150,plain,
    ( spl0_929
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f2518,plain,
    ( spl0_220
  <=> ! [X6,X0,X8] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f2810,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X0),X1)),X0))
    | ~ spl0_201
    | ~ spl0_220 ),
    inference(resolution,[],[f2519,f2312]) ).

fof(f2519,plain,
    ( ! [X0,X8,X6] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool))
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f2518]) ).

fof(f26089,plain,
    ( spl0_928
    | ~ spl0_68
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2747,f2494,f1311,f26087]) ).

fof(f26087,plain,
    ( spl0_928
  <=> ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X0) = X1
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f2494,plain,
    ( spl0_214
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | X1 = X2
        | ~ c_lessequals(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f2747,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X0) = X1
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_214 ),
    inference(resolution,[],[f2495,f1312]) ).

fof(f2495,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,X0)
        | X1 = X2
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0) )
    | ~ spl0_214 ),
    inference(avatar_component_clause,[],[f2494]) ).

fof(f26085,plain,
    ( spl0_927
    | ~ spl0_70
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2733,f2494,f1319,f26083]) ).

fof(f26083,plain,
    ( spl0_927
  <=> ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X1) = X0
        | ~ class_Orderings_Olinorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
        | ~ class_Orderings_Otop(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f2733,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X1) = X0
        | ~ class_Orderings_Olinorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
        | ~ class_Orderings_Otop(X1) )
    | ~ spl0_70
    | ~ spl0_214 ),
    inference(resolution,[],[f2495,f1320]) ).

fof(f26081,plain,
    ( spl0_926
    | ~ spl0_68
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2710,f2490,f1311,f26079]) ).

fof(f26079,plain,
    ( spl0_926
  <=> ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X0) = X1
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | ~ class_Orderings_Obot(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f2490,plain,
    ( spl0_213
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | X14 = X16
        | ~ c_lessequals(X14,X16,X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f2710,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Obot__class_Obot(X0) = X1
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(X0),X1,X0)
        | ~ class_Orderings_Obot(X0) )
    | ~ spl0_68
    | ~ spl0_213 ),
    inference(resolution,[],[f2491,f1312]) ).

fof(f2491,plain,
    ( ! [X0,X16,X14] :
        ( ~ c_lessequals(X14,X16,X0)
        | X14 = X16
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f2490]) ).

fof(f26077,plain,
    ( spl0_925
    | ~ spl0_70
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2696,f2490,f1319,f26075]) ).

fof(f26075,plain,
    ( spl0_925
  <=> ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X1) = X0
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
        | ~ class_Orderings_Otop(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f2696,plain,
    ( ! [X0,X1] :
        ( c_Orderings_Otop__class_Otop(X1) = X0
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_Orderings_Otop__class_Otop(X1),X1)
        | ~ class_Orderings_Otop(X1) )
    | ~ spl0_70
    | ~ spl0_213 ),
    inference(resolution,[],[f2491,f1320]) ).

fof(f26073,plain,
    ( spl0_924
    | ~ spl0_201
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2674,f2486,f2311,f26071]) ).

fof(f26071,plain,
    ( spl0_924
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X1),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f2486,plain,
    ( spl0_212
  <=> ! [X6,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f2674,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X1),X0)))
    | ~ spl0_201
    | ~ spl0_212 ),
    inference(resolution,[],[f2487,f2312]) ).

fof(f2487,plain,
    ( ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool))
    | ~ spl0_212 ),
    inference(avatar_component_clause,[],[f2486]) ).

fof(f26069,plain,
    ( spl0_923
    | ~ spl0_201
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f2667,f2482,f2311,f26067]) ).

fof(f26067,plain,
    ( spl0_923
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f2482,plain,
    ( spl0_211
  <=> ! [X6,X0,X8] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f2667,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),X1)))
    | ~ spl0_201
    | ~ spl0_211 ),
    inference(resolution,[],[f2483,f2312]) ).

fof(f2483,plain,
    ( ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool))
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f2482]) ).

fof(f26065,plain,
    ( spl0_922
    | ~ spl0_91
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2370,f2270,f1410,f26063]) ).

fof(f26063,plain,
    ( spl0_922
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f1410,plain,
    ( spl0_91
  <=> ! [X13,X4] :
        ( ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat)
        | c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f2370,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_91
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1411]) ).

fof(f1411,plain,
    ( ! [X4,X13] :
        ( c_lessequals(c_Suc(X13),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f1410]) ).

fof(f26061,plain,
    ( spl0_921
    | ~ spl0_98
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2369,f2270,f1438,f26059]) ).

fof(f26059,plain,
    ( spl0_921
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f2369,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_98
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1439]) ).

fof(f26057,plain,
    ( spl0_920
    | ~ spl0_87
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2361,f2270,f1394,f26055]) ).

fof(f26055,plain,
    ( spl0_920
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f1394,plain,
    ( spl0_87
  <=> ! [X13,X4] :
        ( ~ c_lessequals(X4,X13,tc_nat)
        | c_lessequals(X4,c_Suc(X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f2361,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,c_Suc(X2),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_87
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1395]) ).

fof(f1395,plain,
    ( ! [X4,X13] :
        ( c_lessequals(X4,c_Suc(X13),tc_nat)
        | ~ c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f1394]) ).

fof(f26053,plain,
    ( spl0_919
    | ~ spl0_126
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2215,f1952,f1632,f26051]) ).

fof(f26051,plain,
    ( spl0_919
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f1952,plain,
    ( spl0_169
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f2215,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_169 ),
    inference(resolution,[],[f1953,f1633]) ).

fof(f1953,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
        | ~ class_Lattices_Oupper__semilattice(X0) )
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f1952]) ).

fof(f26032,plain,
    ( spl0_918
    | ~ spl0_127
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2214,f1952,f1636,f26030]) ).

fof(f26030,plain,
    ( spl0_918
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f2214,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_169 ),
    inference(resolution,[],[f1953,f1637]) ).

fof(f26028,plain,
    ( spl0_917
    | ~ spl0_126
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2199,f1948,f1632,f26026]) ).

fof(f26026,plain,
    ( spl0_917
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f1948,plain,
    ( spl0_168
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f2199,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_168 ),
    inference(resolution,[],[f1949,f1633]) ).

fof(f1949,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
        | ~ class_Lattices_Oupper__semilattice(X0) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1948]) ).

fof(f26024,plain,
    ( spl0_916
    | ~ spl0_127
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2198,f1948,f1636,f26022]) ).

fof(f26022,plain,
    ( spl0_916
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f2198,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_168 ),
    inference(resolution,[],[f1949,f1637]) ).

fof(f26020,plain,
    ( spl0_915
    | ~ spl0_126
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f2183,f1944,f1632,f26018]) ).

fof(f26018,plain,
    ( spl0_915
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f1944,plain,
    ( spl0_167
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f2183,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_167 ),
    inference(resolution,[],[f1945,f1633]) ).

fof(f1945,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0)
        | ~ class_Lattices_Olattice(X0) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1944]) ).

fof(f26016,plain,
    ( spl0_914
    | ~ spl0_127
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f2182,f1944,f1636,f26014]) ).

fof(f26014,plain,
    ( spl0_914
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f2182,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_167 ),
    inference(resolution,[],[f1945,f1637]) ).

fof(f26012,plain,
    ( spl0_913
    | ~ spl0_126
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2163,f1940,f1632,f26010]) ).

fof(f26010,plain,
    ( spl0_913
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f2163,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_166 ),
    inference(resolution,[],[f1941,f1633]) ).

fof(f26008,plain,
    ( spl0_912
    | ~ spl0_127
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2162,f1940,f1636,f26006]) ).

fof(f26006,plain,
    ( spl0_912
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f2162,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_166 ),
    inference(resolution,[],[f1941,f1637]) ).

fof(f26004,plain,
    ( spl0_911
    | ~ spl0_126
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f2106,f1908,f1632,f26002]) ).

fof(f26002,plain,
    ( spl0_911
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f1908,plain,
    ( spl0_158
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f2106,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_158 ),
    inference(resolution,[],[f1909,f1633]) ).

fof(f1909,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0)
        | ~ class_Lattices_Olower__semilattice(X0) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1908]) ).

fof(f26000,plain,
    ( spl0_910
    | ~ spl0_127
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f2105,f1908,f1636,f25998]) ).

fof(f25998,plain,
    ( spl0_910
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f2105,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_158 ),
    inference(resolution,[],[f1909,f1637]) ).

fof(f25996,plain,
    ( spl0_909
    | ~ spl0_126
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f2102,f1904,f1632,f25994]) ).

fof(f25994,plain,
    ( spl0_909
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f1904,plain,
    ( spl0_157
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f2102,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_157 ),
    inference(resolution,[],[f1905,f1633]) ).

fof(f1905,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0)
        | ~ class_Lattices_Olower__semilattice(X0) )
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1904]) ).

fof(f25992,plain,
    ( spl0_908
    | ~ spl0_865
    | ~ spl0_883 ),
    inference(avatar_split_clause,[],[f25360,f25145,f24804,f25990]) ).

fof(f25360,plain,
    ( ! [X0] : c_lessequals(c_fequal(v_x,X0),v_U,tc_fun(X0,tc_bool))
    | ~ spl0_865
    | ~ spl0_883 ),
    inference(superposition,[],[f25146,f24805]) ).

fof(f25988,plain,
    ( spl0_907
    | ~ spl0_127
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f2101,f1904,f1636,f25986]) ).

fof(f25986,plain,
    ( spl0_907
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f2101,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_157 ),
    inference(resolution,[],[f1905,f1637]) ).

fof(f25984,plain,
    ( spl0_906
    | ~ spl0_126
    | ~ spl0_156 ),
    inference(avatar_split_clause,[],[f2090,f1900,f1632,f25982]) ).

fof(f25982,plain,
    ( spl0_906
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).

fof(f2090,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_156 ),
    inference(resolution,[],[f1901,f1633]) ).

fof(f25980,plain,
    ( spl0_905
    | ~ spl0_127
    | ~ spl0_156 ),
    inference(avatar_split_clause,[],[f2089,f1900,f1636,f25978]) ).

fof(f25978,plain,
    ( spl0_905
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f2089,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_156 ),
    inference(resolution,[],[f1901,f1637]) ).

fof(f25976,plain,
    ( spl0_904
    | ~ spl0_126
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f2086,f1896,f1632,f25974]) ).

fof(f25974,plain,
    ( spl0_904
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f2086,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_155 ),
    inference(resolution,[],[f1897,f1633]) ).

fof(f25972,plain,
    ( spl0_903
    | ~ spl0_127
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f2085,f1896,f1636,f25970]) ).

fof(f25970,plain,
    ( spl0_903
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f2085,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_127
    | ~ spl0_155 ),
    inference(resolution,[],[f1897,f1637]) ).

fof(f25968,plain,
    ( spl0_902
    | ~ spl0_93
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f2065,f1892,f1418,f25966]) ).

fof(f25966,plain,
    ( spl0_902
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
        | c_Suc(X1) = X0
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f2065,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
        | c_Suc(X1) = X0
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_93
    | ~ spl0_154 ),
    inference(resolution,[],[f1893,f1419]) ).

fof(f25964,plain,
    ( spl0_901
    | ~ spl0_91
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f2052,f1888,f1410,f25962]) ).

fof(f25962,plain,
    ( spl0_901
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_Suc(X1) = X0
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f2052,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
        | c_Suc(X1) = X0
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_91
    | ~ spl0_153 ),
    inference(resolution,[],[f1889,f1411]) ).

fof(f25960,plain,
    ( spl0_900
    | ~ spl0_55
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1597,f1506,f1259,f25958]) ).

fof(f25958,plain,
    ( spl0_900
  <=> ! [X2,X0,X1] :
        ( c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f1259,plain,
    ( spl0_55
  <=> ! [X55,X56] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X56)
        | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f1506,plain,
    ( spl0_115
  <=> ! [X0,X14] :
        ( c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1597,plain,
    ( ! [X2,X0,X1] :
        ( c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
    | ~ spl0_55
    | ~ spl0_115 ),
    inference(resolution,[],[f1507,f1260]) ).

fof(f1260,plain,
    ( ! [X56,X55] :
        ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X56) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1259]) ).

fof(f1507,plain,
    ( ! [X0,X14] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14 )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f1506]) ).

fof(f25956,plain,
    ( spl0_899
    | ~ spl0_55
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1595,f1502,f1259,f25954]) ).

fof(f25954,plain,
    ( spl0_899
  <=> ! [X2,X0,X1] :
        ( c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f1502,plain,
    ( spl0_114
  <=> ! [X0,X14] :
        ( c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1595,plain,
    ( ! [X2,X0,X1] :
        ( c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Complete__Lattice_Ocomplete__lattice(X2) )
    | ~ spl0_55
    | ~ spl0_114 ),
    inference(resolution,[],[f1503,f1260]) ).

fof(f1503,plain,
    ( ! [X0,X14] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f1502]) ).

fof(f25875,plain,
    ( spl0_898
    | ~ spl0_865
    | ~ spl0_875 ),
    inference(avatar_split_clause,[],[f25291,f25033,f24804,f25873]) ).

fof(f25873,plain,
    ( spl0_898
  <=> ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X1,v_U,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f25291,plain,
    ( ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X1,v_U,X0),X0))
    | ~ spl0_865
    | ~ spl0_875 ),
    inference(superposition,[],[f25034,f24805]) ).

fof(f25667,plain,
    ( spl0_897
    | ~ spl0_104
    | ~ spl0_344 ),
    inference(avatar_split_clause,[],[f5528,f4308,f1462,f25665]) ).

fof(f25665,plain,
    ( spl0_897
  <=> ! [X0,X3,X2,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f4308,plain,
    ( spl0_344
  <=> ! [X6,X0,X1,X8] :
        ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f5528,plain,
    ( ! [X2,X3,X0,X1] : c_lessequals(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,X0,X3),X3),tc_fun(X3,tc_bool))
    | ~ spl0_104
    | ~ spl0_344 ),
    inference(resolution,[],[f4309,f1463]) ).

fof(f4309,plain,
    ( ! [X0,X1,X8,X6] :
        ( ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool))
        | c_lessequals(X6,X8,tc_fun(X0,tc_bool)) )
    | ~ spl0_344 ),
    inference(avatar_component_clause,[],[f4308]) ).

fof(f25638,plain,
    ( spl0_896
    | ~ spl0_21
    | ~ spl0_43
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f5035,f4182,f1211,f1103,f25636]) ).

fof(f25636,plain,
    ( spl0_896
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(c_Suc(X0),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f1211,plain,
    ( spl0_43
  <=> ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f4182,plain,
    ( spl0_313
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X16,X14,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f5035,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(c_Suc(X0),X0,tc_nat) )
    | ~ spl0_43
    | ~ spl0_313 ),
    inference(resolution,[],[f4183,f1212]) ).

fof(f1212,plain,
    ( ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f1211]) ).

fof(f4183,plain,
    ( ! [X0,X16,X14] :
        ( ~ c_HOL_Oord__class_Oless(X16,X14,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f4182]) ).

fof(f25599,plain,
    ( ~ spl0_19
    | spl0_895
    | ~ spl0_44
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f4518,f4075,f1215,f25597,f1093]) ).

fof(f25597,plain,
    ( spl0_895
  <=> ! [X0,X1] : ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f4075,plain,
    ( spl0_287
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X19,X1,X0)
        | c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f4518,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X0,tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_44
    | ~ spl0_287 ),
    inference(resolution,[],[f4076,f1216]) ).

fof(f4076,plain,
    ( ! [X2,X0,X1,X19] :
        ( c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
        | ~ c_lessequals(X19,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f4075]) ).

fof(f25561,plain,
    ( ~ spl0_19
    | spl0_894
    | ~ spl0_44
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f4470,f4071,f1215,f25559,f1093]) ).

fof(f25559,plain,
    ( spl0_894
  <=> ! [X0,X1] : ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f4071,plain,
    ( spl0_286
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X1,X16,X0)
        | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f4470,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1)),X1,tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_44
    | ~ spl0_286 ),
    inference(resolution,[],[f4072,f1216]) ).

fof(f4072,plain,
    ( ! [X0,X1,X16,X14] :
        ( c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0)
        | ~ c_lessequals(X1,X16,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f4071]) ).

fof(f25557,plain,
    ( spl0_893
    | ~ spl0_110
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2920,f2584,f1486,f25555]) ).

fof(f25555,plain,
    ( spl0_893
  <=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Ovimage(X0,c_fequal(hAPP(X0,X1),X2),X3,X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f2920,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Ovimage(X0,c_fequal(hAPP(X0,X1),X2),X3,X2),X1))
    | ~ spl0_110
    | ~ spl0_235 ),
    inference(resolution,[],[f2585,f1487]) ).

fof(f25553,plain,
    ( spl0_892
    | ~ spl0_110
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f2914,f2572,f1486,f25551]) ).

fof(f25551,plain,
    ( spl0_892
  <=> ! [X2,X0,X1,X3] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f2572,plain,
    ( spl0_232
  <=> ! [X0,X14,X16,X8] :
        ( ~ hBOOL(c_in(X14,X8,X0))
        | hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f2914,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | hBOOL(hAPP(c_Set_Oinsert(X3,X1,X2),X0)) )
    | ~ spl0_110
    | ~ spl0_232 ),
    inference(resolution,[],[f2573,f1487]) ).

fof(f2573,plain,
    ( ! [X0,X8,X16,X14] :
        ( hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0))
        | ~ hBOOL(c_in(X14,X8,X0)) )
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2572]) ).

fof(f25549,plain,
    ( spl0_891
    | ~ spl0_77
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2348,f2270,f1349,f25547]) ).

fof(f25547,plain,
    ( spl0_891
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f2348,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_77
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1350]) ).

fof(f25488,plain,
    ( spl0_890
    | ~ spl0_19
    | ~ spl0_86
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2118,f1916,f1390,f1093,f25486]) ).

fof(f25486,plain,
    ( spl0_890
  <=> ! [X0,X1] : c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),c_Suc(X0)),X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f1390,plain,
    ( spl0_86
  <=> ! [X13,X4] :
        ( c_lessequals(X4,X13,tc_nat)
        | ~ c_lessequals(c_Suc(X4),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1916,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f2118,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_nat)
        | c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),c_Suc(X0)),X1),tc_nat) )
    | ~ spl0_86
    | ~ spl0_160 ),
    inference(resolution,[],[f1917,f1391]) ).

fof(f1391,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(c_Suc(X4),X13,tc_nat)
        | c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f1390]) ).

fof(f1917,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1916]) ).

fof(f25427,plain,
    ( spl0_889
    | ~ spl0_19
    | ~ spl0_86
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f2111,f1912,f1390,f1093,f25425]) ).

fof(f25425,plain,
    ( spl0_889
  <=> ! [X0,X1] : c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f1912,plain,
    ( spl0_159
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f2111,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(tc_nat)
        | c_lessequals(X0,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X1),c_Suc(X0)),tc_nat) )
    | ~ spl0_86
    | ~ spl0_159 ),
    inference(resolution,[],[f1913,f1391]) ).

fof(f1913,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1912]) ).

fof(f25423,plain,
    ( spl0_888
    | ~ spl0_56
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1831,f1668,f1263,f25421]) ).

fof(f25421,plain,
    ( spl0_888
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
        | ~ class_Lattices_Olattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f1668,plain,
    ( spl0_135
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1831,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,X1)),X2),X2) = X2
        | ~ class_Lattices_Olattice(X1) )
    | ~ spl0_56
    | ~ spl0_135 ),
    inference(resolution,[],[f1669,f1264]) ).

fof(f1669,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1668]) ).

fof(f25419,plain,
    ( spl0_887
    | ~ spl0_861
    | ~ spl0_865 ),
    inference(avatar_split_clause,[],[f24992,f24804,f23922,f25417]) ).

fof(f25417,plain,
    ( spl0_887
  <=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_U,X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f24992,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,v_U,X0),v_x))
    | ~ spl0_861
    | ~ spl0_865 ),
    inference(superposition,[],[f23923,f24805]) ).

fof(f25415,plain,
    ( spl0_886
    | ~ spl0_57
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1738,f1620,f1267,f25413]) ).

fof(f25413,plain,
    ( spl0_886
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
        | ~ class_Lattices_Olattice(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f1620,plain,
    ( spl0_123
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1738,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,X1)),X2),X2) = X2
        | ~ class_Lattices_Olattice(X1) )
    | ~ spl0_57
    | ~ spl0_123 ),
    inference(resolution,[],[f1621,f1268]) ).

fof(f1621,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1620]) ).

fof(f25372,plain,
    ( spl0_885
    | ~ spl0_1
    | ~ spl0_749 ),
    inference(avatar_split_clause,[],[f20568,f20550,f1003,f25370]) ).

fof(f25370,plain,
    ( spl0_885
  <=> ! [X2,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(X0,tc_Com_Opname)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X0,tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f1003,plain,
    ( spl0_1
  <=> c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f20550,plain,
    ( spl0_749
  <=> ! [X21,X20,X0,X6,X8] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f20568,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(X0,tc_Com_Opname)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X1)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X0,tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,X1)) )
    | ~ spl0_1
    | ~ spl0_749 ),
    inference(resolution,[],[f20551,f1005]) ).

fof(f1005,plain,
    ( c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f1003]) ).

fof(f20551,plain,
    ( ! [X21,X0,X8,X6,X20] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) )
    | ~ spl0_749 ),
    inference(avatar_component_clause,[],[f20550]) ).

fof(f25151,plain,
    ( spl0_884
    | ~ spl0_124
    | ~ spl0_556 ),
    inference(avatar_split_clause,[],[f11260,f11185,f1624,f25149]) ).

fof(f25149,plain,
    ( spl0_884
  <=> ! [X2,X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
        | ~ hBOOL(c_in(X2,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f11185,plain,
    ( spl0_556
  <=> ! [X0,X8,X6,X1] :
        ( ~ hBOOL(c_in(X1,X8,X0))
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f11260,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
        | ~ hBOOL(c_in(X2,X1,X0)) )
    | ~ spl0_124
    | ~ spl0_556 ),
    inference(duplicate_literal_removal,[],[f11249]) ).

fof(f11249,plain,
    ( ! [X2,X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X1
        | ~ hBOOL(c_in(X2,X1,X0))
        | ~ hBOOL(c_in(X2,X1,X0)) )
    | ~ spl0_124
    | ~ spl0_556 ),
    inference(superposition,[],[f11186,f1625]) ).

fof(f11186,plain,
    ( ! [X0,X1,X8,X6] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ hBOOL(c_in(X1,X8,X0)) )
    | ~ spl0_556 ),
    inference(avatar_component_clause,[],[f11185]) ).

fof(f25147,plain,
    ( spl0_883
    | ~ spl0_220
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f5938,f4368,f2518,f25145]) ).

fof(f5938,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_fequal(X1,X0),c_Set_Oinsert(X1,X2,X0),tc_fun(X0,tc_bool))
    | ~ spl0_220
    | ~ spl0_358 ),
    inference(superposition,[],[f2519,f4369]) ).

fof(f25123,plain,
    ( ~ spl0_14
    | spl0_882
    | ~ spl0_40
    | ~ spl0_116
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f5375,f4256,f1513,f1199,f25121,f1068]) ).

fof(f25121,plain,
    ( spl0_882
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f1199,plain,
    ( spl0_40
  <=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f5375,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X1,tc_nat)
        | ~ class_Lattices_Oupper__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_116
    | ~ spl0_331 ),
    inference(forward_demodulation,[],[f5349,f1515]) ).

fof(f5349,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1),X1,tc_nat)
        | ~ class_Lattices_Oupper__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_331 ),
    inference(resolution,[],[f4257,f1200]) ).

fof(f1200,plain,
    ( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f1199]) ).

fof(f25095,plain,
    ( ~ spl0_14
    | spl0_881
    | ~ spl0_40
    | ~ spl0_116
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f5343,f4252,f1513,f1199,f25093,f1068]) ).

fof(f25093,plain,
    ( spl0_881
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).

fof(f5343,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X1),X0,tc_nat)
        | ~ class_Lattices_Oupper__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_116
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f5317,f1515]) ).

fof(f5317,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X0),X1),X0,tc_nat)
        | ~ class_Lattices_Oupper__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_330 ),
    inference(resolution,[],[f4253,f1200]) ).

fof(f25091,plain,
    ( spl0_880
    | ~ spl0_48
    | ~ spl0_301 ),
    inference(avatar_split_clause,[],[f4810,f4134,f1231,f25089]) ).

fof(f25089,plain,
    ( spl0_880
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f4134,plain,
    ( spl0_301
  <=> ! [X0,X28,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X28,X3,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f4810,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0) )
    | ~ spl0_48
    | ~ spl0_301 ),
    inference(duplicate_literal_removal,[],[f4786]) ).

fof(f4786,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_48
    | ~ spl0_301 ),
    inference(resolution,[],[f4135,f1232]) ).

fof(f4135,plain,
    ( ! [X28,X3,X0] :
        ( c_HOL_Oord__class_Oless(X28,X3,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) )
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f4134]) ).

fof(f25087,plain,
    ( spl0_879
    | ~ spl0_82
    | ~ spl0_865 ),
    inference(avatar_split_clause,[],[f24956,f24804,f1369,f25085]) ).

fof(f25085,plain,
    ( spl0_879
  <=> ! [X0] : hBOOL(c_in(v_x,v_U,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f24956,plain,
    ( ! [X0] : hBOOL(c_in(v_x,v_U,X0))
    | ~ spl0_82
    | ~ spl0_865 ),
    inference(superposition,[],[f1370,f24805]) ).

fof(f25083,plain,
    ( spl0_878
    | ~ spl0_48
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f4781,f4123,f1231,f25081]) ).

fof(f25081,plain,
    ( spl0_878
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f4123,plain,
    ( spl0_299
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f4781,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0) )
    | ~ spl0_48
    | ~ spl0_299 ),
    inference(duplicate_literal_removal,[],[f4757]) ).

fof(f4757,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_48
    | ~ spl0_299 ),
    inference(resolution,[],[f4124,f1232]) ).

fof(f4124,plain,
    ( ! [X0,X16,X14] :
        ( c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) )
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f4123]) ).

fof(f25059,plain,
    ( ~ spl0_15
    | spl0_877
    | ~ spl0_40
    | ~ spl0_242
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f4744,f4119,f2943,f1199,f25057,f1073]) ).

fof(f25057,plain,
    ( spl0_877
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f4744,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X1),tc_nat)
        | ~ class_Lattices_Olower__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_242
    | ~ spl0_298 ),
    inference(forward_demodulation,[],[f4719,f2945]) ).

fof(f4719,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X1),tc_nat)
        | ~ class_Lattices_Olower__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_298 ),
    inference(resolution,[],[f4120,f1200]) ).

fof(f25039,plain,
    ( ~ spl0_15
    | spl0_876
    | ~ spl0_40
    | ~ spl0_242
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f4708,f4115,f2943,f1199,f25037,f1073]) ).

fof(f25037,plain,
    ( spl0_876
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f4708,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X1),X0),tc_nat)
        | ~ class_Lattices_Olower__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_242
    | ~ spl0_297 ),
    inference(forward_demodulation,[],[f4683,f2945]) ).

fof(f4683,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),X0),tc_nat)
        | ~ class_Lattices_Olower__semilattice(tc_nat) )
    | ~ spl0_40
    | ~ spl0_297 ),
    inference(resolution,[],[f4116,f1200]) ).

fof(f25035,plain,
    ( spl0_875
    | ~ spl0_104
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f3736,f3037,f1462,f25033]) ).

fof(f3736,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3))
    | ~ spl0_104
    | ~ spl0_264 ),
    inference(resolution,[],[f3038,f1463]) ).

fof(f25012,plain,
    ( ~ spl0_37
    | spl0_874
    | ~ spl0_104
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f3555,f2996,f1462,f25010,f1183]) ).

fof(f25010,plain,
    ( spl0_874
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f3555,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Set_Oinsert(X0,X1,X2),X1,tc_fun(X2,tc_bool))
        | ~ class_HOL_Oord(tc_bool) )
    | ~ spl0_104
    | ~ spl0_254 ),
    inference(resolution,[],[f2997,f1463]) ).

fof(f24998,plain,
    ( ~ spl0_37
    | spl0_873
    | ~ spl0_105
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f3553,f2996,f1466,f24996,f1183]) ).

fof(f24996,plain,
    ( spl0_873
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f3553,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1,tc_fun(X0,tc_bool))
        | ~ class_HOL_Oord(tc_bool) )
    | ~ spl0_105
    | ~ spl0_254 ),
    inference(resolution,[],[f2997,f1467]) ).

fof(f24951,plain,
    ( spl0_872
    | ~ spl0_165
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2445,f2311,f1936,f24949]) ).

fof(f24949,plain,
    ( spl0_872
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(t_a,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f2445,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(t_a,tc_bool))))
    | ~ spl0_165
    | ~ spl0_201 ),
    inference(resolution,[],[f2312,f1937]) ).

fof(f24908,plain,
    ( ~ spl0_22
    | spl0_871
    | ~ spl0_68
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2368,f2270,f1311,f24906,f1108]) ).

fof(f1108,plain,
    ( spl0_22
  <=> class_Orderings_Obot(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f24906,plain,
    ( spl0_871
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f2368,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
        | c_lessequals(X0,X1,tc_nat)
        | ~ class_Orderings_Obot(tc_nat) )
    | ~ spl0_68
    | ~ spl0_191 ),
    inference(resolution,[],[f2271,f1312]) ).

fof(f24904,plain,
    ( spl0_870
    | ~ spl0_126
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2130,f1924,f1632,f24902]) ).

fof(f24902,plain,
    ( spl0_870
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f1924,plain,
    ( spl0_162
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f2130,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0) )
    | ~ spl0_126
    | ~ spl0_162 ),
    inference(duplicate_literal_removal,[],[f2128]) ).

fof(f2128,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_162 ),
    inference(resolution,[],[f1925,f1633]) ).

fof(f1925,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1924]) ).

fof(f24900,plain,
    ( spl0_869
    | ~ spl0_126
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f2126,f1920,f1632,f24898]) ).

fof(f24898,plain,
    ( spl0_869
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f1920,plain,
    ( spl0_161
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f2126,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) )
    | ~ spl0_126
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f2124]) ).

fof(f2124,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_161 ),
    inference(resolution,[],[f1921,f1633]) ).

fof(f1921,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1920]) ).

fof(f24896,plain,
    ( spl0_868
    | ~ spl0_126
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2122,f1916,f1632,f24894]) ).

fof(f24894,plain,
    ( spl0_868
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f2122,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0) )
    | ~ spl0_126
    | ~ spl0_160 ),
    inference(duplicate_literal_removal,[],[f2120]) ).

fof(f2120,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_160 ),
    inference(resolution,[],[f1917,f1633]) ).

fof(f24892,plain,
    ( spl0_867
    | ~ spl0_126
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f2115,f1912,f1632,f24890]) ).

fof(f24890,plain,
    ( spl0_867
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f2115,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0) )
    | ~ spl0_126
    | ~ spl0_159 ),
    inference(duplicate_literal_removal,[],[f2113]) ).

fof(f2113,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_126
    | ~ spl0_159 ),
    inference(resolution,[],[f1913,f1633]) ).

fof(f24849,plain,
    ( ~ spl0_22
    | spl0_866
    | ~ spl0_68
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f2050,f1888,f1311,f24847,f1108]) ).

fof(f24847,plain,
    ( spl0_866
  <=> ! [X0] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
        | c_Orderings_Obot__class_Obot(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f2050,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
        | c_Orderings_Obot__class_Obot(tc_nat) = X0
        | ~ class_Orderings_Obot(tc_nat) )
    | ~ spl0_68
    | ~ spl0_153 ),
    inference(resolution,[],[f1889,f1312]) ).

fof(f24806,plain,
    ( spl0_865
    | ~ spl0_118
    | ~ spl0_852 ),
    inference(avatar_split_clause,[],[f24436,f23886,f1599,f24804]) ).

fof(f1599,plain,
    ( spl0_118
  <=> hBOOL(hAPP(v_U,v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f24436,plain,
    ( ! [X0] : v_U = c_Set_Oinsert(v_x,v_U,X0)
    | ~ spl0_118
    | ~ spl0_852 ),
    inference(resolution,[],[f23887,f1601]) ).

fof(f1601,plain,
    ( hBOOL(hAPP(v_U,v_x))
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f1599]) ).

fof(f24048,plain,
    ( spl0_864
    | ~ spl0_496
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f9862,f9437,f9425,f24046]) ).

fof(f24046,plain,
    ( spl0_864
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f9425,plain,
    ( spl0_496
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f9437,plain,
    ( spl0_499
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f9862,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) )
    | ~ spl0_496
    | ~ spl0_499 ),
    inference(duplicate_literal_removal,[],[f9842]) ).

fof(f9842,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_496
    | ~ spl0_499 ),
    inference(resolution,[],[f9438,f9426]) ).

fof(f9426,plain,
    ( ! [X0,X16,X14,X15] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_496 ),
    inference(avatar_component_clause,[],[f9425]) ).

fof(f9438,plain,
    ( ! [X0,X16,X14,X15] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_499 ),
    inference(avatar_component_clause,[],[f9437]) ).

fof(f24044,plain,
    ( spl0_863
    | ~ spl0_487
    | ~ spl0_488 ),
    inference(avatar_split_clause,[],[f9655,f9393,f9389,f24042]) ).

fof(f24042,plain,
    ( spl0_863
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f9389,plain,
    ( spl0_487
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X14,X16,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f9393,plain,
    ( spl0_488
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f9655,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1) )
    | ~ spl0_487
    | ~ spl0_488 ),
    inference(duplicate_literal_removal,[],[f9610]) ).

fof(f9610,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_487
    | ~ spl0_488 ),
    inference(resolution,[],[f9394,f9390]) ).

fof(f9390,plain,
    ( ! [X0,X16,X14,X15] :
        ( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0)
        | c_lessequals(X14,X16,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_487 ),
    inference(avatar_component_clause,[],[f9389]) ).

fof(f9394,plain,
    ( ! [X0,X16,X14,X15] :
        ( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0)
        | ~ c_lessequals(X14,X16,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_488 ),
    inference(avatar_component_clause,[],[f9393]) ).

fof(f23930,plain,
    ( spl0_862
    | ~ spl0_37
    | ~ spl0_51
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6256,f5988,f1243,f1183,f23928]) ).

fof(f23928,plain,
    ( spl0_862
  <=> ! [X0,X1] : c_lessequals(hAPP(X0,X1),hAPP(X0,X1),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f6256,plain,
    ( ! [X0,X1] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(X0,X1),hAPP(X0,X1),tc_bool) )
    | ~ spl0_51
    | ~ spl0_369 ),
    inference(resolution,[],[f5989,f1244]) ).

fof(f23924,plain,
    ( spl0_861
    | ~ spl0_72
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f5898,f4364,f1327,f23922]) ).

fof(f5898,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X0))
    | ~ spl0_72
    | ~ spl0_357 ),
    inference(superposition,[],[f1328,f4365]) ).

fof(f23920,plain,
    ( spl0_860
    | ~ spl0_46
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f5885,f4360,f1223,f23918]) ).

fof(f23918,plain,
    ( spl0_860
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
        | c_Finite__Set_Ofinite(X1,X2)
        | ~ class_Finite__Set_Ofinite_Ofinite(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f1223,plain,
    ( spl0_46
  <=> ! [X6,X0] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X0)
        | c_Finite__Set_Ofinite(X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f4360,plain,
    ( spl0_356
  <=> ! [X20,X0,X6,X25] :
        ( c_Finite__Set_Ofinite(X6,X20)
        | ~ c_Fun_Oinj__on(X25,X6,X20,X0)
        | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f5885,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Fun_Oinj__on(X0,X1,X2,X3)
        | c_Finite__Set_Ofinite(X1,X2)
        | ~ class_Finite__Set_Ofinite_Ofinite(X3) )
    | ~ spl0_46
    | ~ spl0_356 ),
    inference(resolution,[],[f4361,f1224]) ).

fof(f1224,plain,
    ( ! [X0,X6] :
        ( c_Finite__Set_Ofinite(X6,X0)
        | ~ class_Finite__Set_Ofinite_Ofinite(X0) )
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f1223]) ).

fof(f4361,plain,
    ( ! [X0,X6,X25,X20] :
        ( ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0)
        | ~ c_Fun_Oinj__on(X25,X6,X20,X0)
        | c_Finite__Set_Ofinite(X6,X20) )
    | ~ spl0_356 ),
    inference(avatar_component_clause,[],[f4360]) ).

fof(f23916,plain,
    ( ~ spl0_858
    | spl0_859
    | ~ spl0_44
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2898,f2568,f1215,f23914,f23910]) ).

fof(f23910,plain,
    ( spl0_858
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f23914,plain,
    ( spl0_859
  <=> ! [X0] : ~ hBOOL(c_in(c_Suc(c_Complete__Lattice_OSup__class_OSup(X0,tc_nat)),X0,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f2898,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Suc(c_Complete__Lattice_OSup__class_OSup(X0,tc_nat)),X0,tc_nat))
        | ~ class_Complete__Lattice_Ocomplete__lattice(tc_nat) )
    | ~ spl0_44
    | ~ spl0_231 ),
    inference(resolution,[],[f2569,f1216]) ).

fof(f23908,plain,
    ( spl0_857
    | ~ spl0_186
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2450,f2329,f2032,f23906]) ).

fof(f23906,plain,
    ( spl0_857
  <=> ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oinsert(X0,c_fequal(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f2329,plain,
    ( spl0_204
  <=> ! [X6,X0,X1] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f2450,plain,
    ( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oinsert(X0,c_fequal(X0,X1),X1)
    | ~ spl0_186
    | ~ spl0_204 ),
    inference(superposition,[],[f2330,f2033]) ).

fof(f2330,plain,
    ( ! [X0,X1,X6] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0)
    | ~ spl0_204 ),
    inference(avatar_component_clause,[],[f2329]) ).

fof(f23904,plain,
    ( spl0_856
    | ~ spl0_29
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2448,f2319,f1143,f23902]) ).

fof(f23902,plain,
    ( spl0_856
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f1143,plain,
    ( spl0_29
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f2319,plain,
    ( spl0_203
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f2448,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0)
    | ~ spl0_29
    | ~ spl0_203 ),
    inference(resolution,[],[f2320,f1145]) ).

fof(f1145,plain,
    ( class_Lattices_Obounded__lattice(tc_bool)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f1143]) ).

fof(f2320,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) )
    | ~ spl0_203 ),
    inference(avatar_component_clause,[],[f2319]) ).

fof(f23900,plain,
    ( spl0_855
    | ~ spl0_29
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f2446,f2315,f1143,f23898]) ).

fof(f23898,plain,
    ( spl0_855
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f2315,plain,
    ( spl0_202
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f2446,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool))
    | ~ spl0_29
    | ~ spl0_202 ),
    inference(resolution,[],[f2316,f1145]) ).

fof(f2316,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f2315]) ).

fof(f23896,plain,
    ( spl0_854
    | ~ spl0_29
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2384,f2295,f1143,f23894]) ).

fof(f23894,plain,
    ( spl0_854
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f2295,plain,
    ( spl0_197
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f2384,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool))
    | ~ spl0_29
    | ~ spl0_197 ),
    inference(resolution,[],[f2296,f1145]) ).

fof(f2296,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f2295]) ).

fof(f23892,plain,
    ( spl0_853
    | ~ spl0_29
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f2382,f2291,f1143,f23890]) ).

fof(f23890,plain,
    ( spl0_853
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f2291,plain,
    ( spl0_196
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f2382,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0)
    | ~ spl0_29
    | ~ spl0_196 ),
    inference(resolution,[],[f2292,f1145]) ).

fof(f2292,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) )
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f2291]) ).

fof(f23888,plain,
    ( spl0_852
    | ~ spl0_109
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2253,f2028,f1482,f23886]) ).

fof(f2028,plain,
    ( spl0_185
  <=> ! [X6,X0,X14] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | c_Set_Oinsert(X14,X6,X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f2253,plain,
    ( ! [X2,X0,X1] :
        ( c_Set_Oinsert(X0,X1,X2) = X1
        | ~ hBOOL(hAPP(X1,X0)) )
    | ~ spl0_109
    | ~ spl0_185 ),
    inference(resolution,[],[f2029,f1483]) ).

fof(f2029,plain,
    ( ! [X0,X6,X14] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | c_Set_Oinsert(X14,X6,X0) = X6 )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f2028]) ).

fof(f23884,plain,
    ( spl0_851
    | ~ spl0_789
    | ~ spl0_809 ),
    inference(avatar_split_clause,[],[f23058,f22632,f22317,f23882]) ).

fof(f23882,plain,
    ( spl0_851
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f22317,plain,
    ( spl0_789
  <=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f22632,plain,
    ( spl0_809
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f23058,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x))
    | ~ spl0_789
    | ~ spl0_809 ),
    inference(superposition,[],[f22318,f22633]) ).

fof(f22633,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
    | ~ spl0_809 ),
    inference(avatar_component_clause,[],[f22632]) ).

fof(f22318,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x)))
    | ~ spl0_789 ),
    inference(avatar_component_clause,[],[f22317]) ).

fof(f23880,plain,
    ( spl0_850
    | ~ spl0_126
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1864,f1691,f1632,f23878]) ).

fof(f23878,plain,
    ( spl0_850
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f1864,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2) )
    | ~ spl0_126
    | ~ spl0_140 ),
    inference(duplicate_literal_removal,[],[f1853]) ).

fof(f1853,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_126
    | ~ spl0_140 ),
    inference(resolution,[],[f1692,f1633]) ).

fof(f23876,plain,
    ( spl0_849
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1823,f1664,f1345,f23874]) ).

fof(f23874,plain,
    ( spl0_849
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f1345,plain,
    ( spl0_76
  <=> ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1823,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) )
    | ~ spl0_76
    | ~ spl0_134 ),
    inference(resolution,[],[f1665,f1346]) ).

fof(f1346,plain,
    ( ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f1345]) ).

fof(f23872,plain,
    ( spl0_848
    | ~ spl0_77
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1784,f1640,f1349,f23870]) ).

fof(f23870,plain,
    ( spl0_848
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f1640,plain,
    ( spl0_128
  <=> ! [X13,X4] :
        ( c_lessequals(X13,X4,tc_nat)
        | ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1784,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) )
    | ~ spl0_77
    | ~ spl0_128 ),
    inference(resolution,[],[f1641,f1350]) ).

fof(f1641,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat)
        | c_lessequals(X13,X4,tc_nat) )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1640]) ).

fof(f23868,plain,
    ( spl0_847
    | ~ spl0_88
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f1581,f1446,f1398,f23866]) ).

fof(f23866,plain,
    ( spl0_847
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f1398,plain,
    ( spl0_88
  <=> ! [X13,X4] :
        ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f1581,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_88
    | ~ spl0_100 ),
    inference(resolution,[],[f1447,f1399]) ).

fof(f1399,plain,
    ( ! [X4,X13] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat)
        | c_HOL_Oord__class_Oless(X4,X13,tc_nat) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f1398]) ).

fof(f23864,plain,
    ( spl0_846
    | ~ spl0_87
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1566,f1434,f1394,f23862]) ).

fof(f23862,plain,
    ( spl0_846
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
        | ~ c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f1434,plain,
    ( spl0_97
  <=> ! [X13,X4] :
        ( ~ c_lessequals(X4,X13,tc_nat)
        | ~ c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1566,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
        | ~ c_lessequals(c_Suc(X1),X0,tc_nat) )
    | ~ spl0_87
    | ~ spl0_97 ),
    inference(resolution,[],[f1435,f1395]) ).

fof(f1435,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(c_Suc(X13),X4,tc_nat)
        | ~ c_lessequals(X4,X13,tc_nat) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1434]) ).

fof(f23860,plain,
    ( spl0_845
    | ~ spl0_87
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f1540,f1406,f1394,f23858]) ).

fof(f23858,plain,
    ( spl0_845
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f1406,plain,
    ( spl0_90
  <=> ! [X13,X4] :
        ( c_HOL_Oord__class_Oless(X13,X4,tc_nat)
        | ~ c_lessequals(c_Suc(X13),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f1540,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_lessequals(c_Suc(X0),X1,tc_nat) )
    | ~ spl0_87
    | ~ spl0_90 ),
    inference(resolution,[],[f1407,f1395]) ).

fof(f1407,plain,
    ( ! [X4,X13] :
        ( ~ c_lessequals(c_Suc(X13),X4,tc_nat)
        | c_HOL_Oord__class_Oless(X13,X4,tc_nat) )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f1406]) ).

fof(f23856,plain,
    ( spl0_844
    | ~ spl0_88
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f1532,f1402,f1398,f23854]) ).

fof(f23854,plain,
    ( spl0_844
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f1532,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
    | ~ spl0_88
    | ~ spl0_89 ),
    inference(resolution,[],[f1403,f1399]) ).

fof(f23852,plain,
    ( spl0_843
    | ~ spl0_86
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f1525,f1394,f1390,f23850]) ).

fof(f23850,plain,
    ( spl0_843
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f1525,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
        | c_lessequals(X0,c_Suc(X1),tc_nat) )
    | ~ spl0_86
    | ~ spl0_87 ),
    inference(resolution,[],[f1395,f1391]) ).

fof(f23846,plain,
    ( spl0_842
    | ~ spl0_789
    | ~ spl0_808 ),
    inference(avatar_split_clause,[],[f23002,f22628,f22317,f23844]) ).

fof(f23844,plain,
    ( spl0_842
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f22628,plain,
    ( spl0_808
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f23002,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),v_x),v_U,tc_Com_Opname,X0),v_x))
    | ~ spl0_789
    | ~ spl0_808 ),
    inference(superposition,[],[f22318,f22629]) ).

fof(f22629,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
    | ~ spl0_808 ),
    inference(avatar_component_clause,[],[f22628]) ).

fof(f23710,plain,
    ( spl0_841
    | ~ spl0_789
    | ~ spl0_806 ),
    inference(avatar_split_clause,[],[f22949,f22619,f22317,f23708]) ).

fof(f23708,plain,
    ( spl0_841
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omax(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f22619,plain,
    ( spl0_806
  <=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f22949,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omax(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x))
    | ~ spl0_789
    | ~ spl0_806 ),
    inference(superposition,[],[f22318,f22620]) ).

fof(f22620,plain,
    ( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0
    | ~ spl0_806 ),
    inference(avatar_component_clause,[],[f22619]) ).

fof(f23368,plain,
    ( spl0_840
    | ~ spl0_789
    | ~ spl0_805 ),
    inference(avatar_split_clause,[],[f22896,f22615,f22317,f23366]) ).

fof(f23366,plain,
    ( spl0_840
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omin(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f22615,plain,
    ( spl0_805
  <=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f22896,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oimage(hAPP(c_Orderings_Oord__class_Omin(tc_nat),v_x),v_U,tc_Com_Opname,X0),v_x))
    | ~ spl0_789
    | ~ spl0_805 ),
    inference(superposition,[],[f22318,f22616]) ).

fof(f22616,plain,
    ( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0
    | ~ spl0_805 ),
    inference(avatar_component_clause,[],[f22615]) ).

fof(f23312,plain,
    ( spl0_839
    | ~ spl0_46
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f3681,f3012,f1223,f23310]) ).

fof(f23310,plain,
    ( spl0_839
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Fun_Obij(X0,X1,X2)
        | c_Finite__Set_Ofinite(X3,X2)
        | ~ class_Finite__Set_Ofinite_Ofinite(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f3012,plain,
    ( spl0_258
  <=> ! [X35,X20,X0,X33] :
        ( c_Finite__Set_Ofinite(X33,X20)
        | ~ c_Fun_Obij(X35,X0,X20)
        | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f3681,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Fun_Obij(X0,X1,X2)
        | c_Finite__Set_Ofinite(X3,X2)
        | ~ class_Finite__Set_Ofinite_Ofinite(X1) )
    | ~ spl0_46
    | ~ spl0_258 ),
    inference(resolution,[],[f3013,f1224]) ).

fof(f3013,plain,
    ( ! [X0,X35,X33,X20] :
        ( ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0)
        | ~ c_Fun_Obij(X35,X0,X20)
        | c_Finite__Set_Ofinite(X33,X20) )
    | ~ spl0_258 ),
    inference(avatar_component_clause,[],[f3012]) ).

fof(f23308,plain,
    ( spl0_838
    | ~ spl0_103
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2443,f2311,f1458,f23306]) ).

fof(f23306,plain,
    ( spl0_838
  <=> ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f2443,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))
    | ~ spl0_103
    | ~ spl0_201 ),
    inference(resolution,[],[f2312,f1459]) ).

fof(f23304,plain,
    ( spl0_837
    | ~ spl0_104
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2436,f2311,f1462,f23302]) ).

fof(f23302,plain,
    ( spl0_837
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(X0,X1,t_a)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f2436,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(v_P,c_Set_Oinsert(X0,X1,t_a)),X1))
    | ~ spl0_104
    | ~ spl0_201 ),
    inference(resolution,[],[f2312,f1463]) ).

fof(f23300,plain,
    ( spl0_836
    | ~ spl0_105
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2434,f2311,f1466,f23298]) ).

fof(f23298,plain,
    ( spl0_836
  <=> ! [X0] : hBOOL(hAPP(hAPP(v_P,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f2434,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(v_P,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))),X0))
    | ~ spl0_105
    | ~ spl0_201 ),
    inference(resolution,[],[f2312,f1467]) ).

fof(f23296,plain,
    ( spl0_835
    | ~ spl0_105
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f2409,f2307,f1466,f23294]) ).

fof(f23294,plain,
    ( spl0_835
  <=> ! [X0,X1] :
        ( c_Finite__Set_Ofinite(X0,X1)
        | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f2409,plain,
    ( ! [X0,X1] :
        ( c_Finite__Set_Ofinite(X0,X1)
        | ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) )
    | ~ spl0_105
    | ~ spl0_200 ),
    inference(resolution,[],[f2308,f1467]) ).

fof(f23292,plain,
    ( spl0_834
    | ~ spl0_35
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2248,f2020,f1173,f23289]) ).

fof(f23289,plain,
    ( spl0_834
  <=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f1173,plain,
    ( spl0_35
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f2248,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_35
    | ~ spl0_183 ),
    inference(resolution,[],[f2021,f1175]) ).

fof(f1175,plain,
    ( class_Orderings_Obot(tc_bool)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f1173]) ).

fof(f23287,plain,
    ( spl0_833
    | ~ spl0_22
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2247,f2020,f1108,f23284]) ).

fof(f23284,plain,
    ( spl0_833
  <=> c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f2247,plain,
    ( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x)
    | ~ spl0_22
    | ~ spl0_183 ),
    inference(resolution,[],[f2021,f1110]) ).

fof(f1110,plain,
    ( class_Orderings_Obot(tc_nat)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f1108]) ).

fof(f23282,plain,
    ( spl0_832
    | ~ spl0_25
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f2245,f1998,f1123,f23279]) ).

fof(f23279,plain,
    ( spl0_832
  <=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f1123,plain,
    ( spl0_25
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1998,plain,
    ( spl0_178
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f2245,plain,
    ( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
    | ~ spl0_25
    | ~ spl0_178 ),
    inference(resolution,[],[f1999,f1125]) ).

fof(f1125,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f1123]) ).

fof(f1999,plain,
    ( ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1998]) ).

fof(f23277,plain,
    ( spl0_831
    | ~ spl0_34
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f2243,f1994,f1168,f23274]) ).

fof(f23274,plain,
    ( spl0_831
  <=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f1168,plain,
    ( spl0_34
  <=> class_Orderings_Otop(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f2243,plain,
    ( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
    | ~ spl0_34
    | ~ spl0_177 ),
    inference(resolution,[],[f1995,f1170]) ).

fof(f1170,plain,
    ( class_Orderings_Otop(tc_bool)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f1168]) ).

fof(f23272,plain,
    ( spl0_830
    | ~ spl0_79
    | ~ spl0_789 ),
    inference(avatar_split_clause,[],[f22598,f22317,f1357,f23270]) ).

fof(f23270,plain,
    ( spl0_830
  <=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_U,tc_Com_Opname,X3),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f22598,plain,
    ( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oimage(c_COMBK(X0,X1,X2),v_U,tc_Com_Opname,X3),X0))
    | ~ spl0_79
    | ~ spl0_789 ),
    inference(superposition,[],[f22318,f1358]) ).

fof(f23268,plain,
    ( spl0_829
    | ~ spl0_25
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2237,f1990,f1123,f23265]) ).

fof(f23265,plain,
    ( spl0_829
  <=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f1990,plain,
    ( spl0_176
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f2237,plain,
    ( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
    | ~ spl0_25
    | ~ spl0_176 ),
    inference(resolution,[],[f1991,f1125]) ).

fof(f1991,plain,
    ( ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1990]) ).

fof(f23263,plain,
    ( spl0_828
    | ~ spl0_25
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2235,f1986,f1123,f23260]) ).

fof(f23260,plain,
    ( spl0_828
  <=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f1986,plain,
    ( spl0_175
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f2235,plain,
    ( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
    | ~ spl0_25
    | ~ spl0_175 ),
    inference(resolution,[],[f1987,f1125]) ).

fof(f1987,plain,
    ( ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1986]) ).

fof(f23258,plain,
    ( spl0_827
    | ~ spl0_29
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2229,f1964,f1143,f23256]) ).

fof(f23256,plain,
    ( spl0_827
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f2229,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),c_Orderings_Obot__class_Obot(tc_bool)) = X0
    | ~ spl0_29
    | ~ spl0_172 ),
    inference(resolution,[],[f1965,f1145]) ).

fof(f23254,plain,
    ( spl0_826
    | ~ spl0_29
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2227,f1960,f1143,f23252]) ).

fof(f23252,plain,
    ( spl0_826
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f2227,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X0) = X0
    | ~ spl0_29
    | ~ spl0_171 ),
    inference(resolution,[],[f1961,f1145]) ).

fof(f23250,plain,
    ( spl0_825
    | ~ spl0_25
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f2155,f1932,f1123,f23247]) ).

fof(f23247,plain,
    ( spl0_825
  <=> c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f1932,plain,
    ( spl0_164
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f2155,plain,
    ( c_Orderings_Otop__class_Otop(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool)
    | ~ spl0_25
    | ~ spl0_164 ),
    inference(resolution,[],[f1933,f1125]) ).

fof(f1933,plain,
    ( ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1932]) ).

fof(f23245,plain,
    ( spl0_824
    | ~ spl0_29
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f2037,f1879,f1143,f23243]) ).

fof(f23243,plain,
    ( spl0_824
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f2037,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),c_Orderings_Otop__class_Otop(tc_bool)) = X0
    | ~ spl0_29
    | ~ spl0_151 ),
    inference(resolution,[],[f1880,f1145]) ).

fof(f23241,plain,
    ( spl0_823
    | ~ spl0_29
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f2035,f1875,f1143,f23239]) ).

fof(f23239,plain,
    ( spl0_823
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f2035,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X0) = X0
    | ~ spl0_29
    | ~ spl0_150 ),
    inference(resolution,[],[f1876,f1145]) ).

fof(f23237,plain,
    ( spl0_822
    | ~ spl0_68
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1772,f1636,f1311,f23235]) ).

fof(f23235,plain,
    ( spl0_822
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f1772,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_68
    | ~ spl0_127 ),
    inference(resolution,[],[f1637,f1312]) ).

fof(f23233,plain,
    ( spl0_821
    | ~ spl0_70
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1767,f1636,f1319,f23231]) ).

fof(f23231,plain,
    ( spl0_821
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f1767,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_127 ),
    inference(resolution,[],[f1637,f1320]) ).

fof(f23229,plain,
    ( spl0_820
    | ~ spl0_68
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1755,f1632,f1311,f23227]) ).

fof(f23227,plain,
    ( spl0_820
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Orderings_Obot(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f1755,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(X1),X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Orderings_Obot(X1) )
    | ~ spl0_68
    | ~ spl0_126 ),
    inference(resolution,[],[f1633,f1312]) ).

fof(f23175,plain,
    ( spl0_819
    | ~ spl0_70
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1750,f1632,f1319,f23173]) ).

fof(f23173,plain,
    ( spl0_819
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ class_Orderings_Otop(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f1750,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Orderings_Otop__class_Otop(X0),X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_70
    | ~ spl0_126 ),
    inference(resolution,[],[f1633,f1320]) ).

fof(f23171,plain,
    ( spl0_818
    | ~ spl0_77
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f1536,f1406,f1349,f23169]) ).

fof(f23169,plain,
    ( spl0_818
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f1536,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_77
    | ~ spl0_90 ),
    inference(resolution,[],[f1407,f1350]) ).

fof(f23167,plain,
    ( spl0_817
    | ~ spl0_76
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f1531,f1402,f1345,f23165]) ).

fof(f23165,plain,
    ( spl0_817
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f1531,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_Suc(X1),tc_nat) )
    | ~ spl0_76
    | ~ spl0_89 ),
    inference(resolution,[],[f1403,f1346]) ).

fof(f23163,plain,
    ( spl0_816
    | ~ spl0_77
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1520,f1390,f1349,f23161]) ).

fof(f23161,plain,
    ( spl0_816
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f1520,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_77
    | ~ spl0_86 ),
    inference(resolution,[],[f1391,f1350]) ).

fof(f23017,plain,
    ( spl0_815
    | ~ spl0_82
    | ~ spl0_771 ),
    inference(avatar_split_clause,[],[f21633,f21374,f1369,f23015]) ).

fof(f23015,plain,
    ( spl0_815
  <=> ! [X0,X1] : hBOOL(c_in(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f21374,plain,
    ( spl0_771
  <=> ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f21633,plain,
    ( ! [X0,X1] : hBOOL(c_in(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1))
    | ~ spl0_82
    | ~ spl0_771 ),
    inference(superposition,[],[f1370,f21375]) ).

fof(f21375,plain,
    ( ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)
    | ~ spl0_771 ),
    inference(avatar_component_clause,[],[f21374]) ).

fof(f22657,plain,
    ( spl0_814
    | ~ spl0_106
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2257,f2032,f1470,f22655]) ).

fof(f22655,plain,
    ( spl0_814
  <=> ! [X0,X1] : c_fequal(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f2257,plain,
    ( ! [X0,X1] : c_fequal(X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
    | ~ spl0_106
    | ~ spl0_186 ),
    inference(superposition,[],[f1471,f2033]) ).

fof(f22653,plain,
    ( spl0_813
    | ~ spl0_33
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1870,f1711,f1163,f22651]) ).

fof(f22651,plain,
    ( spl0_813
  <=> ! [X0] : c_fequal(X0,tc_bool) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f1163,plain,
    ( spl0_33
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f1870,plain,
    ( ! [X0] : c_fequal(X0,tc_bool) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_bool)
    | ~ spl0_33
    | ~ spl0_145 ),
    inference(resolution,[],[f1712,f1165]) ).

fof(f1165,plain,
    ( class_Orderings_Oorder(tc_bool)
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f1163]) ).

fof(f22649,plain,
    ( spl0_812
    | ~ spl0_21
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1869,f1711,f1103,f22647]) ).

fof(f22647,plain,
    ( spl0_812
  <=> ! [X0] : c_fequal(X0,tc_nat) = c_SetInterval_Oord__class_OatLeastAtMost(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f22645,plain,
    ( spl0_811
    | ~ spl0_19
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1868,f1707,f1093,f22643]) ).

fof(f22643,plain,
    ( spl0_811
  <=> ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_fequal(X0,tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f1707,plain,
    ( spl0_144
  <=> ! [X0,X14] :
        ( hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1868,plain,
    ( ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_fequal(X0,tc_nat)) = X0
    | ~ spl0_19
    | ~ spl0_144 ),
    inference(resolution,[],[f1708,f1095]) ).

fof(f1708,plain,
    ( ! [X0,X14] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14 )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1707]) ).

fof(f22638,plain,
    ( spl0_810
    | ~ spl0_19
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1867,f1703,f1093,f22636]) ).

fof(f22636,plain,
    ( spl0_810
  <=> ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_fequal(X0,tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f1703,plain,
    ( spl0_143
  <=> ! [X0,X14] :
        ( hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1867,plain,
    ( ! [X0] : hAPP(c_Finite__Set_Olinorder__class_OMin(tc_nat),c_fequal(X0,tc_nat)) = X0
    | ~ spl0_19
    | ~ spl0_143 ),
    inference(resolution,[],[f1704,f1095]) ).

fof(f1704,plain,
    ( ! [X0,X14] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14 )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1703]) ).

fof(f22634,plain,
    ( spl0_809
    | ~ spl0_26
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1830,f1668,f1128,f22632]) ).

fof(f1128,plain,
    ( spl0_26
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1830,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X0),X0) = X0
    | ~ spl0_26
    | ~ spl0_135 ),
    inference(resolution,[],[f1669,f1130]) ).

fof(f1130,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f1128]) ).

fof(f22630,plain,
    ( spl0_808
    | ~ spl0_27
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1737,f1620,f1133,f22628]) ).

fof(f1737,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X0),X0) = X0
    | ~ spl0_27
    | ~ spl0_123 ),
    inference(resolution,[],[f1621,f1135]) ).

fof(f22625,plain,
    ( spl0_807
    | ~ spl0_15
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1736,f1620,f1073,f22623]) ).

fof(f22623,plain,
    ( spl0_807
  <=> ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f1736,plain,
    ( ! [X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X0),X0) = X0
    | ~ spl0_15
    | ~ spl0_123 ),
    inference(resolution,[],[f1621,f1075]) ).

fof(f22621,plain,
    ( spl0_806
    | ~ spl0_19
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f1727,f1608,f1093,f22619]) ).

fof(f1608,plain,
    ( spl0_120
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1727,plain,
    ( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_nat),X0),X0) = X0
    | ~ spl0_19
    | ~ spl0_120 ),
    inference(resolution,[],[f1609,f1095]) ).

fof(f1609,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 )
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f1608]) ).

fof(f22617,plain,
    ( spl0_805
    | ~ spl0_19
    | ~ spl0_119 ),
    inference(avatar_split_clause,[],[f1722,f1604,f1093,f22615]) ).

fof(f1604,plain,
    ( spl0_119
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1722,plain,
    ( ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_nat),X0),X0) = X0
    | ~ spl0_19
    | ~ spl0_119 ),
    inference(resolution,[],[f1605,f1095]) ).

fof(f1605,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f1604]) ).

fof(f22613,plain,
    ( spl0_804
    | ~ spl0_89
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f1573,f1442,f1402,f22611]) ).

fof(f22611,plain,
    ( spl0_804
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f1573,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_89
    | ~ spl0_99 ),
    inference(resolution,[],[f1443,f1403]) ).

fof(f22609,plain,
    ( spl0_803
    | ~ spl0_90
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1569,f1438,f1406,f22607]) ).

fof(f22607,plain,
    ( spl0_803
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f1569,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_90
    | ~ spl0_98 ),
    inference(resolution,[],[f1439,f1407]) ).

fof(f22605,plain,
    ( spl0_802
    | ~ spl0_91
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1558,f1434,f1410,f22603]) ).

fof(f22603,plain,
    ( spl0_802
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f1558,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_91
    | ~ spl0_97 ),
    inference(resolution,[],[f1435,f1411]) ).

fof(f22577,plain,
    ( ~ spl0_1
    | spl0_801
    | ~ spl0_2
    | ~ spl0_726 ),
    inference(avatar_split_clause,[],[f18983,f18841,f1008,f22575,f1003]) ).

fof(f22575,plain,
    ( spl0_801
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_Finite__Set_Osetsum(X1,v_U,tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,v_x)),c_Finite__Set_Osetsum(X1,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f1008,plain,
    ( spl0_2
  <=> hBOOL(c_in(v_x,v_U,tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f18841,plain,
    ( spl0_726
  <=> ! [X20,X0,X14,X6,X25] :
        ( c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X14,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f18983,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
        | c_Finite__Set_Osetsum(X1,v_U,tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,v_x)),c_Finite__Set_Osetsum(X1,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X0)) )
    | ~ spl0_2
    | ~ spl0_726 ),
    inference(resolution,[],[f18842,f1010]) ).

fof(f1010,plain,
    ( hBOOL(c_in(v_x,v_U,tc_Com_Opname))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f1008]) ).

fof(f18842,plain,
    ( ! [X0,X6,X14,X25,X20] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20)) )
    | ~ spl0_726 ),
    inference(avatar_component_clause,[],[f18841]) ).

fof(f22573,plain,
    ( spl0_799
    | ~ spl0_800
    | ~ spl0_1
    | ~ spl0_709 ),
    inference(avatar_split_clause,[],[f18380,f17575,f1003,f22570,f22567]) ).

fof(f22567,plain,
    ( spl0_799
  <=> ! [X0,X1] : c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f22570,plain,
    ( spl0_800
  <=> class_Lattices_Olower__semilattice(tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f17575,plain,
    ( spl0_709
  <=> ! [X0,X14,X6,X16] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f18380,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(tc_Com_Opname)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) )
    | ~ spl0_1
    | ~ spl0_709 ),
    inference(resolution,[],[f17576,f1005]) ).

fof(f17576,plain,
    ( ! [X0,X6,X16,X14] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ class_Lattices_Olower__semilattice(X0)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) )
    | ~ spl0_709 ),
    inference(avatar_component_clause,[],[f17575]) ).

fof(f22565,plain,
    ( spl0_797
    | ~ spl0_798
    | ~ spl0_1
    | ~ spl0_708 ),
    inference(avatar_split_clause,[],[f18361,f17571,f1003,f22562,f22559]) ).

fof(f22559,plain,
    ( spl0_797
  <=> ! [X0,X1] : c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f22562,plain,
    ( spl0_798
  <=> class_Lattices_Oupper__semilattice(tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f17571,plain,
    ( spl0_708
  <=> ! [X0,X14,X6,X16] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f18361,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(tc_Com_Opname)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X1),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),X0,v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)) )
    | ~ spl0_1
    | ~ spl0_708 ),
    inference(resolution,[],[f17572,f1005]) ).

fof(f17572,plain,
    ( ! [X0,X6,X16,X14] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) )
    | ~ spl0_708 ),
    inference(avatar_component_clause,[],[f17571]) ).

fof(f22523,plain,
    ( spl0_796
    | ~ spl0_106
    | ~ spl0_771 ),
    inference(avatar_split_clause,[],[f21635,f21374,f1470,f22521]) ).

fof(f22521,plain,
    ( spl0_796
  <=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f21635,plain,
    ( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X0,v_U,tc_Com_Opname,X1)
    | ~ spl0_106
    | ~ spl0_771 ),
    inference(superposition,[],[f1471,f21375]) ).

fof(f22518,plain,
    ( spl0_795
    | ~ spl0_82
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2255,f2032,f1369,f22516]) ).

fof(f22516,plain,
    ( spl0_795
  <=> ! [X0,X1] : hBOOL(c_in(X0,c_fequal(X0,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f2255,plain,
    ( ! [X0,X1] : hBOOL(c_in(X0,c_fequal(X0,X1),X1))
    | ~ spl0_82
    | ~ spl0_186 ),
    inference(superposition,[],[f1370,f2033]) ).

fof(f22514,plain,
    ( spl0_794
    | ~ spl0_111
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1866,f1699,f1490,f22512]) ).

fof(f22512,plain,
    ( spl0_794
  <=> ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X0,X1),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f1490,plain,
    ( spl0_111
  <=> ! [X57,X0,X47] :
        ( X47 = X57
        | ~ hBOOL(hAPP(c_fequal(X47,X0),X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1699,plain,
    ( spl0_142
  <=> ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1866,plain,
    ( ! [X0,X1] : c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X0,X1),X1) = X0
    | ~ spl0_111
    | ~ spl0_142 ),
    inference(resolution,[],[f1700,f1491]) ).

fof(f1491,plain,
    ( ! [X0,X47,X57] :
        ( ~ hBOOL(hAPP(c_fequal(X47,X0),X57))
        | X47 = X57 )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1490]) ).

fof(f1700,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0)))
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1699]) ).

fof(f22510,plain,
    ( spl0_793
    | ~ spl0_25
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1596,f1506,f1123,f22508]) ).

fof(f22508,plain,
    ( spl0_793
  <=> ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f1596,plain,
    ( ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_fequal(X0,tc_bool),tc_bool) = X0
    | ~ spl0_25
    | ~ spl0_115 ),
    inference(resolution,[],[f1507,f1125]) ).

fof(f22506,plain,
    ( spl0_792
    | ~ spl0_25
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1594,f1502,f1123,f22504]) ).

fof(f22504,plain,
    ( spl0_792
  <=> ! [X0] : c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f1594,plain,
    ( ! [X0] : c_Complete__Lattice_OInf__class_OInf(c_fequal(X0,tc_bool),tc_bool) = X0
    | ~ spl0_25
    | ~ spl0_114 ),
    inference(resolution,[],[f1503,f1125]) ).

fof(f22327,plain,
    ( spl0_791
    | ~ spl0_3
    | ~ spl0_390
    | ~ spl0_703 ),
    inference(avatar_split_clause,[],[f17773,f17551,f6638,f1013,f22325]) ).

fof(f22325,plain,
    ( spl0_791
  <=> ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f6638,plain,
    ( spl0_390
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f17551,plain,
    ( spl0_703
  <=> ! [X20,X0,X6,X25,X8] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f17773,plain,
    ( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool))
    | ~ spl0_3
    | ~ spl0_390
    | ~ spl0_703 ),
    inference(forward_demodulation,[],[f17755,f6639]) ).

fof(f6639,plain,
    ( ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6)
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f6638]) ).

fof(f17755,plain,
    ( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G),tc_fun(t_a,tc_bool))
    | ~ spl0_3
    | ~ spl0_703 ),
    inference(superposition,[],[f17552,f1015]) ).

fof(f17552,plain,
    ( ! [X0,X8,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool))
    | ~ spl0_703 ),
    inference(avatar_component_clause,[],[f17551]) ).

fof(f22323,plain,
    ( spl0_790
    | ~ spl0_3
    | ~ spl0_703 ),
    inference(avatar_split_clause,[],[f17749,f17551,f1013,f22321]) ).

fof(f22321,plain,
    ( spl0_790
  <=> ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f17749,plain,
    ( ! [X0] : c_lessequals(c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),tc_fun(t_a,tc_bool))
    | ~ spl0_3
    | ~ spl0_703 ),
    inference(superposition,[],[f17552,f1015]) ).

fof(f22319,plain,
    ( spl0_789
    | ~ spl0_72
    | ~ spl0_771 ),
    inference(avatar_split_clause,[],[f21632,f21374,f1327,f22317]) ).

fof(f21632,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),hAPP(X0,v_x)))
    | ~ spl0_72
    | ~ spl0_771 ),
    inference(superposition,[],[f1328,f21375]) ).

fof(f22315,plain,
    ( spl0_788
    | ~ spl0_1
    | ~ spl0_688 ),
    inference(avatar_split_clause,[],[f16331,f15876,f1003,f22313]) ).

fof(f22313,plain,
    ( spl0_788
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hBOOL(c_in(X1,v_U,tc_Com_Opname))
        | c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X2,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f15876,plain,
    ( spl0_688
  <=> ! [X20,X0,X14,X33,X25] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | ~ c_Finite__Set_Ofinite(X33,X0)
        | hBOOL(c_in(X14,X33,X0))
        | c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f16331,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hBOOL(c_in(X1,v_U,tc_Com_Opname))
        | c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X1,v_U,tc_Com_Opname),tc_Com_Opname,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X2,X1)),c_Finite__Set_Osetsum(X2,v_U,tc_Com_Opname,X0)) )
    | ~ spl0_1
    | ~ spl0_688 ),
    inference(resolution,[],[f15877,f1005]) ).

fof(f15877,plain,
    ( ! [X0,X14,X25,X33,X20] :
        ( ~ c_Finite__Set_Ofinite(X33,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | hBOOL(c_in(X14,X33,X0))
        | c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) )
    | ~ spl0_688 ),
    inference(avatar_component_clause,[],[f15876]) ).

fof(f22266,plain,
    ( spl0_787
    | ~ spl0_2
    | ~ spl0_698 ),
    inference(avatar_split_clause,[],[f17440,f15916,f1008,f22264]) ).

fof(f22264,plain,
    ( spl0_787
  <=> ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,v_x,X1,tc_Com_Opname,X2),v_U,tc_Com_Opname,X2) = c_Set_Oinsert(X1,c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f15916,plain,
    ( spl0_698
  <=> ! [X2,X20,X0,X6,X25,X1] :
        ( c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0)
        | ~ hBOOL(c_in(X1,X6,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f17440,plain,
    ( ! [X2,X0,X1] : c_Set_Oimage(c_Fun_Ofun__upd(X0,v_x,X1,tc_Com_Opname,X2),v_U,tc_Com_Opname,X2) = c_Set_Oinsert(X1,c_Set_Oimage(X0,c_HOL_Ominus__class_Ominus(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,X2),X2)
    | ~ spl0_2
    | ~ spl0_698 ),
    inference(resolution,[],[f15917,f1010]) ).

fof(f15917,plain,
    ( ! [X2,X0,X1,X6,X25,X20] :
        ( ~ hBOOL(c_in(X1,X6,X20))
        | c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0) )
    | ~ spl0_698 ),
    inference(avatar_component_clause,[],[f15916]) ).

fof(f22073,plain,
    ( spl0_786
    | ~ spl0_3
    | ~ spl0_662 ),
    inference(avatar_split_clause,[],[f15372,f14552,f1013,f22071]) ).

fof(f22071,plain,
    ( spl0_786
  <=> ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f14552,plain,
    ( spl0_662
  <=> ! [X20,X0,X6,X25,X8] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f15372,plain,
    ( ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)),v_G)
    | ~ spl0_3
    | ~ spl0_662 ),
    inference(superposition,[],[f14553,f1015]) ).

fof(f14553,plain,
    ( ! [X0,X8,X6,X25,X20] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0))
    | ~ spl0_662 ),
    inference(avatar_component_clause,[],[f14552]) ).

fof(f22069,plain,
    ( spl0_785
    | ~ spl0_3
    | ~ spl0_662 ),
    inference(avatar_split_clause,[],[f15366,f14552,f1013,f22067]) ).

fof(f22067,plain,
    ( spl0_785
  <=> ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f15366,plain,
    ( ! [X0] : c_Set_Oimage(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_G),c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a))
    | ~ spl0_3
    | ~ spl0_662 ),
    inference(superposition,[],[f14553,f1015]) ).

fof(f21806,plain,
    ( spl0_784
    | ~ spl0_2
    | ~ spl0_663 ),
    inference(avatar_split_clause,[],[f15468,f14556,f1008,f21804]) ).

fof(f21804,plain,
    ( spl0_784
  <=> ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X0,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f14556,plain,
    ( spl0_663
  <=> ! [X54,X20,X0,X6,X28] :
        ( ~ hBOOL(c_in(X28,X54,X0))
        | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f15468,plain,
    ( ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(X0,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_U,X0,tc_Com_Opname,tc_fun(X1,tc_bool)))
    | ~ spl0_2
    | ~ spl0_663 ),
    inference(resolution,[],[f14557,f1010]) ).

fof(f14557,plain,
    ( ! [X28,X0,X54,X6,X20] :
        ( ~ hBOOL(c_in(X28,X54,X0))
        | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) )
    | ~ spl0_663 ),
    inference(avatar_component_clause,[],[f14556]) ).

fof(f21802,plain,
    ( spl0_441
    | ~ spl0_782
    | spl0_783
    | ~ spl0_1
    | ~ spl0_2
    | ~ spl0_655 ),
    inference(avatar_split_clause,[],[f14832,f14524,f1008,f1003,f21800,f21796,f8018]) ).

fof(f8018,plain,
    ( spl0_441
  <=> v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f21796,plain,
    ( spl0_782
  <=> class_Orderings_Olinorder(tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f21800,plain,
    ( spl0_783
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_Com_Opname)
        | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_Com_Opname),tc_Com_Opname),v_U),X0,tc_Com_Opname) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f14524,plain,
    ( spl0_655
  <=> ! [X34,X0,X6,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_HOL_Oord__class_Oless(X34,X1,X0)
        | ~ hBOOL(c_in(X34,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f14832,plain,
    ( ! [X0] :
        ( ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
        | ~ c_HOL_Oord__class_Oless(v_x,X0,tc_Com_Opname)
        | ~ class_Orderings_Olinorder(tc_Com_Opname)
        | v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))
        | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_Com_Opname),tc_Com_Opname),v_U),X0,tc_Com_Opname) )
    | ~ spl0_2
    | ~ spl0_655 ),
    inference(resolution,[],[f14525,f1010]) ).

fof(f14525,plain,
    ( ! [X0,X1,X6,X34] :
        ( ~ hBOOL(c_in(X34,X6,X0))
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_HOL_Oord__class_Oless(X34,X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) )
    | ~ spl0_655 ),
    inference(avatar_component_clause,[],[f14524]) ).

fof(f21794,plain,
    ( spl0_781
    | ~ spl0_3
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f14373,f14138,f1013,f21792]) ).

fof(f21792,plain,
    ( spl0_781
  <=> ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f14138,plain,
    ( spl0_647
  <=> ! [X20,X0,X6,X25,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f14373,plain,
    ( ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ spl0_3
    | ~ spl0_647 ),
    inference(superposition,[],[f14139,f1015]) ).

fof(f14139,plain,
    ( ! [X0,X8,X6,X25,X20] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool))
    | ~ spl0_647 ),
    inference(avatar_component_clause,[],[f14138]) ).

fof(f21790,plain,
    ( spl0_780
    | ~ spl0_3
    | ~ spl0_647 ),
    inference(avatar_split_clause,[],[f14367,f14138,f1013,f21788]) ).

fof(f21788,plain,
    ( spl0_780
  <=> ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f14367,plain,
    ( ! [X0] : c_lessequals(c_HOL_Ominus__class_Ominus(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),c_Set_Oimage(v_mgt__call,c_HOL_Ominus__class_Ominus(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
    | ~ spl0_3
    | ~ spl0_647 ),
    inference(superposition,[],[f14139,f1015]) ).

fof(f21777,plain,
    ( spl0_779
    | ~ spl0_3
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f13453,f13228,f1013,f21775]) ).

fof(f21775,plain,
    ( spl0_779
  <=> ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | v_U = X0
        | ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f13228,plain,
    ( spl0_630
  <=> ! [X20,X0,X6,X25,X8] :
        ( X6 = X8
        | c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
        | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f13453,plain,
    ( ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | v_U = X0
        | ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname,t_a) )
    | ~ spl0_3
    | ~ spl0_630 ),
    inference(superposition,[],[f13229,f1015]) ).

fof(f13229,plain,
    ( ! [X0,X8,X6,X25,X20] :
        ( c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
        | X6 = X8
        | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) )
    | ~ spl0_630 ),
    inference(avatar_component_clause,[],[f13228]) ).

fof(f21773,plain,
    ( spl0_778
    | ~ spl0_3
    | ~ spl0_630 ),
    inference(avatar_split_clause,[],[f13447,f13228,f1013,f21771]) ).

fof(f21771,plain,
    ( spl0_778
  <=> ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | v_U = X0
        | ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f13447,plain,
    ( ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | v_U = X0
        | ~ c_Fun_Oinj__on(v_mgt__call,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname,t_a) )
    | ~ spl0_3
    | ~ spl0_630 ),
    inference(superposition,[],[f13229,f1015]) ).

fof(f21729,plain,
    ( ~ spl0_777
    | ~ spl0_194
    | spl0_774 ),
    inference(avatar_split_clause,[],[f21685,f21678,f2283,f21726]) ).

fof(f21726,plain,
    ( spl0_777
  <=> c_Fun_Obij(v_mgt__call,tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f2283,plain,
    ( spl0_194
  <=> ! [X20,X0,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f21678,plain,
    ( spl0_774
  <=> c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f21685,plain,
    ( ~ c_Fun_Obij(v_mgt__call,tc_Com_Opname,t_a)
    | ~ spl0_194
    | spl0_774 ),
    inference(resolution,[],[f21680,f2284]) ).

fof(f2284,plain,
    ( ! [X0,X25,X20] :
        ( c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | ~ c_Fun_Obij(X25,X0,X20) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f21680,plain,
    ( ~ c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a)
    | spl0_774 ),
    inference(avatar_component_clause,[],[f21678]) ).

fof(f21689,plain,
    ( spl0_776
    | ~ spl0_3
    | ~ spl0_550 ),
    inference(avatar_split_clause,[],[f11117,f10696,f1013,f21687]) ).

fof(f21687,plain,
    ( spl0_776
  <=> ! [X0,X1] :
        ( ~ c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
        | hBOOL(c_in(hAPP(v_mgt__call,X1),X0,t_a))
        | ~ hBOOL(c_in(X1,v_U,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f10696,plain,
    ( spl0_550
  <=> ! [X8,X20,X0,X6,X25,X1] :
        ( ~ hBOOL(c_in(X1,X6,X20))
        | hBOOL(c_in(hAPP(X25,X1),X8,X0))
        | ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f11117,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
        | hBOOL(c_in(hAPP(v_mgt__call,X1),X0,t_a))
        | ~ hBOOL(c_in(X1,v_U,tc_Com_Opname)) )
    | ~ spl0_3
    | ~ spl0_550 ),
    inference(superposition,[],[f10697,f1015]) ).

fof(f10697,plain,
    ( ! [X0,X1,X8,X6,X25,X20] :
        ( ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool))
        | hBOOL(c_in(hAPP(X25,X1),X8,X0))
        | ~ hBOOL(c_in(X1,X6,X20)) )
    | ~ spl0_550 ),
    inference(avatar_component_clause,[],[f10696]) ).

fof(f21684,plain,
    ( ~ spl0_774
    | spl0_775
    | ~ spl0_3
    | ~ spl0_548 ),
    inference(avatar_split_clause,[],[f11045,f10681,f1013,f21682,f21678]) ).

fof(f21682,plain,
    ( spl0_775
  <=> ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | v_U = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f10681,plain,
    ( spl0_548
  <=> ! [X20,X0,X6,X25,X8] :
        ( X6 = X8
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f11045,plain,
    ( ! [X0] :
        ( v_G != c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a)
        | ~ c_Fun_Oinj__on(v_mgt__call,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,t_a)
        | v_U = X0 )
    | ~ spl0_3
    | ~ spl0_548 ),
    inference(superposition,[],[f10682,f1015]) ).

fof(f10682,plain,
    ( ! [X0,X8,X6,X25,X20] :
        ( c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | X6 = X8 )
    | ~ spl0_548 ),
    inference(avatar_component_clause,[],[f10681]) ).

fof(f21676,plain,
    ( spl0_773
    | ~ spl0_1
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f10590,f10355,f1003,f21674]) ).

fof(f21674,plain,
    ( spl0_773
  <=> ! [X0] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_U,c_fequal(X0,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f10590,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(v_U,c_fequal(X0,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname))
    | ~ spl0_1
    | ~ spl0_528 ),
    inference(resolution,[],[f10356,f1005]) ).

fof(f21447,plain,
    ( spl0_772
    | ~ spl0_109
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f19018,f17547,f1482,f21445]) ).

fof(f21445,plain,
    ( spl0_772
  <=> ! [X0] :
        ( v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a)
        | ~ hBOOL(hAPP(v_U,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f17547,plain,
    ( spl0_702
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f19018,plain,
    ( ! [X0] :
        ( v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a)
        | ~ hBOOL(hAPP(v_U,X0)) )
    | ~ spl0_109
    | ~ spl0_702 ),
    inference(resolution,[],[f17548,f1483]) ).

fof(f17548,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) )
    | ~ spl0_702 ),
    inference(avatar_component_clause,[],[f17547]) ).

fof(f21376,plain,
    ( spl0_771
    | ~ spl0_2
    | ~ spl0_527 ),
    inference(avatar_split_clause,[],[f10568,f10351,f1008,f21374]) ).

fof(f10351,plain,
    ( spl0_527
  <=> ! [X20,X0,X6,X25,X1] :
        ( ~ hBOOL(c_in(X1,X6,X0))
        | c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f10568,plain,
    ( ! [X0,X1] : c_Set_Oimage(X0,v_U,tc_Com_Opname,X1) = c_Set_Oinsert(hAPP(X0,v_x),c_Set_Oimage(X0,v_U,tc_Com_Opname,X1),X1)
    | ~ spl0_2
    | ~ spl0_527 ),
    inference(resolution,[],[f10352,f1010]) ).

fof(f10352,plain,
    ( ! [X0,X1,X6,X25,X20] :
        ( ~ hBOOL(c_in(X1,X6,X0))
        | c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) )
    | ~ spl0_527 ),
    inference(avatar_component_clause,[],[f10351]) ).

fof(f21372,plain,
    ( spl0_770
    | ~ spl0_2
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f10437,f10335,f1008,f21370]) ).

fof(f21370,plain,
    ( spl0_770
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f10335,plain,
    ( spl0_523
  <=> ! [X0,X8,X6,X1] :
        ( ~ hBOOL(c_in(X1,X8,X0))
        | c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f10437,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_2
    | ~ spl0_523 ),
    inference(resolution,[],[f10336,f1010]) ).

fof(f10336,plain,
    ( ! [X0,X1,X8,X6] :
        ( ~ hBOOL(c_in(X1,X8,X0))
        | c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) )
    | ~ spl0_523 ),
    inference(avatar_component_clause,[],[f10335]) ).

fof(f21368,plain,
    ( spl0_769
    | ~ spl0_3
    | ~ spl0_513 ),
    inference(avatar_split_clause,[],[f10265,f9495,f1013,f21366]) ).

fof(f21366,plain,
    ( spl0_769
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f9495,plain,
    ( spl0_513
  <=> ! [X20,X0,X6,X25,X1] :
        ( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f10265,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0),v_U,tc_Com_Opname)) )
    | ~ spl0_3
    | ~ spl0_513 ),
    inference(superposition,[],[f9496,f1015]) ).

fof(f9496,plain,
    ( ! [X0,X1,X6,X25,X20] :
        ( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) )
    | ~ spl0_513 ),
    inference(avatar_component_clause,[],[f9495]) ).

fof(f21364,plain,
    ( spl0_768
    | ~ spl0_3
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f10250,f9491,f1013,f21362]) ).

fof(f21362,plain,
    ( spl0_768
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f9491,plain,
    ( spl0_512
  <=> ! [X2,X20,X0,X6,X25] :
        ( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f10250,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,hAPP(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0)) = X0 )
    | ~ spl0_3
    | ~ spl0_512 ),
    inference(superposition,[],[f9492,f1015]) ).

fof(f9492,plain,
    ( ! [X2,X0,X6,X25,X20] :
        ( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 )
    | ~ spl0_512 ),
    inference(avatar_component_clause,[],[f9491]) ).

fof(f21360,plain,
    ( spl0_767
    | ~ spl0_3
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f10117,f9479,f1013,f21358]) ).

fof(f21358,plain,
    ( spl0_767
  <=> ! [X0] :
        ( c_lessequals(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
        | ~ c_lessequals(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f9479,plain,
    ( spl0_509
  <=> ! [X20,X0,X6,X25,X1] :
        ( ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool))
        | c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f10117,plain,
    ( ! [X0] :
        ( c_lessequals(c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),v_G,tc_fun(t_a,tc_bool))
        | ~ c_lessequals(X0,v_U,tc_fun(tc_Com_Opname,tc_bool)) )
    | ~ spl0_3
    | ~ spl0_509 ),
    inference(superposition,[],[f9480,f1015]) ).

fof(f9480,plain,
    ( ! [X0,X1,X6,X25,X20] :
        ( c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool))
        | ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool)) )
    | ~ spl0_509 ),
    inference(avatar_component_clause,[],[f9479]) ).

fof(f21356,plain,
    ( spl0_766
    | ~ spl0_3
    | ~ spl0_509 ),
    inference(avatar_split_clause,[],[f10112,f9479,f1013,f21354]) ).

fof(f21354,plain,
    ( spl0_766
  <=> ! [X0] :
        ( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
        | ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f10112,plain,
    ( ! [X0] :
        ( c_lessequals(v_G,c_Set_Oimage(v_mgt__call,X0,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool))
        | ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool)) )
    | ~ spl0_3
    | ~ spl0_509 ),
    inference(superposition,[],[f9480,f1015]) ).

fof(f21352,plain,
    ( spl0_764
    | ~ spl0_765
    | ~ spl0_1
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f9310,f8169,f1003,f21349,f21345]) ).

fof(f21345,plain,
    ( spl0_764
  <=> c_Complete__Lattice_OSup__class_OSup(v_U,tc_Com_Opname) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_Com_Opname),v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f21349,plain,
    ( spl0_765
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f8169,plain,
    ( spl0_478
  <=> ! [X6,X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f9310,plain,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(tc_Com_Opname)
    | c_Complete__Lattice_OSup__class_OSup(v_U,tc_Com_Opname) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_Com_Opname),v_U,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)
    | ~ spl0_1
    | ~ spl0_478 ),
    inference(resolution,[],[f8170,f1005]) ).

fof(f8170,plain,
    ( ! [X0,X6] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) )
    | ~ spl0_478 ),
    inference(avatar_component_clause,[],[f8169]) ).

fof(f21198,plain,
    ( spl0_763
    | ~ spl0_3
    | ~ spl0_477 ),
    inference(avatar_split_clause,[],[f9249,f8165,f1013,f21196]) ).

fof(f21196,plain,
    ( spl0_763
  <=> ! [X0] : c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f9249,plain,
    ( ! [X0] : c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) = c_Set_Oimage(v_mgt__call,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname,t_a)
    | ~ spl0_3
    | ~ spl0_477 ),
    inference(superposition,[],[f8166,f1015]) ).

fof(f21194,plain,
    ( spl0_762
    | ~ spl0_3
    | ~ spl0_471 ),
    inference(avatar_split_clause,[],[f9150,f8141,f1013,f21192]) ).

fof(f21192,plain,
    ( spl0_762
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f8141,plain,
    ( spl0_471
  <=> ! [X16,X20,X0,X6,X25] :
        ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f9150,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) )
    | ~ spl0_3
    | ~ spl0_471 ),
    inference(superposition,[],[f8142,f1015]) ).

fof(f8142,plain,
    ( ! [X0,X6,X16,X25,X20] :
        ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) )
    | ~ spl0_471 ),
    inference(avatar_component_clause,[],[f8141]) ).

fof(f21190,plain,
    ( spl0_761
    | ~ spl0_3
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f9140,f8137,f1013,f21188]) ).

fof(f21188,plain,
    ( spl0_761
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f8137,plain,
    ( spl0_470
  <=> ! [X19,X20,X0,X6,X25] :
        ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f9140,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a)) = X0 )
    | ~ spl0_3
    | ~ spl0_470 ),
    inference(superposition,[],[f8138,f1015]) ).

fof(f8138,plain,
    ( ! [X0,X19,X6,X25,X20] :
        ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 )
    | ~ spl0_470 ),
    inference(avatar_component_clause,[],[f8137]) ).

fof(f21186,plain,
    ( spl0_760
    | ~ spl0_3
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f9049,f8125,f1013,f21184]) ).

fof(f21184,plain,
    ( spl0_760
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
        | c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f9049,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
        | c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_U,v_mgt__call,tc_Com_Opname,t_a),X0,t_a,tc_Com_Opname) )
    | ~ spl0_3
    | ~ spl0_467 ),
    inference(superposition,[],[f8126,f1015]) ).

fof(f21182,plain,
    ( spl0_759
    | ~ spl0_82
    | ~ spl0_737 ),
    inference(avatar_split_clause,[],[f20181,f19332,f1369,f21179]) ).

fof(f21179,plain,
    ( spl0_759
  <=> hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f19332,plain,
    ( spl0_737
  <=> v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f20181,plain,
    ( hBOOL(c_in(hAPP(v_mgt__call,v_x),v_G,t_a))
    | ~ spl0_82
    | ~ spl0_737 ),
    inference(superposition,[],[f1370,f19334]) ).

fof(f19334,plain,
    ( v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a)
    | ~ spl0_737 ),
    inference(avatar_component_clause,[],[f19332]) ).

fof(f21177,plain,
    ( spl0_758
    | ~ spl0_3
    | ~ spl0_462 ),
    inference(avatar_split_clause,[],[f9003,f8103,f1013,f21175]) ).

fof(f21175,plain,
    ( spl0_758
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f8103,plain,
    ( spl0_462
  <=> ! [X19,X20,X0,X6,X25] :
        ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f9003,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_U,v_mgt__call,X0,tc_Com_Opname,t_a),v_U,tc_Com_Opname)) )
    | ~ spl0_3
    | ~ spl0_462 ),
    inference(superposition,[],[f8104,f1015]) ).

fof(f8104,plain,
    ( ! [X0,X19,X6,X25,X20] :
        ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) )
    | ~ spl0_462 ),
    inference(avatar_component_clause,[],[f8103]) ).

fof(f21173,plain,
    ( spl0_757
    | ~ spl0_3
    | ~ spl0_461 ),
    inference(avatar_split_clause,[],[f8989,f8099,f1013,f21171]) ).

fof(f21171,plain,
    ( spl0_757
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f8099,plain,
    ( spl0_461
  <=> ! [X16,X20,X0,X6,X25] :
        ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f8989,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_G,t_a))
        | hAPP(v_mgt__call,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_U,X0,v_mgt__call,tc_Com_Opname,t_a)) = X0 )
    | ~ spl0_3
    | ~ spl0_461 ),
    inference(superposition,[],[f8100,f1015]) ).

fof(f8100,plain,
    ( ! [X0,X6,X16,X25,X20] :
        ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
        | hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 )
    | ~ spl0_461 ),
    inference(avatar_component_clause,[],[f8099]) ).

fof(f21169,plain,
    ( ~ spl0_1
    | spl0_755
    | ~ spl0_756
    | ~ spl0_3
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f8980,f8095,f1013,f21166,f21162,f1003]) ).

fof(f21162,plain,
    ( spl0_755
  <=> c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f21166,plain,
    ( spl0_756
  <=> c_Finite__Set_Ocard(v_U,tc_Com_Opname) = c_Finite__Set_Ocard(v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f8095,plain,
    ( spl0_460
  <=> ! [X20,X0,X6,X25] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f8980,plain,
    ( c_Finite__Set_Ocard(v_U,tc_Com_Opname) != c_Finite__Set_Ocard(v_G,t_a)
    | c_Fun_Oinj__on(v_mgt__call,v_U,tc_Com_Opname,t_a)
    | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_3
    | ~ spl0_460 ),
    inference(superposition,[],[f8096,f1015]) ).

fof(f8096,plain,
    ( ! [X0,X6,X25,X20] :
        ( c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20)
        | c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_Finite__Set_Ofinite(X6,X0) )
    | ~ spl0_460 ),
    inference(avatar_component_clause,[],[f8095]) ).

fof(f20774,plain,
    ( spl0_754
    | ~ spl0_390
    | ~ spl0_399
    | ~ spl0_733
    | ~ spl0_735
    | ~ spl0_753 ),
    inference(avatar_split_clause,[],[f20770,f20766,f19324,f19316,f6699,f6638,f20772]) ).

fof(f20772,plain,
    ( spl0_754
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),X8)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f6699,plain,
    ( spl0_399
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f19316,plain,
    ( spl0_733
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f19324,plain,
    ( spl0_735
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f20766,plain,
    ( spl0_753
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f20770,plain,
    ( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),X8)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)))
    | ~ spl0_390
    | ~ spl0_399
    | ~ spl0_733
    | ~ spl0_735
    | ~ spl0_753 ),
    inference(forward_demodulation,[],[f20769,f19337]) ).

fof(f19337,plain,
    ( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X1),X3))
    | ~ spl0_399
    | ~ spl0_733 ),
    inference(superposition,[],[f19317,f6700]) ).

fof(f6700,plain,
    ( ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6)
    | ~ spl0_399 ),
    inference(avatar_component_clause,[],[f6699]) ).

fof(f19317,plain,
    ( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7))
    | ~ spl0_733 ),
    inference(avatar_component_clause,[],[f19316]) ).

fof(f20769,plain,
    ( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),X8))
    | ~ spl0_390
    | ~ spl0_735
    | ~ spl0_753 ),
    inference(forward_demodulation,[],[f20767,f19747]) ).

fof(f19747,plain,
    ( ! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X3),X1)),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X3),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X2),X1))
    | ~ spl0_390
    | ~ spl0_735 ),
    inference(superposition,[],[f19325,f6639]) ).

fof(f19325,plain,
    ( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6))
    | ~ spl0_735 ),
    inference(avatar_component_clause,[],[f19324]) ).

fof(f20767,plain,
    ( ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)))
    | ~ spl0_753 ),
    inference(avatar_component_clause,[],[f20766]) ).

fof(f20768,plain,
    spl0_753,
    inference(avatar_split_clause,[],[f939,f20766]) ).

fof(f939,plain,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),
    inference(forward_demodulation,[],[f938,f514]) ).

fof(f514,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

fof(f938,plain,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))),
    inference(forward_demodulation,[],[f364,f259]) ).

fof(f259,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

fof(f364,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

fof(f20702,plain,
    spl0_752,
    inference(avatar_split_clause,[],[f333,f20700]) ).

fof(f20700,plain,
    ( spl0_752
  <=> ! [X6,X0,X8] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f333,axiom,
    ! [X0,X8,X6] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).

fof(f20698,plain,
    spl0_751,
    inference(avatar_split_clause,[],[f332,f20696]) ).

fof(f20696,plain,
    ( spl0_751
  <=> ! [X6,X0,X8] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f332,axiom,
    ! [X0,X8,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).

fof(f20579,plain,
    spl0_750,
    inference(avatar_split_clause,[],[f479,f20577]) ).

fof(f20577,plain,
    ( spl0_750
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
        | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
        | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f479,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
      | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
      | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

fof(f20552,plain,
    spl0_749,
    inference(avatar_split_clause,[],[f178,f20550]) ).

fof(f178,axiom,
    ! [X21,X0,X8,X6,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)),c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).

fof(f20508,plain,
    spl0_748,
    inference(avatar_split_clause,[],[f38,f20506]) ).

fof(f20506,plain,
    ( spl0_748
  <=> ! [X21,X20,X0,X6,X8] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
        | c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f38,axiom,
    ! [X21,X0,X8,X6,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)
      | c_Finite__Set_Osetsum(X21,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),c_Finite__Set_Osetsum(X21,X6,X0,X20)),c_Finite__Set_Osetsum(X21,X8,X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).

fof(f20410,plain,
    spl0_747,
    inference(avatar_split_clause,[],[f452,f20408]) ).

fof(f20408,plain,
    ( spl0_747
  <=> ! [X8,X20,X0,X6,X25,X7] :
        ( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
        | ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f452,axiom,
    ! [X0,X8,X6,X7,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
      | ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

fof(f20406,plain,
    ( spl0_746
    | ~ spl0_72
    | ~ spl0_737 ),
    inference(avatar_split_clause,[],[f20180,f19332,f1327,f20403]) ).

fof(f20180,plain,
    ( hBOOL(hAPP(v_G,hAPP(v_mgt__call,v_x)))
    | ~ spl0_72
    | ~ spl0_737 ),
    inference(superposition,[],[f1328,f19334]) ).

fof(f20363,plain,
    spl0_745,
    inference(avatar_split_clause,[],[f464,f20361]) ).

fof(f20361,plain,
    ( spl0_745
  <=> ! [X6,X0,X8] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f464,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__Un_0) ).

fof(f20359,plain,
    spl0_744,
    inference(avatar_split_clause,[],[f463,f20357]) ).

fof(f20357,plain,
    ( spl0_744
  <=> ! [X6,X0,X8] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f463,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__Un_0) ).

fof(f20240,plain,
    spl0_743,
    inference(avatar_split_clause,[],[f717,f20238]) ).

fof(f20238,plain,
    ( spl0_743
  <=> ! [X21,X20,X0,X6,X25,X8] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(X8,X20)
        | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_Fun_Oinj__on(X21,X8,X20,X0)
        | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(X8,X20)
        | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool))
        | ~ c_lessequals(c_Set_Oimage(X21,X8,X20,X0),X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f717,axiom,
    ! [X21,X0,X8,X6,X25,X20] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(X8,X20)
      | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | ~ c_Fun_Oinj__on(X21,X8,X20,X0)
      | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(X8,X20)
      | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool))
      | ~ c_lessequals(c_Set_Oimage(X21,X8,X20,X0),X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

fof(f20236,plain,
    spl0_742,
    inference(avatar_split_clause,[],[f478,f20234]) ).

fof(f20234,plain,
    ( spl0_742
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
        | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f478,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20)
      | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool)),X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

fof(f20087,plain,
    spl0_741,
    inference(avatar_split_clause,[],[f1001,f20085]) ).

fof(f20085,plain,
    ( spl0_741
  <=> ! [X16,X0,X14,X6,X1] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ hBOOL(c_in(X14,X6,X0))
        | hBOOL(c_in(X16,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f1001,plain,
    ! [X0,X1,X6,X16,X14] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
      | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1)) ),
    inference(forward_demodulation,[],[f319,f926]) ).

fof(f926,plain,
    ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_fequal(X14,X0),
    inference(forward_demodulation,[],[f774,f665]) ).

fof(f665,axiom,
    ! [X0,X26] : c_Collect(X26,X0) = X26,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).

fof(f774,axiom,
    ! [X0,X14] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(c_fequal(X14,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).

fof(f319,axiom,
    ! [X0,X1,X6,X16,X14] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X1))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).

fof(f20083,plain,
    spl0_740,
    inference(avatar_split_clause,[],[f1000,f20081]) ).

fof(f20081,plain,
    ( spl0_740
  <=> ! [X16,X0,X14,X6,X1] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
        | ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | ~ hBOOL(c_in(X14,X6,X0))
        | hBOOL(c_in(X16,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f1000,plain,
    ! [X0,X1,X6,X16,X14] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1))
      | ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1)) ),
    inference(forward_demodulation,[],[f320,f926]) ).

fof(f320,axiom,
    ! [X0,X1,X6,X16,X14] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X1))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,c_Set_Oinsert(X16,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),X0,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).

fof(f20079,plain,
    spl0_739,
    inference(avatar_split_clause,[],[f747,f20077]) ).

fof(f20077,plain,
    ( spl0_739
  <=> ! [X8,X20,X0,X6,X25,X7] :
        ( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
        | ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f747,axiom,
    ! [X0,X8,X6,X7,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X7,X0,X20)
      | ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

fof(f20074,plain,
    spl0_738,
    inference(avatar_split_clause,[],[f363,f20072]) ).

fof(f20072,plain,
    ( spl0_738
  <=> ! [X15,X0,X14,X16,X22] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X22)),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X22)),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f363,axiom,
    ! [X0,X16,X14,X15,X22] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X22)),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X22)),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f19335,plain,
    ( spl0_737
    | ~ spl0_2
    | ~ spl0_702 ),
    inference(avatar_split_clause,[],[f19031,f17547,f1008,f19332]) ).

fof(f19031,plain,
    ( v_G = c_Set_Oinsert(hAPP(v_mgt__call,v_x),v_G,t_a)
    | ~ spl0_2
    | ~ spl0_702 ),
    inference(resolution,[],[f17548,f1010]) ).

fof(f19330,plain,
    spl0_736,
    inference(avatar_split_clause,[],[f198,f19328]) ).

fof(f19328,plain,
    ( spl0_736
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f198,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

fof(f19326,plain,
    spl0_735,
    inference(avatar_split_clause,[],[f197,f19324]) ).

fof(f197,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X6)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

fof(f19322,plain,
    spl0_734,
    inference(avatar_split_clause,[],[f119,f19320]) ).

fof(f19320,plain,
    ( spl0_734
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f119,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)),X6) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

fof(f19318,plain,
    spl0_733,
    inference(avatar_split_clause,[],[f118,f19316]) ).

fof(f118,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

fof(f19036,plain,
    spl0_732,
    inference(avatar_split_clause,[],[f473,f19034]) ).

fof(f19034,plain,
    ( spl0_732
  <=> ! [X6,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X1,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f473,axiom,
    ! [X0,X1,X6] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X1,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).

fof(f19017,plain,
    spl0_731,
    inference(avatar_split_clause,[],[f472,f19015]) ).

fof(f19015,plain,
    ( spl0_731
  <=> ! [X6,X0,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X1,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f472,axiom,
    ! [X0,X1,X6] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X1,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).

fof(f19013,plain,
    spl0_730,
    inference(avatar_split_clause,[],[f453,f19011]) ).

fof(f19011,plain,
    ( spl0_730
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f453,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),c_Set_Oimage(X25,X6,X0,X20)),c_Set_Oimage(X25,X8,X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

fof(f19009,plain,
    spl0_729,
    inference(avatar_split_clause,[],[f329,f19007]) ).

fof(f19007,plain,
    ( spl0_729
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f329,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

fof(f19005,plain,
    spl0_728,
    inference(avatar_split_clause,[],[f328,f19003]) ).

fof(f19003,plain,
    ( spl0_728
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f328,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

fof(f18999,plain,
    spl0_727,
    inference(avatar_split_clause,[],[f766,f18997]) ).

fof(f18997,plain,
    ( spl0_727
  <=> ! [X20,X0,X6,X25,X2,X1] :
        ( X1 = X2
        | ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X0,X20),X20))
        | ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
        | hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f766,axiom,
    ! [X2,X0,X1,X6,X25,X20] :
      ( X1 = X2
      | ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X0,X20),X20))
      | ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
      | hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X1) != hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

fof(f18843,plain,
    spl0_726,
    inference(avatar_split_clause,[],[f991,f18841]) ).

fof(f991,plain,
    ! [X0,X6,X14,X25,X20] :
      ( c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20))
      | ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0)) ),
    inference(forward_demodulation,[],[f440,f926]) ).

fof(f440,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_Finite__Set_Osetsum(X25,X6,X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).

fof(f18839,plain,
    spl0_725,
    inference(avatar_split_clause,[],[f748,f18837]) ).

fof(f18837,plain,
    ( spl0_725
  <=> ! [X48,X20,X0,X6,X8] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X48,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X20,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X48,X20,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f748,axiom,
    ! [X48,X0,X8,X6,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X48,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X20,tc_fun(X0,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X48,X20,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).

fof(f18835,plain,
    spl0_724,
    inference(avatar_split_clause,[],[f426,f18833]) ).

fof(f18833,plain,
    ( spl0_724
  <=> ! [X16,X19,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hBOOL(c_in(X16,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X2))
        | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f426,axiom,
    ! [X2,X0,X6,X19,X16] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X16,X6,X0,X0),X2))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X19),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).

fof(f18831,plain,
    spl0_723,
    inference(avatar_split_clause,[],[f425,f18829]) ).

fof(f18829,plain,
    ( spl0_723
  <=> ! [X16,X19,X0,X6,X2] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | hBOOL(c_in(X16,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X2))
        | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f425,axiom,
    ! [X2,X0,X6,X19,X16] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | hBOOL(c_in(X16,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X16,X6,X0,X0),X2))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X19,c_Set_Oinsert(X16,X6,X0),X0,X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X19),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).

fof(f18827,plain,
    spl0_722,
    inference(avatar_split_clause,[],[f390,f18825]) ).

fof(f18825,plain,
    ( spl0_722
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f390,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f18823,plain,
    spl0_721,
    inference(avatar_split_clause,[],[f12,f18821]) ).

fof(f18821,plain,
    ( spl0_721
  <=> ! [X10,X9,X11,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f12,axiom,
    ! [X10,X0,X11,X9,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X10),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f18695,plain,
    ( ~ spl0_19
    | spl0_720
    | ~ spl0_126
    | ~ spl0_712 ),
    inference(avatar_split_clause,[],[f18442,f17675,f1632,f18693,f1093]) ).

fof(f18693,plain,
    ( spl0_720
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(c_fequal(X0,X1),X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f17675,plain,
    ( spl0_712
  <=> ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f18442,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(c_fequal(X0,X1),X1),tc_nat)
        | ~ class_Orderings_Olinorder(tc_nat) )
    | ~ spl0_126
    | ~ spl0_712 ),
    inference(resolution,[],[f17676,f1633]) ).

fof(f17676,plain,
    ( ! [X0,X1] : c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
    | ~ spl0_712 ),
    inference(avatar_component_clause,[],[f17675]) ).

fof(f18606,plain,
    ( spl0_719
    | ~ spl0_390
    | ~ spl0_634
    | ~ spl0_716 ),
    inference(avatar_split_clause,[],[f18510,f18507,f13536,f6638,f18604]) ).

fof(f18604,plain,
    ( spl0_719
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f13536,plain,
    ( spl0_634
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f18507,plain,
    ( spl0_716
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f18510,plain,
    ( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool))
    | ~ spl0_390
    | ~ spl0_634
    | ~ spl0_716 ),
    inference(forward_demodulation,[],[f18508,f13578]) ).

fof(f13578,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),X2),X3,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X0,tc_bool))),X1)
    | ~ spl0_390
    | ~ spl0_634 ),
    inference(superposition,[],[f13537,f6639]) ).

fof(f13537,plain,
    ( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool)))
    | ~ spl0_634 ),
    inference(avatar_component_clause,[],[f13536]) ).

fof(f18508,plain,
    ( ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7)
    | ~ spl0_716 ),
    inference(avatar_component_clause,[],[f18507]) ).

fof(f18518,plain,
    spl0_718,
    inference(avatar_split_clause,[],[f987,f18516]) ).

fof(f18516,plain,
    ( spl0_718
  <=> ! [X19,X20,X0,X6,X25,X2,X1] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0,X20),X2))
        | ~ hBOOL(c_in(X1,X6,X0))
        | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f987,plain,
    ! [X2,X0,X1,X19,X6,X25,X20] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0,X20),X2))
      | ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2))) ),
    inference(forward_demodulation,[],[f354,f926]) ).

fof(f354,axiom,
    ! [X2,X0,X1,X6,X19,X25,X20] :
      ( ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),hAPP(hAPP(X25,X1),X2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

fof(f18514,plain,
    spl0_717,
    inference(avatar_split_clause,[],[f937,f18512]) ).

fof(f18512,plain,
    ( spl0_717
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f937,plain,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),X8,tc_fun(X0,tc_bool)),
    inference(forward_demodulation,[],[f9,f151]) ).

fof(f151,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

fof(f9,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X8),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

fof(f18509,plain,
    spl0_716,
    inference(avatar_split_clause,[],[f8,f18507]) ).

fof(f8,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

fof(f18505,plain,
    spl0_715,
    inference(avatar_split_clause,[],[f3,f18503]) ).

fof(f18503,plain,
    ( spl0_715
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f3,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7),X8,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

fof(f18482,plain,
    spl0_714,
    inference(avatar_split_clause,[],[f998,f18480]) ).

fof(f18480,plain,
    ( spl0_714
  <=> ! [X0,X8,X6,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
        | hBOOL(c_in(X1,X8,X0))
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f998,plain,
    ! [X0,X1,X8,X6] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
      | hBOOL(c_in(X1,X8,X0))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    inference(forward_demodulation,[],[f471,f926]) ).

fof(f471,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X8,X0))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

fof(f18437,plain,
    spl0_713,
    inference(avatar_split_clause,[],[f522,f18435]) ).

fof(f18435,plain,
    ( spl0_713
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f522,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

fof(f17677,plain,
    ( ~ spl0_1
    | spl0_712
    | ~ spl0_334
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f9370,f8212,f4268,f17675,f1003]) ).

fof(f4268,plain,
    ( spl0_334
  <=> ! [X6,X20,X0,X25] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f8212,plain,
    ( spl0_483
  <=> ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f9370,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_Finite__Set_Ocard(c_fequal(X0,X1),X1),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
        | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
    | ~ spl0_334
    | ~ spl0_483 ),
    inference(superposition,[],[f4269,f8213]) ).

fof(f8213,plain,
    ( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1)
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f8212]) ).

fof(f4269,plain,
    ( ! [X0,X6,X25,X20] :
        ( c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat)
        | ~ c_Finite__Set_Ofinite(X6,X0) )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f4268]) ).

fof(f17585,plain,
    spl0_711,
    inference(avatar_split_clause,[],[f996,f17583]) ).

fof(f17583,plain,
    ( spl0_711
  <=> ! [X0,X8,X6,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
        | ~ hBOOL(c_in(X1,X6,X0))
        | hBOOL(c_in(X1,X8,X0))
        | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f996,plain,
    ! [X0,X1,X8,X6] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
      | ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    inference(forward_demodulation,[],[f352,f926]) ).

fof(f352,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

fof(f17581,plain,
    spl0_710,
    inference(avatar_split_clause,[],[f995,f17579]) ).

fof(f17579,plain,
    ( spl0_710
  <=> ! [X0,X8,X6,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
        | ~ hBOOL(c_in(X1,X6,X0))
        | hBOOL(c_in(X1,X8,X0))
        | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f995,plain,
    ! [X0,X1,X8,X6] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
      | ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    inference(forward_demodulation,[],[f351,f926]) ).

fof(f351,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

fof(f17577,plain,
    spl0_709,
    inference(avatar_split_clause,[],[f920,f17575]) ).

fof(f920,plain,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0)) ),
    inference(definition_unfolding,[],[f438,f57,f57]) ).

fof(f57,axiom,
    ! [X0,X19,X6,X25,X20] : c_Finite__Set_Ofold(X25,X19,X6,X20,X0) = c_The(c_Finite__Set_Ofold__graph(X25,X19,X6,X20,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__def_0) ).

fof(f438,axiom,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).

fof(f17573,plain,
    spl0_708,
    inference(avatar_split_clause,[],[f919,f17571]) ).

fof(f919,plain,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0)) ),
    inference(definition_unfolding,[],[f444,f57,f57]) ).

fof(f444,axiom,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,c_Set_Oinsert(X14,X6,X0),X0,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).

fof(f17569,plain,
    spl0_707,
    inference(avatar_split_clause,[],[f721,f17567]) ).

fof(f17567,plain,
    ( spl0_707
  <=> ! [X30,X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f721,axiom,
    ! [X0,X8,X6,X7,X30] :
      ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

fof(f17565,plain,
    spl0_706,
    inference(avatar_split_clause,[],[f515,f17563]) ).

fof(f17563,plain,
    ( spl0_706
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f515,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X8,X7,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

fof(f17561,plain,
    spl0_705,
    inference(avatar_split_clause,[],[f336,f17559]) ).

fof(f17559,plain,
    ( spl0_705
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f336,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

fof(f17557,plain,
    spl0_704,
    inference(avatar_split_clause,[],[f335,f17555]) ).

fof(f17555,plain,
    ( spl0_704
  <=> ! [X0,X6,X8,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f335,axiom,
    ! [X0,X8,X6,X7] : c_HOL_Ominus__class_Ominus(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),c_HOL_Ominus__class_Ominus(X6,X7,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

fof(f17553,plain,
    spl0_703,
    inference(avatar_split_clause,[],[f327,f17551]) ).

fof(f327,axiom,
    ! [X0,X8,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X20,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

fof(f17549,plain,
    ( spl0_702
    | ~ spl0_185
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f8659,f8149,f2028,f17547]) ).

fof(f8149,plain,
    ( spl0_473
  <=> ! [X0] :
        ( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
        | ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f8659,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | v_G = c_Set_Oinsert(hAPP(v_mgt__call,X0),v_G,t_a) )
    | ~ spl0_185
    | ~ spl0_473 ),
    inference(resolution,[],[f8150,f2029]) ).

fof(f8150,plain,
    ( ! [X0] :
        ( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
        | ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
    | ~ spl0_473 ),
    inference(avatar_component_clause,[],[f8149]) ).

fof(f17545,plain,
    spl0_701,
    inference(avatar_split_clause,[],[f150,f17543]) ).

fof(f17543,plain,
    ( spl0_701
  <=> ! [X30,X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f150,axiom,
    ! [X0,X8,X6,X7,X30] :
      ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X30,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X7),X30),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

fof(f15926,plain,
    spl0_700,
    inference(avatar_split_clause,[],[f994,f15924]) ).

fof(f15924,plain,
    ( spl0_700
  <=> ! [X0,X6,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_fequal(X1,X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ hBOOL(c_in(X2,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f994,plain,
    ! [X2,X0,X1,X6] :
      ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_fequal(X1,X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | ~ hBOOL(c_in(X2,X6,X0)) ),
    inference(forward_demodulation,[],[f993,f926]) ).

fof(f993,plain,
    ! [X2,X0,X1,X6] :
      ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | ~ hBOOL(c_in(X2,X6,X0)) ),
    inference(forward_demodulation,[],[f992,f934]) ).

fof(f934,plain,
    ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_fequal(X14,X0),tc_fun(X0,tc_bool)),
    inference(forward_demodulation,[],[f787,f926]) ).

fof(f787,axiom,
    ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

fof(f992,plain,
    ! [X2,X0,X1,X6] :
      ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),c_fequal(X2,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | ~ hBOOL(c_in(X2,X6,X0)) ),
    inference(forward_demodulation,[],[f485,f926]) ).

fof(f485,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | ~ hBOOL(c_in(X2,X6,X0))
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).

fof(f15922,plain,
    spl0_699,
    inference(avatar_split_clause,[],[f988,f15920]) ).

fof(f15920,plain,
    ( spl0_699
  <=> ! [X20,X0,X14,X6,X25] :
        ( hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
        | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f988,plain,
    ! [X0,X6,X14,X25,X20] :
      ( hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
      | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
    inference(forward_demodulation,[],[f770,f926]) ).

fof(f770,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20)
      | hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

fof(f15918,plain,
    spl0_698,
    inference(avatar_split_clause,[],[f959,f15916]) ).

fof(f959,plain,
    ! [X2,X0,X1,X6,X25,X20] :
      ( c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X20),tc_fun(X20,tc_bool)),X20,X0),X0)
      | ~ hBOOL(c_in(X1,X6,X20)) ),
    inference(forward_demodulation,[],[f769,f926]) ).

fof(f769,axiom,
    ! [X2,X0,X1,X6,X25,X20] :
      ( ~ hBOOL(c_in(X1,X6,X20))
      | c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) = c_Set_Oinsert(X2,c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),tc_fun(X20,tc_bool)),X20,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

fof(f15914,plain,
    ( ~ spl0_696
    | spl0_697
    | ~ spl0_140
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f6654,f6571,f1691,f15912,f15908]) ).

fof(f15908,plain,
    ( spl0_696
  <=> class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f15912,plain,
    ( spl0_697
  <=> ! [X0] :
        ( c_Finite__Set_Ofinite(X0,t_a)
        | c_lessequals(v_G,X0,tc_fun(t_a,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f6571,plain,
    ( spl0_388
  <=> ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
        | c_Finite__Set_Ofinite(X0,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f6654,plain,
    ( ! [X0] :
        ( c_Finite__Set_Ofinite(X0,t_a)
        | c_lessequals(v_G,X0,tc_fun(t_a,tc_bool))
        | ~ class_Orderings_Olinorder(tc_fun(t_a,tc_bool)) )
    | ~ spl0_140
    | ~ spl0_388 ),
    inference(resolution,[],[f6572,f1692]) ).

fof(f6572,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
        | c_Finite__Set_Ofinite(X0,t_a) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f6571]) ).

fof(f15906,plain,
    spl0_695,
    inference(avatar_split_clause,[],[f541,f15904]) ).

fof(f15904,plain,
    ( spl0_695
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f541,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

fof(f15902,plain,
    spl0_694,
    inference(avatar_split_clause,[],[f540,f15900]) ).

fof(f15900,plain,
    ( spl0_694
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f540,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),X7) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

fof(f15898,plain,
    spl0_693,
    inference(avatar_split_clause,[],[f474,f15896]) ).

fof(f15896,plain,
    ( spl0_693
  <=> ! [X6,X0,X8] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X8,X0)
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X8),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f474,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X8,X0)
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X8),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).

fof(f15894,plain,
    spl0_692,
    inference(avatar_split_clause,[],[f396,f15892]) ).

fof(f15892,plain,
    ( spl0_692
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f396,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).

fof(f15890,plain,
    spl0_691,
    inference(avatar_split_clause,[],[f371,f15888]) ).

fof(f15888,plain,
    ( spl0_691
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f371,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).

fof(f15886,plain,
    spl0_690,
    inference(avatar_split_clause,[],[f307,f15884]) ).

fof(f15884,plain,
    ( spl0_690
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f307,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

fof(f15882,plain,
    spl0_689,
    inference(avatar_split_clause,[],[f306,f15880]) ).

fof(f15880,plain,
    ( spl0_689
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f306,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

fof(f15878,plain,
    spl0_688,
    inference(avatar_split_clause,[],[f292,f15876]) ).

fof(f292,axiom,
    ! [X0,X14,X25,X20,X33] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X20)
      | ~ c_Finite__Set_Ofinite(X33,X0)
      | hBOOL(c_in(X14,X33,X0))
      | c_Finite__Set_Osetsum(X25,c_Set_Oinsert(X14,X33,X0),X0,X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),hAPP(X25,X14)),c_Finite__Set_Osetsum(X25,X33,X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).

fof(f15874,plain,
    spl0_687,
    inference(avatar_split_clause,[],[f275,f15872]) ).

fof(f15872,plain,
    ( spl0_687
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f275,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X14,X16,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X15,X17,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greaterThanAtMost_0) ).

fof(f15870,plain,
    spl0_686,
    inference(avatar_split_clause,[],[f192,f15868]) ).

fof(f15868,plain,
    ( spl0_686
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f192,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X15),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastLessThan_0) ).

fof(f15862,plain,
    spl0_685,
    inference(avatar_split_clause,[],[f157,f15860]) ).

fof(f15860,plain,
    ( spl0_685
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f157,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).

fof(f15858,plain,
    spl0_684,
    inference(avatar_split_clause,[],[f23,f15856]) ).

fof(f15856,plain,
    ( spl0_684
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f23,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

fof(f15854,plain,
    spl0_683,
    inference(avatar_split_clause,[],[f22,f15852]) ).

fof(f15852,plain,
    ( spl0_683
  <=> ! [X0,X6,X8,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f22,axiom,
    ! [X0,X8,X6,X7] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

fof(f15762,plain,
    ( ~ spl0_31
    | spl0_682
    | ~ spl0_127
    | ~ spl0_639 ),
    inference(avatar_split_clause,[],[f14095,f13556,f1636,f15760,f1153]) ).

fof(f1153,plain,
    ( spl0_31
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f15760,plain,
    ( spl0_682
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(v_U,X0),hAPP(c_fequal(v_x,tc_Com_Opname),X0),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f13556,plain,
    ( spl0_639
  <=> ! [X0] : c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f14095,plain,
    ( ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(v_U,X0),hAPP(c_fequal(v_x,tc_Com_Opname),X0),tc_bool)
        | ~ class_Orderings_Opreorder(tc_bool) )
    | ~ spl0_127
    | ~ spl0_639 ),
    inference(resolution,[],[f13557,f1637]) ).

fof(f13557,plain,
    ( ! [X0] : c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool)
    | ~ spl0_639 ),
    inference(avatar_component_clause,[],[f13556]) ).

fof(f15687,plain,
    spl0_681,
    inference(avatar_split_clause,[],[f404,f15685]) ).

fof(f15685,plain,
    ( spl0_681
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f404,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).

fof(f15680,plain,
    spl0_680,
    inference(avatar_split_clause,[],[f379,f15678]) ).

fof(f15678,plain,
    ( spl0_680
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f379,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).

fof(f15676,plain,
    spl0_679,
    inference(avatar_split_clause,[],[f299,f15674]) ).

fof(f15674,plain,
    ( spl0_679
  <=> ! [X19,X0,X20,X6,X25,X2,X1] :
        ( hBOOL(c_in(X1,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X2))
        | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Set_Oinsert(X1,X6,X0),X0,X20),hAPP(hAPP(X25,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f299,axiom,
    ! [X2,X0,X1,X6,X19,X25,X20] :
      ( hBOOL(c_in(X1,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X2))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Set_Oinsert(X1,X6,X0),X0,X20),hAPP(hAPP(X25,X1),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).

fof(f15672,plain,
    spl0_678,
    inference(avatar_split_clause,[],[f286,f15670]) ).

fof(f15670,plain,
    ( spl0_678
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f286,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X19)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f15668,plain,
    spl0_677,
    inference(avatar_split_clause,[],[f285,f15666]) ).

fof(f15666,plain,
    ( spl0_677
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f285,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f15664,plain,
    spl0_676,
    inference(avatar_split_clause,[],[f284,f15662]) ).

fof(f15662,plain,
    ( spl0_676
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f284,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X15)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f15660,plain,
    spl0_675,
    inference(avatar_split_clause,[],[f261,f15658]) ).

fof(f15658,plain,
    ( spl0_675
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f261,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).

fof(f15656,plain,
    spl0_674,
    inference(avatar_split_clause,[],[f200,f15654]) ).

fof(f15654,plain,
    ( spl0_674
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X19),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f200,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X19),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

fof(f15652,plain,
    spl0_673,
    inference(avatar_split_clause,[],[f199,f15650]) ).

fof(f15650,plain,
    ( spl0_673
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f199,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

fof(f15648,plain,
    spl0_672,
    inference(avatar_split_clause,[],[f168,f15646]) ).

fof(f15646,plain,
    ( spl0_672
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X19),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f168,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X19),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).

fof(f15644,plain,
    spl0_671,
    inference(avatar_split_clause,[],[f167,f15642]) ).

fof(f15642,plain,
    ( spl0_671
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f167,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).

fof(f15582,plain,
    spl0_670,
    inference(avatar_split_clause,[],[f160,f15580]) ).

fof(f15580,plain,
    ( spl0_670
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X19),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f160,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)),X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X19),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).

fof(f15578,plain,
    spl0_669,
    inference(avatar_split_clause,[],[f117,f15576]) ).

fof(f15576,plain,
    ( spl0_669
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f117,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

fof(f15574,plain,
    spl0_668,
    inference(avatar_split_clause,[],[f116,f15572]) ).

fof(f15572,plain,
    ( spl0_668
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X19),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f116,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X19),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

fof(f15570,plain,
    spl0_667,
    inference(avatar_split_clause,[],[f71,f15568]) ).

fof(f15568,plain,
    ( spl0_667
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X15,X14,X0)
        | ~ c_lessequals(X15,X17,X0)
        | ~ c_lessequals(X15,X14,X0)
        | ~ c_lessequals(X16,X17,X0)
        | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f71,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X15,X14,X0)
      | ~ c_lessequals(X15,X17,X0)
      | ~ c_lessequals(X15,X14,X0)
      | ~ c_lessequals(X16,X17,X0)
      | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).

fof(f15566,plain,
    spl0_666,
    inference(avatar_split_clause,[],[f70,f15564]) ).

fof(f15564,plain,
    ( spl0_666
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X16,X17,X0)
        | ~ c_lessequals(X15,X17,X0)
        | ~ c_lessequals(X15,X14,X0)
        | ~ c_lessequals(X16,X17,X0)
        | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f70,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X16,X17,X0)
      | ~ c_lessequals(X15,X17,X0)
      | ~ c_lessequals(X15,X14,X0)
      | ~ c_lessequals(X16,X17,X0)
      | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).

fof(f14569,plain,
    spl0_665,
    inference(avatar_split_clause,[],[f922,f14567]) ).

fof(f14567,plain,
    ( spl0_665
  <=> ! [X6,X0,X14] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X14,X6,X0))
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f922,plain,
    ! [X0,X6,X14] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X14,X6,X0))
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f326,f57]) ).

fof(f326,axiom,
    ! [X0,X6,X14] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X14,X6,X0))
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X0),X14,X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).

fof(f14562,plain,
    spl0_664,
    inference(avatar_split_clause,[],[f921,f14560]) ).

fof(f14560,plain,
    ( spl0_664
  <=> ! [X6,X0,X14] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X14,X6,X0))
        | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f921,plain,
    ! [X0,X6,X14] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X14,X6,X0))
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f325,f57]) ).

fof(f325,axiom,
    ! [X0,X6,X14] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X14,X6,X0))
      | hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X0),X0),c_Set_Oinsert(X14,X6,X0)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X0),X14,X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).

fof(f14558,plain,
    spl0_663,
    inference(avatar_split_clause,[],[f676,f14556]) ).

fof(f676,axiom,
    ! [X28,X0,X54,X6,X20] :
      ( ~ hBOOL(c_in(X28,X54,X0))
      | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),hAPP(X6,X28)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X0,tc_fun(X20,tc_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).

fof(f14554,plain,
    spl0_662,
    inference(avatar_split_clause,[],[f636,f14552]) ).

fof(f636,axiom,
    ! [X0,X8,X6,X25,X20] : c_Set_Oimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X20,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oimage(X25,X6,X20,X0)),c_Set_Oimage(X25,X8,X20,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

fof(f14550,plain,
    spl0_661,
    inference(avatar_split_clause,[],[f506,f14548]) ).

fof(f14548,plain,
    ( spl0_661
  <=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f506,axiom,
    ! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

fof(f14546,plain,
    spl0_660,
    inference(avatar_split_clause,[],[f468,f14544]) ).

fof(f14544,plain,
    ( spl0_660
  <=> ! [X34,X0,X6,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_lessequals(X1,X34,X0)
        | ~ hBOOL(c_in(X34,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | ~ c_lessequals(X1,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f468,axiom,
    ! [X0,X1,X6,X34] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_lessequals(X1,X34,X0)
      | ~ hBOOL(c_in(X34,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | ~ c_lessequals(X1,hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

fof(f14542,plain,
    spl0_659,
    inference(avatar_split_clause,[],[f467,f14540]) ).

fof(f14540,plain,
    ( spl0_659
  <=> ! [X34,X0,X6,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_lessequals(X34,X1,X0)
        | ~ hBOOL(c_in(X34,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f467,axiom,
    ! [X0,X1,X6,X34] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_lessequals(X34,X1,X0)
      | ~ hBOOL(c_in(X34,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).

fof(f14538,plain,
    spl0_658,
    inference(avatar_split_clause,[],[f446,f14536]) ).

fof(f14536,plain,
    ( spl0_658
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X4,X0)
        | ~ c_lessequals(X4,X5,X0)
        | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f446,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X4,X0)
      | ~ c_lessequals(X4,X5,X0)
      | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).

fof(f14534,plain,
    spl0_657,
    inference(avatar_split_clause,[],[f445,f14532]) ).

fof(f14532,plain,
    ( spl0_657
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X4,X0)
        | ~ c_lessequals(X4,X5,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f445,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X4,X0)
      | ~ c_lessequals(X4,X5,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).

fof(f14530,plain,
    spl0_656,
    inference(avatar_split_clause,[],[f416,f14528]) ).

fof(f14528,plain,
    ( spl0_656
  <=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f416,axiom,
    ! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X20,tc_bool)),X6),X8),X0,X20) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,X6,X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

fof(f14526,plain,
    spl0_655,
    inference(avatar_split_clause,[],[f324,f14524]) ).

fof(f324,axiom,
    ! [X0,X1,X6,X34] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_HOL_Oord__class_Oless(X34,X1,X0)
      | ~ hBOOL(c_in(X34,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_HOL_Oord__class_Oless(hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).

fof(f14522,plain,
    ( spl0_654
    | ~ spl0_109
    | ~ spl0_622 ),
    inference(avatar_split_clause,[],[f14228,f12656,f1482,f14520]) ).

fof(f14520,plain,
    ( spl0_654
  <=> ! [X0] :
        ( hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f12656,plain,
    ( spl0_622
  <=> ! [X0] :
        ( hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f14228,plain,
    ( ! [X0] :
        ( hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) )
    | ~ spl0_109
    | ~ spl0_622 ),
    inference(resolution,[],[f12657,f1483]) ).

fof(f12657,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname))
        | hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
    | ~ spl0_622 ),
    inference(avatar_component_clause,[],[f12656]) ).

fof(f14518,plain,
    spl0_653,
    inference(avatar_split_clause,[],[f323,f14516]) ).

fof(f14516,plain,
    ( spl0_653
  <=> ! [X34,X0,X6,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_HOL_Oord__class_Oless(X1,X34,X0)
        | ~ hBOOL(c_in(X34,X6,X0))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f323,axiom,
    ! [X0,X1,X6,X34] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_HOL_Oord__class_Oless(X1,X34,X0)
      | ~ hBOOL(c_in(X34,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | ~ c_HOL_Oord__class_Oless(X1,hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).

fof(f14514,plain,
    spl0_652,
    inference(avatar_split_clause,[],[f318,f14512]) ).

fof(f14512,plain,
    ( spl0_652
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X4,X0)
        | ~ c_lessequals(X4,X5,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f318,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X4,X0)
      | ~ c_lessequals(X4,X5,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

fof(f14510,plain,
    spl0_651,
    inference(avatar_split_clause,[],[f317,f14508]) ).

fof(f14508,plain,
    ( spl0_651
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X3,X4,X0)
        | ~ c_lessequals(X4,X5,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f317,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X4,X0)
      | ~ c_lessequals(X4,X5,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).

fof(f14152,plain,
    spl0_650,
    inference(avatar_split_clause,[],[f694,f14150]) ).

fof(f14150,plain,
    ( spl0_650
  <=> ! [X30,X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X30,X8,tc_fun(X0,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X30,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f694,axiom,
    ! [X0,X8,X6,X7,X30] :
      ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X30,X8,tc_fun(X0,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X7,X30,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

fof(f14148,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f639,f14146]) ).

fof(f14146,plain,
    ( spl0_649
  <=> ! [X21,X20,X0,X25,X1] :
        ( c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20)
        | hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) != hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f639,axiom,
    ! [X21,X0,X1,X25,X20] :
      ( c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20)
      | hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) != hAPP(X21,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_1) ).

fof(f14144,plain,
    spl0_648,
    inference(avatar_split_clause,[],[f554,f14142]) ).

fof(f14142,plain,
    ( spl0_648
  <=> ! [X20,X0,X6,X25,X8] :
        ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f554,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),c_Set_Oimage(X25,X8,X0,X20),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

fof(f14140,plain,
    spl0_647,
    inference(avatar_split_clause,[],[f542,f14138]) ).

fof(f542,axiom,
    ! [X0,X8,X6,X25,X20] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X25,X6,X20,X0),c_Set_Oimage(X25,X8,X20,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X20,X0),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

fof(f14136,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f502,f14134]) ).

fof(f14134,plain,
    ( spl0_646
  <=> ! [X8,X20,X0,X6,X25] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
        | c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f502,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
      | c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

fof(f14132,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f462,f14130]) ).

fof(f14130,plain,
    ( spl0_645
  <=> ! [X6,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f462,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).

fof(f14128,plain,
    spl0_644,
    inference(avatar_split_clause,[],[f461,f14126]) ).

fof(f14126,plain,
    ( spl0_644
  <=> ! [X6,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f461,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X1,X6,X0)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).

fof(f14124,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f305,f14122]) ).

fof(f14122,plain,
    ( spl0_643
  <=> ! [X0,X14,X6,X8] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f305,axiom,
    ! [X0,X8,X6,X14] :
      ( ~ hBOOL(c_in(X14,X6,X0))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

fof(f14093,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f304,f14091]) ).

fof(f14091,plain,
    ( spl0_642
  <=> ! [X0,X14,X8,X7] :
        ( ~ hBOOL(c_in(X14,X7,X0))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f304,axiom,
    ! [X0,X8,X7,X14] :
      ( ~ hBOOL(c_in(X14,X7,X0))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

fof(f13566,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f936,f13564]) ).

fof(f13564,plain,
    ( spl0_641
  <=> ! [X20,X0,X14,X25,X8] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_fequal(X14,X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f936,plain,
    ! [X0,X8,X14,X25,X20] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_fequal(X14,X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
    inference(forward_demodulation,[],[f620,f926]) ).

fof(f620,axiom,
    ! [X0,X8,X14,X25,X20] : c_Set_Ovimage(X25,c_Set_Oinsert(X14,X8,X20),X0,X20) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Ovimage(X25,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X0,X20)),c_Set_Ovimage(X25,X8,X0,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

fof(f13562,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f924,f13560]) ).

fof(f13560,plain,
    ( spl0_640
  <=> ! [X0,X14,X6,X16] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X14,X6,X0))
        | c_lessequals(c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f924,plain,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ),
    inference(definition_unfolding,[],[f389,f57]) ).

fof(f389,axiom,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X16,X6,X0,X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).

fof(f13558,plain,
    ( spl0_639
    | ~ spl0_37
    | ~ spl0_369
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12378,f11986,f5988,f1183,f13556]) ).

fof(f11986,plain,
    ( spl0_584
  <=> c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f12378,plain,
    ( ! [X0] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(c_fequal(v_x,tc_Com_Opname),X0),hAPP(v_U,X0),tc_bool) )
    | ~ spl0_369
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f5989]) ).

fof(f11988,plain,
    ( c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f11986]) ).

fof(f13554,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f923,f13552]) ).

fof(f13552,plain,
    ( spl0_638
  <=> ! [X0,X14,X6,X16] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X14,X6,X0))
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f923,plain,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0),X0) ),
    inference(definition_unfolding,[],[f460,f57]) ).

fof(f460,axiom,
    ! [X0,X6,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X16,X6,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).

fof(f13550,plain,
    spl0_637,
    inference(avatar_split_clause,[],[f710,f13548]) ).

fof(f710,axiom,
    ! [X0,X8,X6,X14,X20] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X14,X6,X20),X8,X20,tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),hAPP(X8,X14)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).

fof(f13546,plain,
    spl0_636,
    inference(avatar_split_clause,[],[f709,f13544]) ).

fof(f13544,plain,
    ( spl0_636
  <=> ! [X48,X0,X49] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X49,X0)
        | ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
        | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X49),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X48),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f709,axiom,
    ! [X48,X0,X49] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X49,X0)
      | ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
      | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X49),hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X48),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

fof(f13542,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f543,f13540]) ).

fof(f13540,plain,
    ( spl0_635
  <=> ! [X48,X0,X49] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X49,X0)
        | ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
        | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X48),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X49),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f543,axiom,
    ! [X48,X0,X49] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X49,X0)
      | ~ c_lessequals(X48,X49,tc_fun(X0,tc_bool))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X48
      | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X48),hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X49),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

fof(f13538,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f151,f13536]) ).

fof(f13374,plain,
    ( spl0_633
    | ~ spl0_378
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12373,f11986,f6030,f13372]) ).

fof(f13372,plain,
    ( spl0_633
  <=> ! [X0,X1] :
        ( c_Fun_Oinj__on(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname,X1)
        | ~ c_Fun_Oinj__on(X0,v_U,tc_Com_Opname,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f12373,plain,
    ( ! [X0,X1] :
        ( c_Fun_Oinj__on(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname,X1)
        | ~ c_Fun_Oinj__on(X0,v_U,tc_Com_Opname,X1) )
    | ~ spl0_378
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f6031]) ).

fof(f13238,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f964,f13236]) ).

fof(f13236,plain,
    ( spl0_632
  <=> ! [X20,X0,X14,X6,X25] :
        ( ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
        | ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f964,plain,
    ! [X0,X6,X14,X25,X20] :
      ( ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0,X20),X20))
      | ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
    inference(forward_demodulation,[],[f771,f926]) ).

fof(f771,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20)
      | ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0,X20),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

fof(f13234,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f684,f13232]) ).

fof(f13232,plain,
    ( spl0_631
  <=> ! [X17,X4,X20,X0,X14,X16,X15] :
        ( X14 = X15
        | c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X14,X16,X0,X20),X15,X17,X0,X20) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X15,X17,X0,X20),X14,X16,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f684,axiom,
    ! [X0,X16,X14,X4,X17,X15,X20] :
      ( X14 = X15
      | c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X14,X16,X0,X20),X15,X17,X0,X20) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X4,X15,X17,X0,X20),X14,X16,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

fof(f13230,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f672,f13228]) ).

fof(f672,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( X6 = X8
      | c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20)
      | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

fof(f13226,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f552,f13224]) ).

fof(f13224,plain,
    ( spl0_629
  <=> ! [X51,X20,X0,X6,X25] :
        ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_lessequals(X51,X6,tc_fun(X0,tc_bool))
        | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),c_Set_Oimage(X25,X51,X0,X20),X20,X0) = X51 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f552,axiom,
    ! [X51,X0,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | ~ c_lessequals(X51,X6,tc_fun(X0,tc_bool))
      | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(X6,X25,X0,X20),c_Set_Oimage(X25,X51,X0,X20),X20,X0) = X51 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).

fof(f13222,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f508,f13220]) ).

fof(f13220,plain,
    ( spl0_628
  <=> ! [X47,X20,X0,X25] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),c_Set_Oimage(X25,X47,X0,X20),X20,X0) = X47 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f508,axiom,
    ! [X0,X47,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),c_Set_Oimage(X25,X47,X0,X20),X20,X0) = X47 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).

fof(f13218,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f477,f13216]) ).

fof(f13216,plain,
    ( spl0_627
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X20)
        | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X20),tc_nat)
        | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f477,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Finite__Set_Ofinite(X8,X20)
      | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X20),tc_nat)
      | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X20),X8,tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).

fof(f13214,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f439,f13212]) ).

fof(f13212,plain,
    ( spl0_626
  <=> ! [X0,X14,X6,X8] : c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X6,X0)),c_Set_Oinsert(X14,X8,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f439,axiom,
    ! [X0,X8,X6,X14] : c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X6,X0)),c_Set_Oinsert(X14,X8,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

fof(f13210,plain,
    ( spl0_625
    | ~ spl0_376
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12372,f11986,f6022,f13207]) ).

fof(f13207,plain,
    ( spl0_625
  <=> v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),c_fequal(v_x,tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f6022,plain,
    ( spl0_376
  <=> ! [X6,X0,X8] :
        ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f12372,plain,
    ( v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),c_fequal(v_x,tc_Com_Opname))
    | ~ spl0_376
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f6023]) ).

fof(f6023,plain,
    ( ! [X0,X8,X6] :
        ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 )
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f6022]) ).

fof(f13205,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f395,f13203]) ).

fof(f13203,plain,
    ( spl0_624
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_HOL_Oord__class_Oless(X15,X14,X0)
        | c_HOL_Oord__class_Oless(X16,X17,X0)
        | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f395,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_HOL_Oord__class_Oless(X15,X14,X0)
      | c_HOL_Oord__class_Oless(X16,X17,X0)
      | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).

fof(f12965,plain,
    ( spl0_623
    | ~ spl0_375
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12371,f11986,f6018,f12962]) ).

fof(f12962,plain,
    ( spl0_623
  <=> v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_fequal(v_x,tc_Com_Opname)),v_U) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f6018,plain,
    ( spl0_375
  <=> ! [X6,X0,X8] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f12371,plain,
    ( v_U = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_fequal(v_x,tc_Com_Opname)),v_U)
    | ~ spl0_375
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f6019]) ).

fof(f6019,plain,
    ( ! [X0,X8,X6] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f6018]) ).

fof(f12658,plain,
    ( spl0_622
    | ~ spl0_368
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12370,f11986,f5984,f12656]) ).

fof(f5984,plain,
    ( spl0_368
  <=> ! [X0,X6,X8,X46] :
        ( ~ hBOOL(c_in(X46,X6,X0))
        | hBOOL(c_in(X46,X8,X0))
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f12370,plain,
    ( ! [X0] :
        ( hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | ~ hBOOL(c_in(X0,c_fequal(v_x,tc_Com_Opname),tc_Com_Opname)) )
    | ~ spl0_368
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f5985]) ).

fof(f5985,plain,
    ( ! [X0,X46,X8,X6] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | hBOOL(c_in(X46,X8,X0))
        | ~ hBOOL(c_in(X46,X6,X0)) )
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f5984]) ).

fof(f12553,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f756,f12551]) ).

fof(f12551,plain,
    ( spl0_621
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f756,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_HOL_Ominus__class_Ominus(X8,c_HOL_Ominus__class_Ominus(X7,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

fof(f12549,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f675,f12547]) ).

fof(f12547,plain,
    ( spl0_620
  <=> ! [X8,X54,X20,X0,X6,X1] :
        ( ~ hBOOL(c_in(X1,X54,X20))
        | c_lessequals(hAPP(X6,X1),X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X20,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f675,axiom,
    ! [X0,X1,X54,X6,X8,X20] :
      ( ~ hBOOL(c_in(X1,X54,X20))
      | c_lessequals(hAPP(X6,X1),X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X54,X6,X20,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).

fof(f12545,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f662,f12543]) ).

fof(f12543,plain,
    ( spl0_619
  <=> ! [X20,X0,X6,X25,X8] : c_Set_Ovimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X25,X6,X0,X20),c_Set_Ovimage(X25,X8,X0,X20),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f662,axiom,
    ! [X0,X8,X6,X25,X20] : c_Set_Ovimage(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X20,tc_bool)),X0,X20) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(X25,X6,X0,X20),c_Set_Ovimage(X25,X8,X0,X20),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

fof(f12541,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f646,f12539]) ).

fof(f12539,plain,
    ( spl0_618
  <=> ! [X20,X8,X0,X6,X1] :
        ( ~ hBOOL(c_in(X1,X6,X20))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X8,X1)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f646,axiom,
    ! [X0,X1,X8,X6,X20] :
      ( ~ hBOOL(c_in(X1,X6,X20))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X8,X1)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X20,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).

fof(f12533,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f625,f12531]) ).

fof(f12531,plain,
    ( spl0_617
  <=> ! [X6,X25,X0] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Fun_Oinj__on(X25,X6,X0,X0)
        | c_Set_Oimage(X25,X6,X0,X0) = X6
        | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X0),X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f625,axiom,
    ! [X0,X6,X25] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Fun_Oinj__on(X25,X6,X0,X0)
      | c_Set_Oimage(X25,X6,X0,X0) = X6
      | ~ c_lessequals(c_Set_Oimage(X25,X6,X0,X0),X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

fof(f12529,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f563,f12527]) ).

fof(f12527,plain,
    ( spl0_616
  <=> ! [X34,X0,X6,X25,X1,X20] :
        ( X1 = X34
        | ~ hBOOL(c_in(X34,X6,X0))
        | ~ hBOOL(c_in(X1,X6,X0))
        | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | hAPP(X25,X1) != hAPP(X25,X34) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f563,axiom,
    ! [X0,X1,X6,X34,X25,X20] :
      ( X1 = X34
      | ~ hBOOL(c_in(X34,X6,X0))
      | ~ hBOOL(c_in(X1,X6,X0))
      | ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | hAPP(X25,X1) != hAPP(X25,X34) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

fof(f12525,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f539,f12523]) ).

fof(f12523,plain,
    ( spl0_615
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f539,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

fof(f12521,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f538,f12519]) ).

fof(f12519,plain,
    ( spl0_614
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f538,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

fof(f12517,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f537,f12515]) ).

fof(f12515,plain,
    ( spl0_613
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f537,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

fof(f12513,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f536,f12511]) ).

fof(f12511,plain,
    ( spl0_612
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f536,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

fof(f12509,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f532,f12507]) ).

fof(f12507,plain,
    ( spl0_611
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f532,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

fof(f12505,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f457,f12503]) ).

fof(f12503,plain,
    ( spl0_610
  <=> ! [X20,X0,X6,X25] : c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f457,axiom,
    ! [X0,X6,X25,X20] : c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

fof(f12501,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f443,f12499]) ).

fof(f12499,plain,
    ( spl0_609
  <=> ! [X0,X8,X6,X1] :
        ( hBOOL(c_in(X1,X6,X0))
        | hBOOL(c_in(X1,X8,X0))
        | c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f443,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

fof(f12497,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f442,f12495]) ).

fof(f12495,plain,
    ( spl0_608
  <=> ! [X0,X8,X6,X1] :
        ( hBOOL(c_in(X1,X8,X0))
        | hBOOL(c_in(X1,X6,X0))
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f442,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X8,X0))
      | hBOOL(c_in(X1,X6,X0))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

fof(f12493,plain,
    ( ~ spl0_37
    | ~ spl0_607
    | ~ spl0_254
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12379,f11986,f2996,f12490,f1183]) ).

fof(f12490,plain,
    ( spl0_607
  <=> c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f12379,plain,
    ( ~ c_HOL_Oord__class_Oless(v_U,c_fequal(v_x,tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool))
    | ~ class_HOL_Oord(tc_bool)
    | ~ spl0_254
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f2997]) ).

fof(f12488,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f406,f12486]) ).

fof(f12486,plain,
    ( spl0_606
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f406,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).

fof(f12484,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f405,f12482]) ).

fof(f12482,plain,
    ( spl0_605
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f405,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).

fof(f12480,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f301,f12478]) ).

fof(f12478,plain,
    ( spl0_604
  <=> ! [X0,X14,X6,X8] :
        ( hBOOL(c_in(X14,X6,X0))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f301,axiom,
    ! [X0,X8,X6,X14] :
      ( hBOOL(c_in(X14,X6,X0))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

fof(f12476,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f300,f12474]) ).

fof(f12474,plain,
    ( spl0_603
  <=> ! [X0,X14,X8,X7] :
        ( hBOOL(c_in(X14,X7,X0))
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f300,axiom,
    ! [X0,X8,X7,X14] :
      ( hBOOL(c_in(X14,X7,X0))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X8),X7) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

fof(f12472,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f282,f12470]) ).

fof(f12470,plain,
    ( spl0_602
  <=> ! [X11,X0,X12,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f282,axiom,
    ! [X0,X11,X9,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f12468,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f281,f12466]) ).

fof(f12466,plain,
    ( spl0_601
  <=> ! [X11,X0,X12,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f281,axiom,
    ! [X0,X11,X9,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X11),X12)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(f12464,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f279,f12462]) ).

fof(f12462,plain,
    ( spl0_600
  <=> ! [X10,X11,X0,X9] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f279,axiom,
    ! [X10,X0,X11,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X10)),X11) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X9),X11)),X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f12460,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f278,f12458]) ).

fof(f12458,plain,
    ( spl0_599
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f278,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f12456,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f246,f12454]) ).

fof(f12454,plain,
    ( spl0_598
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f246,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

fof(f12452,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f245,f12450]) ).

fof(f12450,plain,
    ( spl0_597
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f245,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)),X19) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

fof(f12448,plain,
    ( spl0_596
    | ~ spl0_272
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f12365,f11986,f3069,f12446]) ).

fof(f12446,plain,
    ( spl0_596
  <=> ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f12365,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(v_U,X0))
        | ~ hBOOL(hAPP(c_fequal(v_x,tc_Com_Opname),X0)) )
    | ~ spl0_272
    | ~ spl0_584 ),
    inference(resolution,[],[f11988,f3070]) ).

fof(f12444,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f224,f12442]) ).

fof(f12442,plain,
    ( spl0_595
  <=> ! [X17,X0,X14,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X17)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f224,axiom,
    ! [X0,X14,X17,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X17)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f12440,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f223,f12438]) ).

fof(f12438,plain,
    ( spl0_594
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f223,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f12436,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f222,f12434]) ).

fof(f12434,plain,
    ( spl0_593
  <=> ! [X17,X0,X14,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f222,axiom,
    ! [X0,X14,X17,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X17)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(f12432,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f221,f12430]) ).

fof(f12430,plain,
    ( spl0_592
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f221,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f12428,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f220,f12426]) ).

fof(f12426,plain,
    ( spl0_591
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f220,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f12424,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f219,f12422]) ).

fof(f12422,plain,
    ( spl0_590
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f219,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f12420,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f113,f12418]) ).

fof(f12418,plain,
    ( spl0_589
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
        | c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f113,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X8,tc_fun(X0,tc_bool))
      | c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

fof(f12416,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f27,f12414]) ).

fof(f12414,plain,
    ( spl0_588
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f27,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

fof(f12412,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f26,f12410]) ).

fof(f12410,plain,
    ( spl0_587
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f26,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

fof(f12408,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f25,f12406]) ).

fof(f12406,plain,
    ( spl0_586
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f25,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

fof(f12363,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f24,f12361]) ).

fof(f12361,plain,
    ( spl0_585
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f24,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)),X19) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

fof(f11989,plain,
    ( spl0_584
    | ~ spl0_78
    | ~ spl0_265
    | ~ spl0_409
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f11795,f11730,f6739,f3041,f1353,f11986]) ).

fof(f1353,plain,
    ( spl0_78
  <=> ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f6739,plain,
    ( spl0_409
  <=> ! [X20,X0,X6,X15,X1] :
        ( c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20)
        | ~ hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f11730,plain,
    ( spl0_569
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f11795,plain,
    ( c_lessequals(c_fequal(v_x,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_78
    | ~ spl0_265
    | ~ spl0_409
    | ~ spl0_569 ),
    inference(forward_demodulation,[],[f11788,f7217]) ).

fof(f7217,plain,
    ( ! [X2,X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X1)
    | ~ spl0_78
    | ~ spl0_409 ),
    inference(resolution,[],[f6740,f1354]) ).

fof(f1354,plain,
    ( ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f1353]) ).

fof(f6740,plain,
    ( ! [X0,X1,X6,X15,X20] :
        ( ~ hBOOL(c_in(X1,X6,X0))
        | c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f6739]) ).

fof(f11788,plain,
    ( ! [X0] : c_lessequals(c_Set_Oimage(c_COMBK(v_x,tc_Com_Opname,X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,tc_Com_Opname),v_U,tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_265
    | ~ spl0_569 ),
    inference(superposition,[],[f3042,f11731]) ).

fof(f11731,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname)
    | ~ spl0_569 ),
    inference(avatar_component_clause,[],[f11730]) ).

fof(f11817,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f654,f11815]) ).

fof(f11815,plain,
    ( spl0_583
  <=> ! [X0,X8,X6,X1] :
        ( hBOOL(c_in(X1,X8,X0))
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f654,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X8,X0))
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

fof(f11813,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f600,f11811]) ).

fof(f11811,plain,
    ( spl0_582
  <=> ! [X20,X0,X14,X6,X25] :
        ( hBOOL(c_in(X14,X6,X0))
        | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,X6,X0,X20),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f600,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( hBOOL(c_in(X14,X6,X0))
      | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | ~ hBOOL(c_in(hAPP(X25,X14),c_Set_Oimage(X25,X6,X0,X20),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

fof(f11809,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f598,f11807]) ).

fof(f11807,plain,
    ( spl0_581
  <=> ! [X2,X20,X0,X6,X25,X1] :
        ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
        | c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X6,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f598,axiom,
    ! [X2,X0,X1,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X0,X20),X20))
      | c_Fun_Oinj__on(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X6,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

fof(f11805,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f511,f11803]) ).

fof(f11803,plain,
    ( spl0_580
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f511,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

fof(f11801,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f500,f11799]) ).

fof(f11799,plain,
    ( spl0_579
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f500,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

fof(f11785,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f499,f11783]) ).

fof(f11783,plain,
    ( spl0_578
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
        | c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f499,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
      | c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

fof(f11781,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f458,f11779]) ).

fof(f11779,plain,
    ( spl0_577
  <=> ! [X0,X14,X6,X25,X1] :
        ( hBOOL(c_in(X14,X6,X0))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X14,X6,X0,X0),X1))
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,X6,X0),X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f458,axiom,
    ! [X0,X1,X6,X14,X25] :
      ( hBOOL(c_in(X14,X6,X0))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X14,X6,X0,X0),X1))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,X6,X0),X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).

fof(f11777,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f456,f11775]) ).

fof(f11775,plain,
    ( spl0_576
  <=> ! [X8,X20,X0,X6,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | ~ c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool))
        | c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f456,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | ~ c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool))
      | c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_0) ).

fof(f11773,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f455,f11771]) ).

fof(f11771,plain,
    ( spl0_575
  <=> ! [X8,X20,X0,X6,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
        | c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f455,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
      | c_lessequals(c_Set_Ovimage(X25,X8,X0,X20),X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_1) ).

fof(f11769,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f415,f11767]) ).

fof(f11767,plain,
    ( spl0_574
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ c_lessequals(X15,X17,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f415,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | ~ c_lessequals(X15,X17,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

fof(f11765,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f414,f11763]) ).

fof(f11763,plain,
    ( spl0_573
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X15,X17,X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f414,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X15,X17,X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

fof(f11761,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f196,f11759]) ).

fof(f11759,plain,
    ( spl0_572
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X14,X16,X0)
        | ~ c_lessequals(X15,X17,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f196,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X14,X16,X0)
      | ~ c_lessequals(X15,X17,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

fof(f11757,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f123,f11755]) ).

fof(f11755,plain,
    ( spl0_571
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f123,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

fof(f11753,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f82,f11751]) ).

fof(f11751,plain,
    ( spl0_570
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ c_HOL_Oord__class_Oless(X15,X17,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f82,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | ~ c_HOL_Oord__class_Oless(X15,X17,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X17),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f11732,plain,
    ( spl0_569
    | ~ spl0_2
    | ~ spl0_430 ),
    inference(avatar_split_clause,[],[f7752,f7307,f1008,f11730]) ).

fof(f7307,plain,
    ( spl0_430
  <=> ! [X20,X0,X6,X15] :
        ( ~ hBOOL(c_in(X15,X6,X20))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f7752,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,X0),v_U,X0,tc_Com_Opname)
    | ~ spl0_2
    | ~ spl0_430 ),
    inference(resolution,[],[f7308,f1010]) ).

fof(f7308,plain,
    ( ! [X0,X6,X15,X20] :
        ( ~ hBOOL(c_in(X15,X6,X20))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) )
    | ~ spl0_430 ),
    inference(avatar_component_clause,[],[f7307]) ).

fof(f11236,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f973,f11234]) ).

fof(f11234,plain,
    ( spl0_568
  <=> ! [X6,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f973,plain,
    ! [X0,X1,X6] :
      ( c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f486,f926]) ).

fof(f486,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

fof(f11232,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f972,f11230]) ).

fof(f11230,plain,
    ( spl0_567
  <=> ! [X6,X0,X1] :
        ( c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f972,plain,
    ! [X0,X1,X6] :
      ( c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f487,f926]) ).

fof(f487,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_Finite__Set_Ocard(X6,X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

fof(f11228,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f935,f11226]) ).

fof(f11226,plain,
    ( spl0_566
  <=> ! [X0,X14,X6,X8] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f935,plain,
    ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
    inference(forward_demodulation,[],[f786,f926]) ).

fof(f786,axiom,
    ! [X0,X8,X6,X14] : c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

fof(f11224,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f934,f11222]) ).

fof(f11220,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f918,f11218]) ).

fof(f11218,plain,
    ( spl0_564
  <=> ! [X6,X0,X8] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f918,plain,
    ! [X0,X8,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f210,f57]) ).

fof(f210,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X8),c_Complete__Lattice_OInf__class_OInf(X6,X0)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),X8,X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).

fof(f11216,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f917,f11214]) ).

fof(f11214,plain,
    ( spl0_563
  <=> ! [X6,X0,X8] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f917,plain,
    ! [X0,X8,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f451,f57]) ).

fof(f451,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X8),c_Complete__Lattice_OSup__class_OSup(X6,X0)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),X8,X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).

fof(f11212,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f632,f11210]) ).

fof(f11210,plain,
    ( spl0_562
  <=> ! [X0,X14,X8,X7] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f632,axiom,
    ! [X0,X8,X7,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,X8,X0)),X7) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X7),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

fof(f11208,plain,
    ( ~ spl0_19
    | ~ spl0_561
    | ~ spl0_126
    | ~ spl0_531 ),
    inference(avatar_split_clause,[],[f10518,f10370,f1632,f11205,f1093]) ).

fof(f11205,plain,
    ( spl0_561
  <=> c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f10370,plain,
    ( spl0_531
  <=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f10518,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | ~ spl0_126
    | ~ spl0_531 ),
    inference(resolution,[],[f10372,f1633]) ).

fof(f10372,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat)
    | ~ spl0_531 ),
    inference(avatar_component_clause,[],[f10370]) ).

fof(f11203,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f631,f11201]) ).

fof(f11201,plain,
    ( spl0_560
  <=> ! [X0,X14,X6,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f631,axiom,
    ! [X0,X8,X6,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Set_Oinsert(X14,X8,X0)) = c_Set_Oinsert(X14,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

fof(f11199,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f570,f11197]) ).

fof(f11197,plain,
    ( spl0_559
  <=> ! [X16,X20,X0,X14,X6,X8] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | ~ hBOOL(c_in(X16,hAPP(X8,X14),X20))
        | hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f570,axiom,
    ! [X0,X8,X6,X16,X14,X20] :
      ( ~ hBOOL(c_in(X14,X6,X0))
      | ~ hBOOL(c_in(X16,hAPP(X8,X14),X20))
      | hBOOL(c_in(X16,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).

fof(f11195,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f553,f11193]) ).

fof(f11193,plain,
    ( spl0_558
  <=> ! [X20,X21,X25] :
        ( ~ class_Lattices_Olattice(X20)
        | hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f553,axiom,
    ! [X21,X25,X20] :
      ( ~ class_Lattices_Olattice(X20)
      | hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

fof(f11191,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f321,f11189]) ).

fof(f11189,plain,
    ( spl0_557
  <=> ! [X4,X13,X0,X27] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X27,X13,X0)
        | c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X27,X4,X0),c_SetInterval_Oord__class_OatLeastLessThan(X27,X13,X0),tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f321,axiom,
    ! [X0,X27,X4,X13] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X27,X13,X0)
      | c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(X27,X4,X0),c_SetInterval_Oord__class_OatLeastLessThan(X27,X13,X0),tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).

fof(f11187,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f296,f11185]) ).

fof(f296,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X8,X0))
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

fof(f11183,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f293,f11181]) ).

fof(f11181,plain,
    ( spl0_555
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f293,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).

fof(f11179,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f135,f11177]) ).

fof(f11177,plain,
    ( spl0_554
  <=> ! [X20,X21,X25] :
        ( ~ class_Lattices_Olattice(X20)
        | hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f135,axiom,
    ! [X21,X25,X20] :
      ( ~ class_Lattices_Olattice(X20)
      | hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X20)),X25),X21),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X20),hAPP(X25,v_x)),hAPP(X21,v_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

fof(f10837,plain,
    ( spl0_553
    | ~ spl0_185
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f4130,f4087,f2028,f10835]) ).

fof(f10835,plain,
    ( spl0_553
  <=> ! [X0] : c_Set_Oinsert(X0,v_U,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f4087,plain,
    ( spl0_290
  <=> ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f4130,plain,
    ( ! [X0] : c_Set_Oinsert(X0,v_U,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname)
    | ~ spl0_185
    | ~ spl0_290 ),
    inference(resolution,[],[f4088,f2029]) ).

fof(f4088,plain,
    ( ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname))
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f4087]) ).

fof(f10706,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f974,f10704]) ).

fof(f10704,plain,
    ( spl0_552
  <=> ! [X6,X0,X1] :
        ( c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f974,plain,
    ! [X0,X1,X6] :
      ( c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f655,f926]) ).

fof(f655,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X1,X6,X0))
      | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

fof(f10702,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f853,f10700]) ).

fof(f10700,plain,
    ( spl0_551
  <=> ! [X0,X8,X6,X1] :
        ( X6 = X8
        | hBOOL(c_in(X1,X6,X0))
        | hBOOL(c_in(X1,X8,X0))
        | c_Set_Oinsert(X1,X6,X0) != c_Set_Oinsert(X1,X8,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f853,axiom,
    ! [X0,X1,X8,X6] :
      ( X6 = X8
      | hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,X8,X0))
      | c_Set_Oinsert(X1,X6,X0) != c_Set_Oinsert(X1,X8,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

fof(f10698,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f765,f10696]) ).

fof(f765,axiom,
    ! [X0,X1,X8,X6,X25,X20] :
      ( ~ hBOOL(c_in(X1,X6,X20))
      | hBOOL(c_in(hAPP(X25,X1),X8,X0))
      | ~ c_lessequals(c_Set_Oimage(X25,X6,X20,X0),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

fof(f10687,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f744,f10685]) ).

fof(f10685,plain,
    ( spl0_549
  <=> ! [X53,X0,X25,X1] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X53,X0)
        | hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X25,X53,X0),hAPP(X25,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f744,axiom,
    ! [X0,X1,X53,X25] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X53,X0)
      | hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X53,tc_bool)),X25,X53,X0),hAPP(X25,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).

fof(f10683,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f691,f10681]) ).

fof(f691,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( X6 = X8
      | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | c_Set_Oimage(X25,X6,X0,X20) != c_Set_Oimage(X25,X8,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

fof(f10679,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f679,f10677]) ).

fof(f10677,plain,
    ( spl0_547
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(X15,X14,X0)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f679,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(X15,X14,X0)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

fof(f10675,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f678,f10673]) ).

fof(f10673,plain,
    ( spl0_546
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(X16,X17,X0)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f678,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(X16,X17,X0)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

fof(f10671,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f677,f10669]) ).

fof(f10669,plain,
    ( spl0_545
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X15,X14,X0)
        | ~ c_lessequals(X16,X17,X0)
        | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f677,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X15,X14,X0)
      | ~ c_lessequals(X16,X17,X0)
      | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

fof(f10667,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f519,f10665]) ).

fof(f10665,plain,
    ( spl0_544
  <=> ! [X6,X0] :
        ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
        | c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f519,axiom,
    ! [X0,X6] :
      ( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
      | c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).

fof(f10663,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f518,f10661]) ).

fof(f10661,plain,
    ( spl0_543
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f518,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X8),X6) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

fof(f10659,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f517,f10657]) ).

fof(f10657,plain,
    ( spl0_542
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f517,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

fof(f10655,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f491,f10653]) ).

fof(f10653,plain,
    ( spl0_541
  <=> ! [X15,X0,X6,X8] :
        ( hBOOL(c_in(X15,X8,X0))
        | hBOOL(c_in(X15,X6,X0))
        | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f491,axiom,
    ! [X0,X8,X6,X15] :
      ( hBOOL(c_in(X15,X8,X0))
      | hBOOL(c_in(X15,X6,X0))
      | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

fof(f10651,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f465,f10649]) ).

fof(f10649,plain,
    ( spl0_540
  <=> ! [X20,X0,X6,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | c_Set_Ovimage(X25,X6,X0,X20) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X6,X20,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f465,axiom,
    ! [X0,X6,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | c_Set_Ovimage(X25,X6,X0,X20) = c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X6,X20,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__vimage__eq__inv__image_0) ).

fof(f10647,plain,
    ( ~ spl0_19
    | ~ spl0_539
    | ~ spl0_126
    | ~ spl0_515 ),
    inference(avatar_split_clause,[],[f10298,f10127,f1632,f10644,f1093]) ).

fof(f10644,plain,
    ( spl0_539
  <=> c_HOL_Oord__class_Oless(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f10127,plain,
    ( spl0_515
  <=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f10298,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | ~ spl0_126
    | ~ spl0_515 ),
    inference(resolution,[],[f10129,f1633]) ).

fof(f10129,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat)
    | ~ spl0_515 ),
    inference(avatar_component_clause,[],[f10127]) ).

fof(f10642,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f421,f10640]) ).

fof(f10640,plain,
    ( spl0_538
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X6,X0))
        | ~ hBOOL(c_in(X15,X8,X0))
        | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f421,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X6,X0))
      | ~ hBOOL(c_in(X15,X8,X0))
      | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

fof(f10638,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f334,f10636]) ).

fof(f10636,plain,
    ( spl0_537
  <=> ! [X6,X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f334,axiom,
    ! [X0,X8,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

fof(f10634,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f316,f10632]) ).

fof(f10632,plain,
    ( spl0_536
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X15,X17,X0)
        | c_lessequals(X14,X16,X0)
        | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f316,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X15,X17,X0)
      | c_lessequals(X14,X16,X0)
      | c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).

fof(f10630,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f314,f10628]) ).

fof(f10628,plain,
    ( spl0_535
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(X15,X14,X0)
        | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f314,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(X15,X14,X0)
      | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).

fof(f10626,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f313,f10624]) ).

fof(f10624,plain,
    ( spl0_534
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(X16,X17,X0)
        | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f313,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(X16,X17,X0)
      | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).

fof(f10622,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f309,f10620]) ).

fof(f10620,plain,
    ( spl0_533
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X16,X14,X0)
        | c_lessequals(X15,X14,X0)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f309,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X16,X14,X0)
      | c_lessequals(X15,X14,X0)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).

fof(f10618,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f308,f10616]) ).

fof(f10616,plain,
    ( spl0_532
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X16,X14,X0)
        | c_lessequals(X16,X17,X0)
        | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f308,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X16,X14,X0)
      | c_lessequals(X16,X17,X0)
      | ~ c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0),c_SetInterval_Oord__class_OatLeastLessThan(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).

fof(f10373,plain,
    ( spl0_531
    | ~ spl0_148
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f9899,f9657,f1724,f10370]) ).

fof(f1724,plain,
    ( spl0_148
  <=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f9657,plain,
    ( spl0_514
  <=> ! [X0] :
        ( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
        | c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f9899,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname))),tc_nat)
    | ~ spl0_148
    | ~ spl0_514 ),
    inference(resolution,[],[f9658,f1725]) ).

fof(f1725,plain,
    ( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1724]) ).

fof(f9658,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
        | c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) )
    | ~ spl0_514 ),
    inference(avatar_component_clause,[],[f9657]) ).

fof(f10365,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f983,f10363]) ).

fof(f10363,plain,
    ( spl0_530
  <=> ! [X0,X6,X1,X26] :
        ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
        | ~ hBOOL(hAPP(X26,X1))
        | ~ hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f983,plain,
    ! [X0,X1,X6,X26] :
      ( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
      | ~ hBOOL(hAPP(X26,X1))
      | ~ hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f312,f665]) ).

fof(f312,axiom,
    ! [X0,X1,X6,X26] :
      ( ~ hBOOL(hAPP(X26,X1))
      | ~ hBOOL(c_in(X1,X6,X0))
      | hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Collect(X26,X0)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).

fof(f10361,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f965,f10359]) ).

fof(f10359,plain,
    ( spl0_529
  <=> ! [X0,X1] :
        ( c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = c_Finite__Set_Ocard(c_fequal(X1,X0),X0)
        | hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f965,plain,
    ! [X0,X1] :
      ( c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = c_Finite__Set_Ocard(c_fequal(X1,X0),X0)
      | hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    inference(forward_demodulation,[],[f350,f926]) ).

fof(f350,axiom,
    ! [X0,X1] :
      ( hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
      | c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

fof(f10357,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f948,f10355]) ).

fof(f948,plain,
    ! [X0,X1,X6] :
      ( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0))
      | ~ c_Finite__Set_Ofinite(X6,X0) ),
    inference(forward_demodulation,[],[f475,f926]) ).

fof(f475,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).

fof(f10353,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f852,f10351]) ).

fof(f852,axiom,
    ! [X0,X1,X6,X25,X20] :
      ( ~ hBOOL(c_in(X1,X6,X0))
      | c_Set_Oimage(X25,X6,X0,X20) = c_Set_Oinsert(hAPP(X25,X1),c_Set_Oimage(X25,X6,X0,X20),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

fof(f10349,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f762,f10347]) ).

fof(f10347,plain,
    ( spl0_526
  <=> ! [X21,X20,X0,X25,X1] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20),X1,X0))
        | c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f762,axiom,
    ! [X21,X0,X1,X25,X20] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(X1,X25,X21,X0,X20),X1,X0))
      | c_Set_Oimage(X25,X1,X0,X20) = c_Set_Oimage(X21,X1,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_0) ).

fof(f10345,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f674,f10343]) ).

fof(f10343,plain,
    ( spl0_525
  <=> ! [X53,X0,X6,X25,X1] :
        ( ~ hBOOL(c_in(X1,X6,X53))
        | ~ c_Fun_Oinj__on(X25,X6,X53,X0)
        | hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X53,X0),hAPP(X25,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f674,axiom,
    ! [X0,X1,X6,X53,X25] :
      ( ~ hBOOL(c_in(X1,X6,X53))
      | ~ c_Fun_Oinj__on(X25,X6,X53,X0)
      | hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X53,X0),hAPP(X25,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).

fof(f10341,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f659,f10339]) ).

fof(f10339,plain,
    ( spl0_524
  <=> ! [X2,X20,X0,X6,X25,X1] :
        ( hBOOL(c_in(X1,X6,X20))
        | c_Set_Oimage(X25,X6,X20,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f659,axiom,
    ! [X2,X0,X1,X6,X25,X20] :
      ( hBOOL(c_in(X1,X6,X20))
      | c_Set_Oimage(X25,X6,X20,X0) = c_Set_Oimage(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X6,X20,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

fof(f10337,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f648,f10335]) ).

fof(f648,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X8,X0))
      | c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

fof(f10333,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f579,f10331]) ).

fof(f10331,plain,
    ( spl0_522
  <=> ! [X8,X0,X14,X6,X16,X20] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | ~ hBOOL(hAPP(hAPP(X8,X14),X16))
        | hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X16)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f579,axiom,
    ! [X0,X8,X6,X16,X14,X20] :
      ( ~ hBOOL(c_in(X14,X6,X0))
      | ~ hBOOL(hAPP(hAPP(X8,X14),X16))
      | hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).

fof(f10293,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f388,f10291]) ).

fof(f10291,plain,
    ( spl0_521
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f388,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).

fof(f10289,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f345,f10287]) ).

fof(f10287,plain,
    ( spl0_520
  <=> ! [X20,X0,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) = X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f345,axiom,
    ! [X0,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__inv__eq_0) ).

fof(f10285,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f331,f10283]) ).

fof(f331,axiom,
    ! [X0,X8,X6] :
      ( c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

fof(f10281,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f193,f10279]) ).

fof(f10279,plain,
    ( spl0_518
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f193,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).

fof(f10277,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f128,f10275]) ).

fof(f10275,plain,
    ( spl0_517
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f128,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).

fof(f10273,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f2,f10271]) ).

fof(f10271,plain,
    ( spl0_516
  <=> ! [X4,X0,X5,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f2,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X0)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X0)) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).

fof(f10130,plain,
    ( spl0_515
    | ~ spl0_44
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f9895,f9657,f1215,f10127]) ).

fof(f9895,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Suc(c_Finite__Set_Ocard(v_U,tc_Com_Opname)),tc_nat)
    | ~ spl0_44
    | ~ spl0_514 ),
    inference(resolution,[],[f9658,f1216]) ).

fof(f9659,plain,
    ( spl0_514
    | ~ spl0_77
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f6306,f6058,f1349,f9657]) ).

fof(f6058,plain,
    ( spl0_385
  <=> ! [X0] :
        ( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
        | c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f6306,plain,
    ( ! [X0] :
        ( c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
        | c_lessequals(c_Finite__Set_Ocard(v_G,t_a),X0,tc_nat) )
    | ~ spl0_77
    | ~ spl0_385 ),
    inference(resolution,[],[f6059,f1350]) ).

fof(f6059,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
        | c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) )
    | ~ spl0_385 ),
    inference(avatar_component_clause,[],[f6058]) ).

fof(f9497,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f767,f9495]) ).

fof(f767,axiom,
    ! [X0,X1,X6,X25,X20] :
      ( ~ hBOOL(c_in(X1,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X1),X6,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

fof(f9493,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f761,f9491]) ).

fof(f761,axiom,
    ! [X2,X0,X6,X25,X20] :
      ( ~ hBOOL(c_in(X2,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hAPP(X25,hAPP(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

fof(f9489,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f653,f9487]) ).

fof(f9487,plain,
    ( spl0_511
  <=> ! [X0,X8,X6,X1] :
        ( hBOOL(c_in(X1,X6,X0))
        | c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f653,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X6,X0))
      | c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

fof(f9485,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f647,f9483]) ).

fof(f9483,plain,
    ( spl0_510
  <=> ! [X0,X8,X6,X1] :
        ( ~ hBOOL(c_in(X1,X8,X0))
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f647,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X8,X0))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

fof(f9481,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f637,f9479]) ).

fof(f637,axiom,
    ! [X0,X1,X6,X25,X20] :
      ( ~ c_lessequals(X1,X6,tc_fun(X20,tc_bool))
      | c_lessequals(c_Set_Oimage(X25,X1,X20,X0),c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

fof(f9477,plain,
    spl0_508,
    inference(avatar_split_clause,[],[f568,f9475]) ).

fof(f9475,plain,
    ( spl0_508
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X6,X0))
        | hBOOL(c_in(X15,X8,X0))
        | hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f568,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X6,X0))
      | hBOOL(c_in(X15,X8,X0))
      | hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

fof(f9471,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f520,f9469]) ).

fof(f9469,plain,
    ( spl0_507
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_lessequals(c_Set_Ovimage(X25,X6,X20,X0),c_Set_Ovimage(X25,X8,X20,X0),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f520,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_lessequals(c_Set_Ovimage(X25,X6,X20,X0),c_Set_Ovimage(X25,X8,X20,X0),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

fof(f9467,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f510,f9465]) ).

fof(f9465,plain,
    ( spl0_506
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f510,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

fof(f9463,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f509,f9461]) ).

fof(f9461,plain,
    ( spl0_505
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f509,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

fof(f9459,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f448,f9457]) ).

fof(f9457,plain,
    ( spl0_504
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | X6 = X8
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(c_Finite__Set_Ocard(X8,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f448,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | X6 = X8
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(c_Finite__Set_Ocard(X8,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).

fof(f9455,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f410,f9453]) ).

fof(f9453,plain,
    ( spl0_503
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f410,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).

fof(f9451,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f302,f9449]) ).

fof(f9449,plain,
    ( spl0_502
  <=> ! [X0,X8,X6,X1] :
        ( ~ hBOOL(c_in(X1,X8,X0))
        | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f302,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(c_in(X1,X8,X0))
      | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X6,c_Set_Oinsert(X1,X8,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

fof(f9447,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f194,f9445]) ).

fof(f9445,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f194,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

fof(f9443,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f134,f9441]) ).

fof(f9441,plain,
    ( spl0_500
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X14,X16,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f134,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X14,X16,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f9439,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f133,f9437]) ).

fof(f133,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f9435,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f132,f9433]) ).

fof(f9433,plain,
    ( spl0_498
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f132,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f9431,plain,
    ( ~ spl0_1
    | spl0_497
    | ~ spl0_141
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f9369,f8212,f1695,f9429,f1003]) ).

fof(f9429,plain,
    ( spl0_497
  <=> ! [X0,X1] : c_Finite__Set_Ofinite(c_fequal(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1695,plain,
    ( spl0_141
  <=> ! [X20,X0,X35,X33] :
        ( ~ c_Finite__Set_Ofinite(X33,X0)
        | c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f9369,plain,
    ( ! [X0,X1] :
        ( c_Finite__Set_Ofinite(c_fequal(X0,X1),X1)
        | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
    | ~ spl0_141
    | ~ spl0_483 ),
    inference(superposition,[],[f1696,f8213]) ).

fof(f1696,plain,
    ( ! [X0,X35,X33,X20] :
        ( c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20)
        | ~ c_Finite__Set_Ofinite(X33,X0) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1695]) ).

fof(f9427,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f131,f9425]) ).

fof(f131,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X14,X16,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f9423,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f130,f9421]) ).

fof(f9421,plain,
    ( spl0_495
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f130,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f9419,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f129,f9417]) ).

fof(f9417,plain,
    ( spl0_494
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f129,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f9415,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f122,f9413]) ).

fof(f9413,plain,
    ( spl0_493
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f122,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

fof(f9411,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f121,f9409]) ).

fof(f9409,plain,
    ( spl0_492
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f121,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

fof(f9407,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f101,f9405]) ).

fof(f9405,plain,
    ( spl0_491
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f101,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

fof(f9403,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f100,f9401]) ).

fof(f9401,plain,
    ( spl0_490
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f100,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

fof(f9399,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f99,f9397]) ).

fof(f9397,plain,
    ( spl0_489
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X14,X16,X0)
        | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f99,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X14,X16,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

fof(f9395,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f98,f9393]) ).

fof(f98,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

fof(f9391,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f97,f9389]) ).

fof(f97,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X14,X16,X0)
      | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

fof(f9368,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f96,f9366]) ).

fof(f9366,plain,
    ( spl0_486
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f96,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

fof(f9364,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f64,f9362]) ).

fof(f9362,plain,
    ( spl0_485
  <=> ! [X20,X0,X25,X21] :
        ( ~ class_HOL_Oord(X20)
        | ~ c_lessequals(X25,X21,tc_fun(X0,X20))
        | c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
        | c_lessequals(X21,X25,tc_fun(X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f64,axiom,
    ! [X21,X0,X25,X20] :
      ( ~ class_HOL_Oord(X20)
      | ~ c_lessequals(X25,X21,tc_fun(X0,X20))
      | c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
      | c_lessequals(X21,X25,tc_fun(X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

fof(f8996,plain,
    ( spl0_484
    | ~ spl0_110
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f8660,f8149,f1486,f8994]) ).

fof(f8994,plain,
    ( spl0_484
  <=> ! [X0] :
        ( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f8660,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(X0,v_U,tc_Com_Opname))
        | hBOOL(hAPP(v_G,hAPP(v_mgt__call,X0))) )
    | ~ spl0_110
    | ~ spl0_473 ),
    inference(resolution,[],[f8150,f1487]) ).

fof(f8214,plain,
    ( spl0_483
    | ~ spl0_2
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f7210,f6739,f1008,f8212]) ).

fof(f7210,plain,
    ( ! [X0,X1] : c_fequal(X0,X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_Com_Opname),v_U,tc_Com_Opname,X1)
    | ~ spl0_2
    | ~ spl0_409 ),
    inference(resolution,[],[f6740,f1010]) ).

fof(f8187,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f990,f8185]) ).

fof(f8185,plain,
    ( spl0_482
  <=> ! [X6,X0,X1] :
        ( ~ c_lessequals(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool))
        | c_fequal(X1,X0) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f990,plain,
    ! [X0,X1,X6] :
      ( ~ c_lessequals(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool))
      | c_fequal(X1,X0) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ),
    inference(forward_demodulation,[],[f989,f926]) ).

fof(f989,plain,
    ! [X0,X1,X6] :
      ( c_fequal(X1,X0) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | ~ c_lessequals(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
    inference(forward_demodulation,[],[f775,f926]) ).

fof(f775,axiom,
    ! [X0,X1,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X6
      | ~ c_lessequals(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

fof(f8183,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f978,f8181]) ).

fof(f8181,plain,
    ( spl0_481
  <=> ! [X17,X0,X14,X16,X15] :
        ( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
        | X16 = X17
        | X14 = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f978,plain,
    ! [X0,X16,X14,X17,X15] :
      ( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
      | X16 = X17
      | X14 = X17 ),
    inference(forward_demodulation,[],[f977,f926]) ).

fof(f977,plain,
    ! [X0,X16,X14,X17,X15] :
      ( c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
      | X16 = X17
      | X14 = X17 ),
    inference(forward_demodulation,[],[f825,f926]) ).

fof(f825,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( X16 = X17
      | X14 = X17
      | c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

fof(f8179,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f976,f8177]) ).

fof(f8177,plain,
    ( spl0_480
  <=> ! [X17,X0,X14,X16,X15] :
        ( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
        | X14 = X15
        | X14 = X17 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f976,plain,
    ! [X0,X16,X14,X17,X15] :
      ( c_Set_Oinsert(X14,c_fequal(X16,X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
      | X14 = X15
      | X14 = X17 ),
    inference(forward_demodulation,[],[f975,f926]) ).

fof(f975,plain,
    ! [X0,X16,X14,X17,X15] :
      ( c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_fequal(X17,X0),X0)
      | X14 = X15
      | X14 = X17 ),
    inference(forward_demodulation,[],[f827,f926]) ).

fof(f827,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( X14 = X15
      | X14 = X17
      | c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X15,c_Set_Oinsert(X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

fof(f8175,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f916,f8173]) ).

fof(f8173,plain,
    ( spl0_479
  <=> ! [X6,X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f916,plain,
    ! [X0,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f295,f57]) ).

fof(f295,axiom,
    ! [X0,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Complete__Lattice_OInf__class_OInf(X6,X0) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0),X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fold__inf_0) ).

fof(f8171,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f915,f8169]) ).

fof(f915,plain,
    ! [X0,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_The(c_Finite__Set_Ofold__graph(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0),X0) ),
    inference(definition_unfolding,[],[f357,f57]) ).

fof(f357,axiom,
    ! [X0,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Complete__Lattice_OSup__class_OSup(X6,X0) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0),X6,X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).

fof(f8167,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f817,f8165]) ).

fof(f817,axiom,
    ! [X0,X8,X14,X25,X20] : c_Set_Oimage(X25,c_Set_Oinsert(X14,X8,X20),X20,X0) = c_Set_Oinsert(hAPP(X25,X14),c_Set_Oimage(X25,X8,X20,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

fof(f8163,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f803,f8161]) ).

fof(f8161,plain,
    ( spl0_476
  <=> ! [X6,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f803,axiom,
    ! [X0,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

fof(f8159,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f802,f8157]) ).

fof(f8157,plain,
    ( spl0_475
  <=> ! [X6,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f802,axiom,
    ! [X0,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

fof(f8155,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f773,f8153]) ).

fof(f773,axiom,
    ! [X0,X8,X6,X14] :
      ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

fof(f8151,plain,
    ( spl0_473
    | ~ spl0_3
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f6602,f6050,f1013,f8149]) ).

fof(f6050,plain,
    ( spl0_383
  <=> ! [X53,X0,X6,X25,X1] :
        ( ~ hBOOL(c_in(X1,X6,X53))
        | hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f6602,plain,
    ( ! [X0] :
        ( hBOOL(c_in(hAPP(v_mgt__call,X0),v_G,t_a))
        | ~ hBOOL(c_in(X0,v_U,tc_Com_Opname)) )
    | ~ spl0_3
    | ~ spl0_383 ),
    inference(superposition,[],[f6051,f1015]) ).

fof(f6051,plain,
    ( ! [X0,X1,X6,X53,X25] :
        ( hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0))
        | ~ hBOOL(c_in(X1,X6,X53)) )
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f6050]) ).

fof(f8147,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f772,f8145]) ).

fof(f8145,plain,
    ( spl0_472
  <=> ! [X0,X14,X6,X8] :
        ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f772,axiom,
    ! [X0,X8,X6,X14] :
      ( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

fof(f8143,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f764,f8141]) ).

fof(f764,axiom,
    ! [X0,X6,X16,X25,X20] :
      ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0),X6,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_1) ).

fof(f8139,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f763,f8137]) ).

fof(f763,axiom,
    ! [X0,X19,X6,X25,X20] :
      ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hAPP(X25,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0)) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_1) ).

fof(f8135,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f732,f8133]) ).

fof(f8133,plain,
    ( spl0_469
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f732,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

fof(f8131,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f731,f8129]) ).

fof(f8129,plain,
    ( spl0_468
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f731,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

fof(f8127,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f692,f8125]) ).

fof(f692,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(X6,X25,X20,X0),X8,X0,X20)
      | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X20,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).

fof(f8122,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f690,f8120]) ).

fof(f8120,plain,
    ( spl0_466
  <=> ! [X20,X0,X6,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool))) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f690,axiom,
    ! [X0,X8,X6,X20] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool))) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).

fof(f8117,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f689,f8115]) ).

fof(f8115,plain,
    ( spl0_465
  <=> ! [X20,X0,X6,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X6,X20,tc_fun(X0,tc_bool))),X8) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f689,axiom,
    ! [X0,X8,X6,X20] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X6,X20,tc_fun(X0,tc_bool))),X8) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).

fof(f8113,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f686,f8111]) ).

fof(f8111,plain,
    ( spl0_464
  <=> ! [X6,X0,X1,X8] :
        ( hBOOL(hAPP(X8,X1))
        | hBOOL(hAPP(X6,X1))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f686,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(hAPP(X8,X1))
      | hBOOL(hAPP(X6,X1))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

fof(f8109,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f664,f8107]) ).

fof(f8107,plain,
    ( spl0_463
  <=> ! [X20,X0,X6,X25] :
        ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
        | c_Set_Ovimage(X25,c_Set_Oimage(X25,X6,X0,X20),X0,X20) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f664,axiom,
    ! [X0,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20)
      | c_Set_Ovimage(X25,c_Set_Oimage(X25,X6,X0,X20),X0,X20) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

fof(f8105,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f660,f8103]) ).

fof(f660,axiom,
    ! [X0,X19,X6,X25,X20] :
      ( ~ hBOOL(c_in(X19,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(X6,X25,X19,X20,X0),X6,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_0) ).

fof(f8101,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f658,f8099]) ).

fof(f658,axiom,
    ! [X0,X6,X16,X25,X20] :
      ( ~ hBOOL(c_in(X16,c_Set_Oimage(X25,X6,X20,X0),X0))
      | hAPP(X25,c_ATP__Linkup_Osko__Set__XimageE__1__1(X6,X16,X25,X20,X0)) = X16 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_0) ).

fof(f8097,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f624,f8095]) ).

fof(f624,axiom,
    ! [X0,X6,X25,X20] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

fof(f8093,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f619,f8091]) ).

fof(f8091,plain,
    ( spl0_459
  <=> ! [X6,X0,X8] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f619,axiom,
    ! [X0,X8,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

fof(f8089,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f618,f8087]) ).

fof(f8087,plain,
    ( spl0_458
  <=> ! [X6,X0,X8] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f618,axiom,
    ! [X0,X8,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

fof(f8085,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f558,f8083]) ).

fof(f8083,plain,
    ( spl0_457
  <=> ! [X20,X0,X14,X6,X8] :
        ( ~ hBOOL(c_in(X14,X6,X0))
        | c_lessequals(hAPP(X8,X14),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f558,axiom,
    ! [X0,X8,X6,X14,X20] :
      ( ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(hAPP(X8,X14),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X8,X0,tc_fun(X20,tc_bool)),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).

fof(f8081,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f528,f8079]) ).

fof(f8079,plain,
    ( spl0_456
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X2,X1,X0)
        | ~ c_lessequals(X19,X1,X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f528,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X2,X1,X0)
      | ~ c_lessequals(X19,X1,X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X19),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

fof(f8077,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f516,f8075]) ).

fof(f8075,plain,
    ( spl0_455
  <=> ! [X6,X20,X8] :
        ( ~ class_HOL_Ominus(X20)
        | hAPP(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X6,v_x),hAPP(X8,v_x),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f516,axiom,
    ! [X8,X6,X20] :
      ( ~ class_HOL_Ominus(X20)
      | hAPP(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(t_a,X20)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X6,v_x),hAPP(X8,v_x),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

fof(f8073,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f381,f8071]) ).

fof(f8071,plain,
    ( spl0_454
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f381,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

fof(f8069,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f380,f8067]) ).

fof(f8067,plain,
    ( spl0_453
  <=> ! [X0,X6,X8,X7] :
        ( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f380,axiom,
    ! [X0,X8,X6,X7] :
      ( c_lessequals(X7,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

fof(f8065,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f355,f8063]) ).

fof(f8063,plain,
    ( spl0_452
  <=> ! [X6,X0,X14] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X14,X6,X0))
        | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X14,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f355,axiom,
    ! [X0,X6,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X14,X6,X0))
      | c_lessequals(hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X0),X0),X6),X14,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

fof(f8061,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f349,f8059]) ).

fof(f8059,plain,
    ( spl0_451
  <=> ! [X6,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | hBOOL(c_in(X1,X6,X0))
        | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f349,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | hBOOL(c_in(X1,X6,X0))
      | c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) = c_Suc(c_Finite__Set_Ocard(X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

fof(f8057,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f189,f8055]) ).

fof(f8055,plain,
    ( spl0_450
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f189,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

fof(f8053,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f186,f8051]) ).

fof(f8051,plain,
    ( spl0_449
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X19,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f186,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X19,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).

fof(f8049,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f181,f8047]) ).

fof(f8047,plain,
    ( spl0_448
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X1,X14,X0)
        | ~ c_lessequals(X1,X16,X0)
        | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f181,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X1,X14,X0)
      | ~ c_lessequals(X1,X16,X0)
      | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

fof(f8045,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f174,f8043]) ).

fof(f8043,plain,
    ( spl0_447
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X1,X19,X0)
        | ~ c_lessequals(X2,X19,X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f174,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X1,X19,X0)
      | ~ c_lessequals(X2,X19,X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).

fof(f8041,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f156,f8039]) ).

fof(f8039,plain,
    ( spl0_446
  <=> ! [X6,X0,X1,X8] :
        ( ~ hBOOL(hAPP(X6,X1))
        | ~ hBOOL(hAPP(X8,X1))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f156,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(hAPP(X6,X1))
      | ~ hBOOL(hAPP(X8,X1))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

fof(f8037,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f106,f8035]) ).

fof(f8035,plain,
    ( spl0_445
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X1,X2,X0)
        | ~ c_lessequals(X1,X19,X0)
        | c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f106,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X1,X2,X0)
      | ~ c_lessequals(X1,X19,X0)
      | c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

fof(f8033,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f53,f8031]) ).

fof(f8031,plain,
    ( spl0_444
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X19,X1,X0)
        | c_lessequals(X19,X2,X0)
        | ~ c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f53,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X19,X1,X0)
      | c_lessequals(X19,X2,X0)
      | ~ c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).

fof(f8029,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f37,f8027]) ).

fof(f8027,plain,
    ( spl0_443
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X19,X0)
        | c_lessequals(X2,X19,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f37,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X19,X0)
      | c_lessequals(X2,X19,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

fof(f8025,plain,
    ( spl0_441
    | ~ spl0_442
    | ~ spl0_3
    | ~ spl0_382 ),
    inference(avatar_split_clause,[],[f6583,f6046,f1013,f8022,f8018]) ).

fof(f8022,plain,
    ( spl0_442
  <=> c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) = v_G ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f6046,plain,
    ( spl0_382
  <=> ! [X20,X0,X6,X25] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f6583,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)) != v_G
    | v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))
    | ~ spl0_3
    | ~ spl0_382 ),
    inference(superposition,[],[f6047,f1015]) ).

fof(f6047,plain,
    ( ! [X0,X6,X25,X20] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 )
    | ~ spl0_382 ),
    inference(avatar_component_clause,[],[f6046]) ).

fof(f8016,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f28,f8014]) ).

fof(f8014,plain,
    ( spl0_440
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0)
        | c_HOL_Oord__class_Oless(X19,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f28,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X19,X1,X0)
      | c_HOL_Oord__class_Oless(X19,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).

fof(f8012,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f20,f8010]) ).

fof(f8010,plain,
    ( spl0_439
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0)
        | c_HOL_Oord__class_Oless(X2,X19,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f20,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X1,X19,X0)
      | c_HOL_Oord__class_Oless(X2,X19,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

fof(f7491,plain,
    ( spl0_438
    | ~ spl0_265
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f6673,f6571,f3041,f7489]) ).

fof(f7489,plain,
    ( spl0_438
  <=> ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f6673,plain,
    ( ! [X0,X1] : c_Finite__Set_Ofinite(c_Set_Oimage(X0,c_Set_Ovimage(X0,v_G,X1,t_a),X1,t_a),t_a)
    | ~ spl0_265
    | ~ spl0_388 ),
    inference(resolution,[],[f6572,f3042]) ).

fof(f7342,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f971,f7340]) ).

fof(f971,plain,
    ! [X3,X0,X5] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0),X0)
      | ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0) ),
    inference(forward_demodulation,[],[f970,f613]) ).

fof(f613,axiom,
    ! [X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

fof(f970,plain,
    ! [X3,X0,X5] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0)),X0)
      | ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0) ),
    inference(forward_demodulation,[],[f469,f632]) ).

fof(f469,axiom,
    ! [X3,X0,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0)
      | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X5,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).

fof(f7338,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f969,f7336]) ).

fof(f969,plain,
    ! [X3,X0,X5] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0),X0)
      | ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0) ),
    inference(forward_demodulation,[],[f968,f612]) ).

fof(f612,axiom,
    ! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

fof(f968,plain,
    ! [X3,X0,X5] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = c_Set_Oinsert(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)
      | ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0) ),
    inference(forward_demodulation,[],[f470,f631]) ).

fof(f470,axiom,
    ! [X3,X0,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X3,X5,X0)
      | c_SetInterval_Oord__class_OatLeastAtMost(X3,X5,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X0)),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).

fof(f7329,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f963,f7327]) ).

fof(f7327,plain,
    ( spl0_435
  <=> ! [X20,X0,X6,X15] :
        ( c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_fequal(X15,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f963,plain,
    ! [X0,X6,X15,X20] :
      ( c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_fequal(X15,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6 ),
    inference(forward_demodulation,[],[f810,f926]) ).

fof(f810,axiom,
    ! [X0,X6,X15,X20] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
      | c_Set_Oimage(c_COMBK(X15,X0,X20),X6,X20,X0) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

fof(f7325,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f961,f7323]) ).

fof(f7323,plain,
    ( spl0_434
  <=> ! [X6,X0,X1] :
        ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_fequal(X1,X0),tc_fun(X0,tc_bool)) = X6
        | hBOOL(c_in(X1,X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f961,plain,
    ! [X0,X1,X6] :
      ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_fequal(X1,X0),tc_fun(X0,tc_bool)) = X6
      | hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f809,f926]) ).

fof(f809,axiom,
    ! [X0,X1,X6] :
      ( hBOOL(c_in(X1,X6,X0))
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X6,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

fof(f7321,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f947,f7319]) ).

fof(f7319,plain,
    ( spl0_433
  <=> ! [X6,X0,X1] :
        ( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
        | ~ c_Finite__Set_Ofinite(X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f947,plain,
    ! [X0,X1,X6] :
      ( c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_fequal(X1,X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat)
      | ~ c_Finite__Set_Ofinite(X6,X0) ),
    inference(forward_demodulation,[],[f476,f926]) ).

fof(f476,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_lessequals(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).

fof(f7317,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f848,f7315]) ).

fof(f848,axiom,
    ! [X0,X16,X14] :
      ( X14 = X16
      | c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

fof(f7313,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f804,f7311]) ).

fof(f7311,plain,
    ( spl0_431
  <=> ! [X6,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f804,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

fof(f7309,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f755,f7307]) ).

fof(f755,axiom,
    ! [X0,X6,X15,X20] :
      ( ~ hBOOL(c_in(X15,X6,X20))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).

fof(f7305,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f737,f7303]) ).

fof(f7303,plain,
    ( spl0_429
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f737,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

fof(f7301,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f693,f7299]) ).

fof(f7299,plain,
    ( spl0_428
  <=> ! [X2,X19,X20,X0,X25,X1] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X1,X19,X0,X20) = c_Fun_Ofun__upd(X25,X1,X19,X0,X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f693,axiom,
    ! [X2,X0,X1,X19,X25,X20] : c_Fun_Ofun__upd(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X1,X19,X0,X20) = c_Fun_Ofun__upd(X25,X1,X19,X0,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

fof(f7297,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f685,f7295]) ).

fof(f685,axiom,
    ! [X2,X0,X1,X25,X20] :
      ( X1 = X2
      | hAPP(X25,X1) != hAPP(X25,X2)
      | ~ c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

fof(f7293,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f683,f7291]) ).

fof(f7291,plain,
    ( spl0_426
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X14,X16,X0)
        | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f683,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X14,X16,X0)
      | c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

fof(f7284,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f627,f7282]) ).

fof(f7282,plain,
    ( spl0_425
  <=> ! [X0,X14,X30,X7] :
        ( ~ c_lessequals(X7,X30,tc_fun(X0,tc_bool))
        | c_lessequals(c_Set_Oinsert(X14,X7,X0),c_Set_Oinsert(X14,X30,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f627,axiom,
    ! [X0,X7,X14,X30] :
      ( ~ c_lessequals(X7,X30,tc_fun(X0,tc_bool))
      | c_lessequals(c_Set_Oinsert(X14,X7,X0),c_Set_Oinsert(X14,X30,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

fof(f7280,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f626,f7278]) ).

fof(f7278,plain,
    ( spl0_424
  <=> ! [X6,X25,X0] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Fun_Oinj__on(X25,X6,X0,X0)
        | ~ c_lessequals(X6,c_Set_Oimage(X25,X6,X0,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f626,axiom,
    ! [X0,X6,X25] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Fun_Oinj__on(X25,X6,X0,X0)
      | ~ c_lessequals(X6,c_Set_Oimage(X25,X6,X0,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

fof(f7276,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f582,f7274]) ).

fof(f7274,plain,
    ( spl0_423
  <=> ! [X20,X0,X6,X15] :
        ( hBOOL(c_in(X15,X6,X20))
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f582,axiom,
    ! [X0,X6,X15,X20] :
      ( hBOOL(c_in(X15,X6,X20))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(c_COMBK(X15,X20,X0),X6,X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).

fof(f7272,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f551,f7270]) ).

fof(f7270,plain,
    ( spl0_422
  <=> ! [X35,X20,X0,X33] :
        ( ~ c_Finite__Set_Ofinite(X33,X0)
        | c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X20,X0),X20)
        | ~ c_Fun_Oinj__on(X35,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f551,axiom,
    ! [X0,X35,X33,X20] :
      ( ~ c_Finite__Set_Ofinite(X33,X0)
      | c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X20,X0),X20)
      | ~ c_Fun_Oinj__on(X35,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

fof(f7268,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f546,f7266]) ).

fof(f7266,plain,
    ( spl0_421
  <=> ! [X6,X0,X8] : c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f546,axiom,
    ! [X0,X8,X6] : c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

fof(f7264,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f521,f7262]) ).

fof(f7262,plain,
    ( spl0_420
  <=> ! [X48,X20,X0,X6] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X48,X20,X0),X0,X20) = X48 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f521,axiom,
    ! [X48,X0,X6,X20] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,c_COMBK(X48,X20,X0),X0,X20) = X48 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).

fof(f7260,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f378,f7258]) ).

fof(f7258,plain,
    ( spl0_419
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X15 = X16
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f378,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X15 = X16
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f7256,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f377,f7254]) ).

fof(f7254,plain,
    ( spl0_418
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X15 = X16
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f377,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X15 = X16
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f7252,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f376,f7250]) ).

fof(f7250,plain,
    ( spl0_417
  <=> ! [X0,X14,X16,X15] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X15 = X16
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f376,axiom,
    ! [X0,X16,X14,X15] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X15 = X16
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f7248,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f330,f7246]) ).

fof(f330,axiom,
    ! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_HOL_Ominus__class_Ominus(X8,X6,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

fof(f7244,plain,
    ( spl0_415
    | ~ spl0_212
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f6658,f6571,f2486,f7242]) ).

fof(f7242,plain,
    ( spl0_415
  <=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f6658,plain,
    ( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X0),v_G),t_a)
    | ~ spl0_212
    | ~ spl0_388 ),
    inference(resolution,[],[f6572,f2487]) ).

fof(f7240,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f315,f7238]) ).

fof(f7238,plain,
    ( spl0_414
  <=> ! [X17,X0,X14,X16,X15] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X15,X17,X0)
        | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f315,axiom,
    ! [X0,X16,X14,X17,X15] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X15,X17,X0)
      | ~ c_HOL_Oord__class_Oless(c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0),c_SetInterval_Oord__class_OatLeastAtMost(X15,X17,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).

fof(f7236,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f212,f7234]) ).

fof(f7234,plain,
    ( spl0_413
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f212,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

fof(f7232,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f142,f7230]) ).

fof(f7230,plain,
    ( spl0_412
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f142,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_HOL_Oord__class_Oless(X8,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

fof(f7228,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f141,f7226]) ).

fof(f7226,plain,
    ( spl0_411
  <=> ! [X0,X6,X8,X7] :
        ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f141,axiom,
    ! [X0,X8,X6,X7] :
      ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X7,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

fof(f7118,plain,
    ( spl0_410
    | ~ spl0_211
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f6657,f6571,f2482,f7116]) ).

fof(f7116,plain,
    ( spl0_410
  <=> ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f6657,plain,
    ( ! [X0] : c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),v_G),X0),t_a)
    | ~ spl0_211
    | ~ spl0_388 ),
    inference(resolution,[],[f6572,f2483]) ).

fof(f6741,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f956,f6739]) ).

fof(f956,plain,
    ! [X0,X1,X6,X15,X20] :
      ( c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_fequal(X15,X20)
      | ~ hBOOL(c_in(X1,X6,X0)) ),
    inference(forward_demodulation,[],[f811,f926]) ).

fof(f811,axiom,
    ! [X0,X1,X6,X15,X20] :
      ( ~ hBOOL(c_in(X1,X6,X0))
      | c_Set_Oimage(c_COMBK(X15,X20,X0),X6,X0,X20) = c_Set_Oinsert(X15,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

fof(f6737,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f945,f6735]) ).

fof(f6735,plain,
    ( spl0_408
  <=> ! [X0,X16,X14] :
        ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f945,plain,
    ! [X0,X16,X14] :
      ( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
      | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
    inference(forward_demodulation,[],[f454,f926]) ).

fof(f454,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

fof(f6733,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f944,f6731]) ).

fof(f6731,plain,
    ( spl0_407
  <=> ! [X0,X16,X14] :
        ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
        | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f944,plain,
    ! [X0,X16,X14] :
      ( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_fequal(X16,X0),X0),X0)
      | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
    inference(forward_demodulation,[],[f621,f926]) ).

fof(f621,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

fof(f6729,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f933,f6727]) ).

fof(f6727,plain,
    ( spl0_406
  <=> ! [X20,X0,X14,X8] : c_fequal(X14,X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f933,plain,
    ! [X0,X8,X14,X20] : c_fequal(X14,X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0),
    inference(forward_demodulation,[],[f780,f926]) ).

fof(f780,axiom,
    ! [X0,X8,X14,X20] : c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Set_Oinsert(X14,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).

fof(f6725,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f667,f6723]) ).

fof(f6723,plain,
    ( spl0_405
  <=> ! [X6,X0,X14] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Complete__Lattice_OSup__class_OSup(X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f667,axiom,
    ! [X0,X6,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),c_Complete__Lattice_OSup__class_OSup(X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

fof(f6721,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f581,f6719]) ).

fof(f6719,plain,
    ( spl0_404
  <=> ! [X6,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(c_in(X1,X6,X0))
        | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f581,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(X0),X6),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

fof(f6717,plain,
    ( spl0_403
    | ~ spl0_165
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f6671,f6571,f1936,f6715]) ).

fof(f6715,plain,
    ( spl0_403
  <=> ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f6671,plain,
    ( ! [X0] : c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v_G,X0,tc_fun(t_a,tc_bool)),t_a)
    | ~ spl0_165
    | ~ spl0_388 ),
    inference(resolution,[],[f6572,f1937]) ).

fof(f6713,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f580,f6711]) ).

fof(f580,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_lessequals(X1,hAPP(c_Finite__Set_Olinorder__class_OMax(X0),X6),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

fof(f6709,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f557,f6707]) ).

fof(f6707,plain,
    ( spl0_401
  <=> ! [X48,X20,X0,X6,X27] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
        | ~ hBOOL(c_in(X27,X6,X0))
        | c_lessequals(hAPP(X48,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X0,X20),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f557,axiom,
    ! [X48,X0,X6,X27,X20] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X20)
      | ~ hBOOL(c_in(X27,X6,X0))
      | c_lessequals(hAPP(X48,X27),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X6,X48,X0,X20),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).

fof(f6705,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f548,f6703]) ).

fof(f548,axiom,
    ! [X0,X8,X6,X20] : c_HOL_Ominus__class_Ominus(X6,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X8,X20,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).

fof(f6701,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f514,f6699]) ).

fof(f6697,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f504,f6695]) ).

fof(f6695,plain,
    ( spl0_398
  <=> ! [X20,X0,X6,X25,X8] :
        ( c_Fun_Oinj__on(X25,X8,X0,X20)
        | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f504,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( c_Fun_Oinj__on(X25,X8,X0,X20)
      | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

fof(f6693,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f503,f6691]) ).

fof(f6691,plain,
    ( spl0_397
  <=> ! [X8,X20,X0,X6,X25] :
        ( c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f503,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( c_Fun_Oinj__on(X25,X6,X0,X20)
      | ~ c_Fun_Oinj__on(X25,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

fof(f6689,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f493,f6687]) ).

fof(f6687,plain,
    ( spl0_396
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X6,X0))
        | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f493,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X6,X0))
      | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

fof(f6685,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f492,f6683]) ).

fof(f6683,plain,
    ( spl0_395
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X8,X0))
        | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f492,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X8,X0))
      | hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

fof(f6681,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f449,f6679]) ).

fof(f6679,plain,
    ( spl0_394
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f449,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).

fof(f6677,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f424,f6675]) ).

fof(f6675,plain,
    ( spl0_393
  <=> ! [X15,X0,X6,X8] :
        ( hBOOL(c_in(X15,X6,X0))
        | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f424,axiom,
    ! [X0,X8,X6,X15] :
      ( hBOOL(c_in(X15,X6,X0))
      | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

fof(f6648,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f423,f6646]) ).

fof(f6646,plain,
    ( spl0_392
  <=> ! [X15,X0,X6,X8] :
        ( hBOOL(c_in(X15,X8,X0))
        | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f423,axiom,
    ! [X0,X8,X6,X15] :
      ( hBOOL(c_in(X15,X8,X0))
      | ~ hBOOL(c_in(X15,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

fof(f6644,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f344,f6642]) ).

fof(f6642,plain,
    ( spl0_391
  <=> ! [X6,X0,X14] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Complete__Lattice_OInf__class_OInf(X6,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f344,axiom,
    ! [X0,X6,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,X6,X0),X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),c_Complete__Lattice_OInf__class_OInf(X6,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

fof(f6640,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f259,f6638]) ).

fof(f6636,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f169,f6634]) ).

fof(f6634,plain,
    ( spl0_389
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f169,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X8,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

fof(f6573,plain,
    ( ~ spl0_1
    | spl0_388
    | ~ spl0_3
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f6568,f6038,f1013,f6571,f1003]) ).

fof(f6038,plain,
    ( spl0_380
  <=> ! [X20,X0,X6,X25,X8] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Finite__Set_Ofinite(X8,X20)
        | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f6568,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,v_G,tc_fun(t_a,tc_bool))
        | c_Finite__Set_Ofinite(X0,t_a)
        | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) )
    | ~ spl0_3
    | ~ spl0_380 ),
    inference(superposition,[],[f6039,f1015]) ).

fof(f6039,plain,
    ( ! [X0,X8,X6,X25,X20] :
        ( ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool))
        | c_Finite__Set_Ofinite(X8,X20)
        | ~ c_Finite__Set_Ofinite(X6,X0) )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f6038]) ).

fof(f6068,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f960,f6066]) ).

fof(f6066,plain,
    ( spl0_387
  <=> ! [X20,X0,X14,X16,X25] :
        ( ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(X16,X20),X0,X20),X0))
        | hAPP(X25,X14) = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f960,plain,
    ! [X0,X16,X14,X25,X20] :
      ( ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(X16,X20),X0,X20),X0))
      | hAPP(X25,X14) = X16 ),
    inference(forward_demodulation,[],[f806,f926]) ).

fof(f806,axiom,
    ! [X0,X16,X14,X25,X20] :
      ( hAPP(X25,X14) = X16
      | ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,c_Set_Oinsert(X16,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X0,X20),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

fof(f6064,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f955,f6062]) ).

fof(f6062,plain,
    ( spl0_386
  <=> ! [X0,X6,X1,X26] :
        ( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
        | hBOOL(hAPP(X26,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f955,plain,
    ! [X0,X1,X6,X26] :
      ( ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X26),X0))
      | hBOOL(hAPP(X26,X1)) ),
    inference(forward_demodulation,[],[f311,f665]) ).

fof(f311,axiom,
    ! [X0,X1,X6,X26] :
      ( hBOOL(hAPP(X26,X1))
      | ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Collect(X26,X0)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).

fof(f6060,plain,
    ( spl0_385
    | ~ spl0_191
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f5687,f5440,f2270,f6058]) ).

fof(f5440,plain,
    ( spl0_361
  <=> c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f5687,plain,
    ( ! [X0] :
        ( ~ c_lessequals(X0,c_Finite__Set_Ocard(v_G,t_a),tc_nat)
        | c_lessequals(X0,c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat) )
    | ~ spl0_191
    | ~ spl0_361 ),
    inference(resolution,[],[f5442,f2271]) ).

fof(f5442,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
    | ~ spl0_361 ),
    inference(avatar_component_clause,[],[f5440]) ).

fof(f6056,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f932,f6054]) ).

fof(f6054,plain,
    ( spl0_384
  <=> ! [X6,X0,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f932,plain,
    ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_fequal(X14,X0),tc_fun(X0,tc_bool)),X0),
    inference(forward_demodulation,[],[f793,f926]) ).

fof(f793,axiom,
    ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = c_Set_Oinsert(X14,c_HOL_Ominus__class_Ominus(X6,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

fof(f6052,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f857,f6050]) ).

fof(f857,axiom,
    ! [X0,X1,X6,X53,X25] :
      ( ~ hBOOL(c_in(X1,X6,X53))
      | hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,X6,X53,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

fof(f6048,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f837,f6046]) ).

fof(f837,axiom,
    ! [X0,X6,X25,X20] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X25,X6,X20,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

fof(f6044,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f829,f6042]) ).

fof(f6042,plain,
    ( spl0_381
  <=> ! [X0,X14,X6,X16] :
        ( X14 = X16
        | hBOOL(c_in(X14,X6,X0))
        | ~ hBOOL(c_in(X14,c_Set_Oinsert(X16,X6,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f829,axiom,
    ! [X0,X6,X16,X14] :
      ( X14 = X16
      | hBOOL(c_in(X14,X6,X0))
      | ~ hBOOL(c_in(X14,c_Set_Oinsert(X16,X6,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

fof(f6040,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f798,f6038]) ).

fof(f798,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ofinite(X8,X20)
      | ~ c_lessequals(X8,c_Set_Oimage(X25,X6,X0,X20),tc_fun(X20,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

fof(f6036,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f752,f6034]) ).

fof(f752,axiom,
    ! [X0,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).

fof(f6032,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f738,f6030]) ).

fof(f738,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X8,X0,X20)
      | c_Fun_Oinj__on(X25,X6,X0,X20)
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

fof(f6028,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f708,f6026]) ).

fof(f708,axiom,
    ! [X0,X8,X6] :
      ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) != X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

fof(f6024,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f707,f6022]) ).

fof(f707,axiom,
    ! [X0,X8,X6] :
      ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

fof(f6020,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f706,f6018]) ).

fof(f706,axiom,
    ! [X0,X8,X6] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

fof(f6010,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f671,f6008]) ).

fof(f6008,plain,
    ( spl0_374
  <=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f671,axiom,
    ! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

fof(f6006,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f670,f6004]) ).

fof(f6004,plain,
    ( spl0_373
  <=> ! [X0,X8] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f670,axiom,
    ! [X0,X8] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

fof(f6002,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f588,f6000]) ).

fof(f6000,plain,
    ( spl0_372
  <=> ! [X0,X44,X33] :
        ( ~ c_Finite__Set_Ofinite(X33,X0)
        | ~ c_Finite__Set_Ofinite(X44,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f588,axiom,
    ! [X0,X44,X33] :
      ( ~ c_Finite__Set_Ofinite(X33,X0)
      | ~ c_Finite__Set_Ofinite(X44,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

fof(f5998,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f575,f5996]) ).

fof(f5996,plain,
    ( spl0_371
  <=> ! [X20,X14,X0,X6,X25] :
        ( hBOOL(c_in(hAPP(X25,X14),X6,X20))
        | ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X0,X20),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f575,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( hBOOL(c_in(hAPP(X25,X14),X6,X20))
      | ~ hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X0,X20),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

fof(f5994,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f572,f5992]) ).

fof(f5992,plain,
    ( spl0_370
  <=> ! [X0,X14,X6,X25,X20] :
        ( ~ hBOOL(c_in(hAPP(X25,X14),X6,X0))
        | hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X20,X0),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f572,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( ~ hBOOL(c_in(hAPP(X25,X14),X6,X0))
      | hBOOL(c_in(X14,c_Set_Ovimage(X25,X6,X20,X0),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

fof(f5990,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f498,f5988]) ).

fof(f498,axiom,
    ! [X21,X0,X1,X25,X20] :
      ( ~ class_HOL_Oord(X20)
      | ~ c_lessequals(X25,X21,tc_fun(X0,X20))
      | c_lessequals(hAPP(X25,X1),hAPP(X21,X1),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

fof(f5986,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f497,f5984]) ).

fof(f497,axiom,
    ! [X46,X0,X8,X6] :
      ( ~ hBOOL(c_in(X46,X6,X0))
      | hBOOL(c_in(X46,X8,X0))
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

fof(f5982,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f436,f5980]) ).

fof(f5980,plain,
    ( spl0_367
  <=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f436,axiom,
    ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

fof(f5978,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f435,f5976]) ).

fof(f5976,plain,
    ( spl0_366
  <=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f435,axiom,
    ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

fof(f5974,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f422,f5972]) ).

fof(f5972,plain,
    ( spl0_365
  <=> ! [X15,X0,X6,X8] :
        ( ~ hBOOL(c_in(X15,X6,X0))
        | hBOOL(c_in(X15,X8,X0))
        | ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f422,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X6,X0))
      | hBOOL(c_in(X15,X8,X0))
      | ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

fof(f5970,plain,
    ( ~ spl0_19
    | ~ spl0_364
    | ~ spl0_126
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f5690,f5440,f1632,f5967,f1093]) ).

fof(f5967,plain,
    ( spl0_364
  <=> c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(v_G,t_a),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f5690,plain,
    ( ~ c_HOL_Oord__class_Oless(c_Finite__Set_Ocard(v_U,tc_Com_Opname),c_Finite__Set_Ocard(v_G,t_a),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | ~ spl0_126
    | ~ spl0_361 ),
    inference(resolution,[],[f5442,f1633]) ).

fof(f5965,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f249,f5963]) ).

fof(f249,axiom,
    ! [X0,X8,X6] :
      ( ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

fof(f5961,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f248,f5959]) ).

fof(f248,axiom,
    ! [X0,X8,X6] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

fof(f5443,plain,
    ( ~ spl0_1
    | spl0_361
    | ~ spl0_3
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f5407,f4268,f1013,f5440,f1003]) ).

fof(f5407,plain,
    ( c_lessequals(c_Finite__Set_Ocard(v_G,t_a),c_Finite__Set_Ocard(v_U,tc_Com_Opname),tc_nat)
    | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_3
    | ~ spl0_334 ),
    inference(superposition,[],[f4269,f1015]) ).

fof(f5102,plain,
    ( spl0_360
    | ~ spl0_110
    | ~ spl0_343 ),
    inference(avatar_split_clause,[],[f4890,f4304,f1486,f5100]) ).

fof(f5100,plain,
    ( spl0_360
  <=> ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f4304,plain,
    ( spl0_343
  <=> ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f4890,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),v_x))
    | ~ spl0_110
    | ~ spl0_343 ),
    inference(resolution,[],[f4305,f1487]) ).

fof(f4305,plain,
    ( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname))
    | ~ spl0_343 ),
    inference(avatar_component_clause,[],[f4304]) ).

fof(f4488,plain,
    ( spl0_359
    | ~ spl0_110
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f4348,f4260,f1486,f4486]) ).

fof(f4486,plain,
    ( spl0_359
  <=> ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f4260,plain,
    ( spl0_332
  <=> ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f4348,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),v_x))
    | ~ spl0_110
    | ~ spl0_332 ),
    inference(resolution,[],[f4261,f1487]) ).

fof(f4261,plain,
    ( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname))
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f4260]) ).

fof(f4370,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f931,f4368]) ).

fof(f931,plain,
    ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_fequal(X14,X0)),X6),
    inference(forward_demodulation,[],[f795,f926]) ).

fof(f795,axiom,
    ! [X0,X6,X14] : c_Set_Oinsert(X14,X6,X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

fof(f4366,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f843,f4364]) ).

fof(f843,axiom,
    ! [X2,X0,X1,X6] : c_Set_Oinsert(X1,c_Set_Oinsert(X2,X6,X0),X0) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X6,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

fof(f4362,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f797,f4360]) ).

fof(f797,axiom,
    ! [X0,X6,X25,X20] :
      ( c_Finite__Set_Ofinite(X6,X20)
      | ~ c_Fun_Oinj__on(X25,X6,X20,X0)
      | ~ c_Finite__Set_Ofinite(c_Set_Oimage(X25,X6,X20,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

fof(f4358,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f754,f4356]) ).

fof(f4356,plain,
    ( spl0_355
  <=> ! [X2,X19,X20,X0,X25,X1] :
        ( X1 = X19
        | hAPP(X25,X19) = hAPP(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f754,axiom,
    ! [X2,X0,X1,X19,X25,X20] :
      ( X1 = X19
      | hAPP(X25,X19) = hAPP(c_Fun_Ofun__upd(X25,X1,X2,X0,X20),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

fof(f4354,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f746,f4352]) ).

fof(f4352,plain,
    ( spl0_354
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X14,X16,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f746,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X14,X16,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

fof(f4346,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f745,f4344]) ).

fof(f4344,plain,
    ( spl0_353
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X14,X16,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f745,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X14,X16,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

fof(f4342,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f729,f4340]) ).

fof(f4340,plain,
    ( spl0_352
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X16,X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f729,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X16,X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

fof(f4338,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f728,f4336]) ).

fof(f4336,plain,
    ( spl0_351
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X14,X0)
        | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f728,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X14,X0)
      | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

fof(f4334,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f727,f4332]) ).

fof(f4332,plain,
    ( spl0_350
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X16,X0)
        | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f727,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X16,X0)
      | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

fof(f4330,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f726,f4328]) ).

fof(f4328,plain,
    ( spl0_349
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,X19,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f726,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,X19,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

fof(f4326,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f699,f4324]) ).

fof(f4324,plain,
    ( spl0_348
  <=> ! [X6,X0,X8] :
        ( X6 = X8
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f699,axiom,
    ! [X0,X8,X6] :
      ( X6 = X8
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X8,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

fof(f4322,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f688,f4320]) ).

fof(f688,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(hAPP(X6,X1))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

fof(f4318,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f687,f4316]) ).

fof(f4316,plain,
    ( spl0_346
  <=> ! [X6,X0,X1,X8] :
        ( ~ hBOOL(hAPP(X8,X1))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f687,axiom,
    ! [X0,X1,X8,X6] :
      ( ~ hBOOL(hAPP(X8,X1))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

fof(f4314,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f661,f4312]) ).

fof(f4312,plain,
    ( spl0_345
  <=> ! [X8,X20,X0,X6,X25] :
        ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
        | c_Fun_Oinj__on(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f661,axiom,
    ! [X0,X8,X6,X25,X20] :
      ( ~ c_Fun_Oinj__on(X25,X6,X0,X20)
      | c_Fun_Oinj__on(X25,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

fof(f4310,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f634,f4308]) ).

fof(f634,axiom,
    ! [X0,X1,X8,X6] :
      ( c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

fof(f4306,plain,
    ( spl0_343
    | ~ spl0_221
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f4027,f3748,f2522,f4304]) ).

fof(f3748,plain,
    ( spl0_281
  <=> ! [X0] :
        ( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
        | hBOOL(c_in(v_x,X0,tc_Com_Opname)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f4027,plain,
    ( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),X0),v_U),tc_Com_Opname))
    | ~ spl0_221
    | ~ spl0_281 ),
    inference(resolution,[],[f3749,f2523]) ).

fof(f3749,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
        | hBOOL(c_in(v_x,X0,tc_Com_Opname)) )
    | ~ spl0_281 ),
    inference(avatar_component_clause,[],[f3748]) ).

fof(f4302,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f633,f4300]) ).

fof(f4300,plain,
    ( spl0_342
  <=> ! [X16,X0,X6,X8] :
        ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_lessequals(X6,c_Set_Oinsert(X16,X8,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f633,axiom,
    ! [X0,X8,X6,X16] :
      ( ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_lessequals(X6,c_Set_Oinsert(X16,X8,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

fof(f4298,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f607,f4296]) ).

fof(f4296,plain,
    ( spl0_341
  <=> ! [X6,X0] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
        | ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f607,axiom,
    ! [X0,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
      | ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

fof(f4294,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f597,f4292]) ).

fof(f4292,plain,
    ( spl0_340
  <=> ! [X6,X0,X8] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = X8
        | c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f597,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = X8
      | c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

fof(f4290,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f596,f4288]) ).

fof(f4288,plain,
    ( spl0_339
  <=> ! [X6,X0,X8] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = X6
        | c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f596,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = X6
      | c_Orderings_Obot__class_Obot(X0) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

fof(f4286,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f513,f4284]) ).

fof(f4284,plain,
    ( spl0_338
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f513,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f4282,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f512,f4280]) ).

fof(f512,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f4278,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f489,f4276]) ).

fof(f489,axiom,
    ! [X0,X8,X6,X15] :
      ( ~ hBOOL(c_in(X15,X8,X0))
      | ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

fof(f4274,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f488,f4272]) ).

fof(f488,axiom,
    ! [X0,X8,X6,X15] :
      ( hBOOL(c_in(X15,X6,X0))
      | ~ hBOOL(c_in(X15,c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

fof(f4270,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f450,f4268]) ).

fof(f450,axiom,
    ! [X0,X6,X25,X20] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_lessequals(c_Finite__Set_Ocard(c_Set_Oimage(X25,X6,X0,X20),X20),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).

fof(f4266,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f434,f4264]) ).

fof(f4264,plain,
    ( spl0_333
  <=> ! [X19,X20,X0,X25,X1] :
        ( X1 = X19
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f434,axiom,
    ! [X0,X1,X19,X25,X20] :
      ( X1 = X19
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

fof(f4262,plain,
    ( spl0_332
    | ~ spl0_220
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f4026,f3748,f2518,f4260]) ).

fof(f4026,plain,
    ( ! [X0] : hBOOL(c_in(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_U),X0),tc_Com_Opname))
    | ~ spl0_220
    | ~ spl0_281 ),
    inference(resolution,[],[f3749,f2519]) ).

fof(f4258,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f413,f4256]) ).

fof(f413,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X16,X0)
      | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

fof(f4254,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f412,f4252]) ).

fof(f412,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X14,X0)
      | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

fof(f4250,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f408,f4248]) ).

fof(f4248,plain,
    ( spl0_329
  <=> ! [X6,X0,X1,X8] :
        ( hBOOL(hAPP(X6,X1))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f408,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(hAPP(X6,X1))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

fof(f4246,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f407,f4244]) ).

fof(f4244,plain,
    ( spl0_328
  <=> ! [X6,X0,X1,X8] :
        ( hBOOL(hAPP(X8,X1))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f407,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(hAPP(X8,X1))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

fof(f4242,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f397,f4240]) ).

fof(f4240,plain,
    ( spl0_327
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f397,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).

fof(f4238,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f392,f4236]) ).

fof(f4236,plain,
    ( spl0_326
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f392,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

fof(f4234,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f391,f4232]) ).

fof(f391,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).

fof(f4230,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f387,f4228]) ).

fof(f4228,plain,
    ( spl0_324
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X19,X0)
        | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f387,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X19,X0)
      | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

fof(f4226,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f386,f4224]) ).

fof(f4224,plain,
    ( spl0_323
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X2,X0)
        | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f386,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X2,X0)
      | ~ c_lessequals(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

fof(f4222,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f385,f4220]) ).

fof(f4220,plain,
    ( spl0_322
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X16,X1,X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f385,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X16,X1,X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

fof(f4216,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f384,f4214]) ).

fof(f4214,plain,
    ( spl0_321
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X14,X1,X0)
        | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f384,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X14,X1,X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

fof(f4212,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f368,f4210]) ).

fof(f4210,plain,
    ( spl0_320
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X19,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f368,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X19,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

fof(f4208,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f367,f4206]) ).

fof(f4206,plain,
    ( spl0_319
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f367,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X19,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

fof(f4204,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f366,f4202]) ).

fof(f4202,plain,
    ( spl0_318
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X16,X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f366,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X16,X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

fof(f4200,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f365,f4198]) ).

fof(f4198,plain,
    ( spl0_317
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X14,X1,X0)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f365,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

fof(f4196,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f362,f4194]) ).

fof(f4194,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f362,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

fof(f4192,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f361,f4190]) ).

fof(f4190,plain,
    ( spl0_315
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f361,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f4188,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f346,f4186]) ).

fof(f4186,plain,
    ( spl0_314
  <=> ! [X20,X0,X25] :
        ( ~ c_Fun_Obij(X25,X0,X20)
        | c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f346,axiom,
    ! [X0,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | c_Fun_Obij(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X25,X0,X20),X20,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__imp__bij__inv_0) ).

fof(f4184,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f322,f4182]) ).

fof(f322,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X16,X14,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

fof(f4180,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f298,f4178]) ).

fof(f298,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X16,X14,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

fof(f4176,plain,
    ( spl0_311
    | ~ spl0_110
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f4131,f4087,f1486,f4174]) ).

fof(f4174,plain,
    ( spl0_311
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,tc_Com_Opname),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f4131,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_U,tc_Com_Opname),v_x))
    | ~ spl0_110
    | ~ spl0_290 ),
    inference(resolution,[],[f4088,f1487]) ).

fof(f4172,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f297,f4170]) ).

fof(f297,axiom,
    ! [X3,X28,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X3,X28,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).

fof(f4168,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f264,f4166]) ).

fof(f4166,plain,
    ( spl0_309
  <=> ! [X6,X0,X8] :
        ( X6 = X8
        | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
        | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f264,axiom,
    ! [X0,X8,X6] :
      ( X6 = X8
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool))
      | c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

fof(f4164,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f260,f4162]) ).

fof(f260,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f4160,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f258,f4158]) ).

fof(f4158,plain,
    ( spl0_307
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X2,X19,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f258,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X2,X19,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).

fof(f4156,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f257,f4154]) ).

fof(f4154,plain,
    ( spl0_306
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f257,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X1,X19,X0)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).

fof(f4152,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f256,f4150]) ).

fof(f4150,plain,
    ( spl0_305
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f256,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).

fof(f4148,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f255,f4146]) ).

fof(f4146,plain,
    ( spl0_304
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X19,X1,X0)
        | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f255,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X1,X0)
      | c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).

fof(f4144,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f247,f4142]) ).

fof(f4142,plain,
    ( spl0_303
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f247,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).

fof(f4140,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f205,f4138]) ).

fof(f205,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X14),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f4136,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f188,f4134]) ).

fof(f188,axiom,
    ! [X28,X3,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | c_HOL_Oord__class_Oless(X28,X3,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).

fof(f4129,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f187,f4127]) ).

fof(f4127,plain,
    ( spl0_300
  <=> ! [X0,X28,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X28,X3,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f187,axiom,
    ! [X28,X3,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X28,X3,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X28,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).

fof(f4125,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f146,f4123]) ).

fof(f146,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | c_HOL_Oord__class_Oless(X14,X16,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

fof(f4121,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f85,f4119]) ).

fof(f85,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_HOL_Oord__class_Oless(X14,X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

fof(f4117,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f84,f4115]) ).

fof(f84,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_HOL_Oord__class_Oless(X16,X1,X0)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

fof(f4113,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f83,f4111]) ).

fof(f83,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f4109,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f68,f4107]) ).

fof(f68,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f4105,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f56,f4103]) ).

fof(f4103,plain,
    ( spl0_294
  <=> ! [X0,X14,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f56,axiom,
    ! [X0,X14,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(f4101,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f55,f4099]) ).

fof(f55,axiom,
    ! [X0,X16,X14] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f4097,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f52,f4095]) ).

fof(f4095,plain,
    ( spl0_292
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X19,X0)
        | ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f52,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X19,X0)
      | ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

fof(f4093,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f51,f4091]) ).

fof(f4091,plain,
    ( spl0_291
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X2,X0)
        | ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f51,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X2,X0)
      | ~ c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X2),X19),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

fof(f4089,plain,
    ( spl0_290
    | ~ spl0_104
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f4036,f3748,f1462,f4087]) ).

fof(f4036,plain,
    ( ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_U,tc_Com_Opname),tc_Com_Opname))
    | ~ spl0_104
    | ~ spl0_281 ),
    inference(resolution,[],[f3749,f1463]) ).

fof(f4085,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f50,f4083]) ).

fof(f4083,plain,
    ( spl0_289
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X2,X19,X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f50,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X2,X19,X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

fof(f4081,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f47,f4079]) ).

fof(f4079,plain,
    ( spl0_288
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X14,X1,X0)
        | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f47,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X14,X1,X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

fof(f4077,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f33,f4075]) ).

fof(f33,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X19,X1,X0)
      | c_lessequals(X19,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).

fof(f4073,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f32,f4071]) ).

fof(f32,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X1,X16,X0)
      | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).

fof(f4069,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f30,f4067]) ).

fof(f4067,plain,
    ( spl0_285
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X16,X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f30,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X16,X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).

fof(f4065,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f29,f4063]) ).

fof(f4063,plain,
    ( spl0_284
  <=> ! [X0,X14,X16,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X14,X1,X0)
        | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f29,axiom,
    ! [X0,X1,X16,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X14,X1,X0)
      | ~ c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X14),X16),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).

fof(f4061,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f14,f4059]) ).

fof(f4059,plain,
    ( spl0_283
  <=> ! [X6,X0,X8] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = X8
        | c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f14,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = X8
      | c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

fof(f4057,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f13,f4055]) ).

fof(f4055,plain,
    ( spl0_282
  <=> ! [X6,X0,X8] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = X6
        | c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f13,axiom,
    ! [X0,X8,X6] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = X6
      | c_Orderings_Otop__class_Otop(X0) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X6),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

fof(f3750,plain,
    ( spl0_281
    | ~ spl0_193
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f3740,f3037,f2278,f3748]) ).

fof(f2278,plain,
    ( spl0_193
  <=> v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f3740,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_U,X0,tc_fun(tc_Com_Opname,tc_bool))
        | hBOOL(c_in(v_x,X0,tc_Com_Opname)) )
    | ~ spl0_193
    | ~ spl0_264 ),
    inference(superposition,[],[f3038,f2280]) ).

fof(f2280,plain,
    ( v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname)
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f2278]) ).

fof(f3241,plain,
    ( ~ spl0_280
    | ~ spl0_81
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f3100,f3096,f1365,f3238]) ).

fof(f3238,plain,
    ( spl0_280
  <=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1365,plain,
    ( spl0_81
  <=> ! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f3096,plain,
    ( spl0_278
  <=> c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f3100,plain,
    ( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
    | ~ spl0_81
    | ~ spl0_278 ),
    inference(superposition,[],[f1366,f3098]) ).

fof(f3098,plain,
    ( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f3096]) ).

fof(f1366,plain,
    ( ! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f1365]) ).

fof(f3107,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f834,f3105]) ).

fof(f3105,plain,
    ( spl0_279
  <=> ! [X0,X6,X2,X1] :
        ( X1 = X2
        | hBOOL(hAPP(X6,X1))
        | ~ hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f834,axiom,
    ! [X2,X0,X1,X6] :
      ( X1 = X2
      | hBOOL(hAPP(X6,X1))
      | ~ hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

fof(f3099,plain,
    ( spl0_278
    | ~ spl0_35
    | ~ spl0_183
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f3094,f3090,f2020,f1173,f3096]) ).

fof(f3090,plain,
    ( spl0_277
  <=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f3094,plain,
    ( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_35
    | ~ spl0_183
    | ~ spl0_277 ),
    inference(forward_demodulation,[],[f3092,f2248]) ).

fof(f3092,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f3090]) ).

fof(f3093,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f823,f3090]) ).

fof(f823,axiom,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

fof(f3088,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f768,f3086]) ).

fof(f768,axiom,
    ! [X0,X1,X25,X20] : hBOOL(c_in(hAPP(X25,X1),c_Set_Oimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X20,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

fof(f3084,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f750,f3082]) ).

fof(f3082,plain,
    ( spl0_275
  <=> ! [X20,X0,X6,X25,X1] :
        ( ~ hBOOL(hAPP(X6,hAPP(X25,X1)))
        | hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f750,axiom,
    ! [X0,X1,X6,X25,X20] :
      ( ~ hBOOL(hAPP(X6,hAPP(X25,X1)))
      | hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

fof(f3080,plain,
    ( spl0_274
    | ~ spl0_19
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1557,f1430,f1093,f3077]) ).

fof(f3077,plain,
    ( spl0_274
  <=> c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat) = c_Finite__Set_Olinorder__class_OMin(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f1430,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1557,plain,
    ( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(tc_nat),tc_nat) = c_Finite__Set_Olinorder__class_OMin(tc_nat)
    | ~ spl0_19
    | ~ spl0_96 ),
    inference(resolution,[],[f1431,f1095]) ).

fof(f1431,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f1430]) ).

fof(f3075,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f749,f3073]) ).

fof(f3073,plain,
    ( spl0_273
  <=> ! [X20,X0,X6,X25,X1] :
        ( hBOOL(hAPP(X6,hAPP(X25,X1)))
        | ~ hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f749,axiom,
    ! [X0,X1,X6,X25,X20] :
      ( hBOOL(hAPP(X6,hAPP(X25,X1)))
      | ~ hBOOL(hAPP(c_Set_Ovimage(X25,X6,X0,X20),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

fof(f3071,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f742,f3069]) ).

fof(f742,axiom,
    ! [X50,X0,X1,X26] :
      ( ~ hBOOL(hAPP(X26,X1))
      | hBOOL(hAPP(X50,X1))
      | ~ c_lessequals(X26,X50,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

fof(f3067,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f734,f3065]) ).

fof(f734,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X2,X0)
      | ~ c_lessequals(X2,X19,X0)
      | c_lessequals(X1,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f3063,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f733,f3061]) ).

fof(f733,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X2,X1,X0)
      | ~ c_lessequals(X19,X2,X0)
      | c_lessequals(X19,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f3059,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f720,f3057]) ).

fof(f3057,plain,
    ( spl0_269
  <=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f720,axiom,
    ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

fof(f3055,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f705,f3053]) ).

fof(f705,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

fof(f3051,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f704,f3049]) ).

fof(f3049,plain,
    ( spl0_267
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f704,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

fof(f3047,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f703,f3045]) ).

fof(f703,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X2,X1,X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

fof(f3043,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f663,f3041]) ).

fof(f663,axiom,
    ! [X0,X6,X25,X20] : c_lessequals(c_Set_Oimage(X25,c_Set_Ovimage(X25,X6,X20,X0),X20,X0),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

fof(f3039,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f649,f3037]) ).

fof(f649,axiom,
    ! [X0,X1,X8,X6] :
      ( hBOOL(c_in(X1,X8,X0))
      | ~ c_lessequals(c_Set_Oinsert(X1,X6,X0),X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

fof(f3035,plain,
    ( spl0_263
    | ~ spl0_19
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f1556,f1426,f1093,f3032]) ).

fof(f3032,plain,
    ( spl0_263
  <=> c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f1426,plain,
    ( spl0_95
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1556,plain,
    ( c_Finite__Set_Olinorder__class_OMax(tc_nat) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(tc_nat),tc_nat)
    | ~ spl0_19
    | ~ spl0_95 ),
    inference(resolution,[],[f1427,f1095]) ).

fof(f1427,plain,
    ( ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f1426]) ).

fof(f3030,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f611,f3028]) ).

fof(f611,axiom,
    ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

fof(f3026,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f591,f3024]) ).

fof(f3024,plain,
    ( spl0_261
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X8,X0)
        | c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f591,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

fof(f3022,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f447,f3020]) ).

fof(f3020,plain,
    ( spl0_260
  <=> ! [X6,X0,X1] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f447,axiom,
    ! [X0,X1,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X1,X6,X0),X0),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).

fof(f3018,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f339,f3016]) ).

fof(f3016,plain,
    ( spl0_259
  <=> ! [X35,X20,X0,X33] :
        ( ~ c_Finite__Set_Ofinite(X33,X20)
        | ~ c_Fun_Obij(X35,X0,X20)
        | c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f339,axiom,
    ! [X0,X35,X33,X20] :
      ( ~ c_Finite__Set_Ofinite(X33,X20)
      | ~ c_Fun_Obij(X35,X0,X20)
      | c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_1) ).

fof(f3014,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f338,f3012]) ).

fof(f338,axiom,
    ! [X0,X35,X33,X20] :
      ( c_Finite__Set_Ofinite(X33,X20)
      | ~ c_Fun_Obij(X35,X0,X20)
      | ~ c_Finite__Set_Ofinite(c_Set_Ovimage(X35,X33,X0,X20),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_0) ).

fof(f3010,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f252,f3008]) ).

fof(f252,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X2,X1,X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

fof(f3006,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f251,f3004]) ).

fof(f3004,plain,
    ( spl0_256
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f251,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

fof(f3002,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f250,f3000]) ).

fof(f250,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

fof(f2998,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f239,f2996]) ).

fof(f239,axiom,
    ! [X21,X0,X25,X20] :
      ( ~ class_HOL_Oord(X20)
      | ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
      | ~ c_lessequals(X21,X25,tc_fun(X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

fof(f2994,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f230,f2992]) ).

fof(f230,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X2,X1,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

fof(f2986,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f229,f2984]) ).

fof(f2984,plain,
    ( spl0_252
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f229,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

fof(f2982,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f228,f2980]) ).

fof(f228,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

fof(f2978,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f216,f2976]) ).

fof(f216,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X2,X1,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).

fof(f2974,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f215,f2972]) ).

fof(f2972,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X2,X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f215,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).

fof(f2970,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f214,f2968]) ).

fof(f214,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X1,X2,X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).

fof(f2966,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f213,f2964]) ).

fof(f2964,plain,
    ( spl0_247
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
        | c_HOL_Oord__class_Oless(X19,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f213,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
      | c_HOL_Oord__class_Oless(X19,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f2962,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f211,f2960]) ).

fof(f2960,plain,
    ( spl0_246
  <=> ! [X19,X0,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
        | c_HOL_Oord__class_Oless(X1,X19,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f211,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
      | c_HOL_Oord__class_Oless(X1,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f2958,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f144,f2956]) ).

fof(f144,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_lessequals(X2,X19,X0)
      | c_HOL_Oord__class_Oless(X1,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

fof(f2954,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f143,f2952]) ).

fof(f143,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X19,X0)
      | ~ c_lessequals(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X1,X19,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

fof(f2950,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f137,f2948]) ).

fof(f137,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X19,X2,X0)
      | ~ c_lessequals(X2,X1,X0)
      | c_HOL_Oord__class_Oless(X19,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

fof(f2946,plain,
    ( spl0_242
    | ~ spl0_19
    | ~ spl0_15
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f1553,f1422,f1073,f1093,f2943]) ).

fof(f1553,plain,
    ( ~ class_Orderings_Olinorder(tc_nat)
    | c_Lattices_Olower__semilattice__class_Oinf(tc_nat) = c_Orderings_Oord__class_Omin(tc_nat)
    | ~ spl0_15
    | ~ spl0_94 ),
    inference(resolution,[],[f1423,f1075]) ).

fof(f2941,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f136,f2939]) ).

fof(f136,axiom,
    ! [X2,X0,X1,X19] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_lessequals(X19,X2,X0)
      | c_HOL_Oord__class_Oless(X19,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

fof(f2937,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f89,f2935]) ).

fof(f2935,plain,
    ( spl0_240
  <=> ! [X20,X0,X25,X21] :
        ( ~ class_HOL_Oord(X20)
        | ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
        | c_lessequals(X25,X21,tc_fun(X0,X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f89,axiom,
    ! [X21,X0,X25,X20] :
      ( ~ class_HOL_Oord(X20)
      | ~ c_HOL_Oord__class_Oless(X25,X21,tc_fun(X0,X20))
      | c_lessequals(X25,X21,tc_fun(X0,X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

fof(f2933,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f1,f2931]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

fof(f2610,plain,
    ( spl0_237
    | ~ spl0_238
    | ~ spl0_26
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f1510,f1382,f1128,f2607,f2603]) ).

fof(f2603,plain,
    ( spl0_237
  <=> c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Orderings_Oord__class_Omax(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f2607,plain,
    ( spl0_238
  <=> class_Orderings_Olinorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f1510,plain,
    ( ~ class_Orderings_Olinorder(tc_bool)
    | c_Lattices_Oupper__semilattice__class_Osup(tc_bool) = c_Orderings_Oord__class_Omax(tc_bool)
    | ~ spl0_26
    | ~ spl0_84 ),
    inference(resolution,[],[f1383,f1130]) ).

fof(f2590,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f967,f2588]) ).

fof(f2588,plain,
    ( spl0_236
  <=> ! [X2,X0,X1] :
        ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0) = X2
        | ~ hBOOL(hAPP(c_fequal(X1,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f967,plain,
    ! [X2,X0,X1] :
      ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0) = X2
      | ~ hBOOL(hAPP(c_fequal(X1,X0),X2)) ),
    inference(forward_demodulation,[],[f966,f926]) ).

fof(f966,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(c_fequal(X1,X0),X2))
      | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X2 ),
    inference(forward_demodulation,[],[f790,f926]) ).

fof(f790,axiom,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2))
      | c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

fof(f2586,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f929,f2584]) ).

fof(f929,plain,
    ! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_fequal(hAPP(X25,X14),X0),X53,X0),X53)),
    inference(forward_demodulation,[],[f807,f926]) ).

fof(f807,axiom,
    ! [X0,X14,X53,X25] : hBOOL(c_in(X14,c_Set_Ovimage(X25,c_Set_Oinsert(hAPP(X25,X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X53,X0),X53)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

fof(f2582,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f914,f2580]) ).

fof(f2580,plain,
    ( spl0_234
  <=> ! [X20,X0,X19,X25] : c_The(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),X0) = X19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f914,plain,
    ! [X0,X19,X25,X20] : c_The(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),X0) = X19,
    inference(definition_unfolding,[],[f432,f57]) ).

fof(f432,axiom,
    ! [X0,X19,X25,X20] : c_Finite__Set_Ofold(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).

fof(f2578,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f847,f2576]) ).

fof(f847,axiom,
    ! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

fof(f2574,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f815,f2572]) ).

fof(f815,axiom,
    ! [X0,X8,X16,X14] :
      ( ~ hBOOL(c_in(X14,X8,X0))
      | hBOOL(c_in(X14,c_Set_Oinsert(X16,X8,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

fof(f2570,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f759,f2568]) ).

fof(f759,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

fof(f2566,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f716,f2564]) ).

fof(f716,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ hBOOL(c_in(X1,X6,X0))
      | c_lessequals(c_Complete__Lattice_OInf__class_OInf(X6,X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

fof(f2562,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f700,f2560]) ).

fof(f700,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | X1 = X2
      | ~ c_lessequals(X1,X2,X0)
      | ~ c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

fof(f2552,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f666,f2550]) ).

fof(f2550,plain,
    ( spl0_228
  <=> ! [X20,X0,X25] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X0,X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f666,axiom,
    ! [X0,X25,X20] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_bool)),X0,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

fof(f2548,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f635,f2546]) ).

fof(f2546,plain,
    ( spl0_227
  <=> ! [X20,X0,X14,X6,X25] :
        ( c_Fun_Oinj__on(X25,X6,X0,X20)
        | ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f635,axiom,
    ! [X0,X6,X14,X25,X20] :
      ( c_Fun_Oinj__on(X25,X6,X0,X20)
      | ~ c_Fun_Oinj__on(X25,c_Set_Oinsert(X14,X6,X0),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

fof(f2544,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f613,f2542]) ).

fof(f2542,plain,
    ( spl0_226
  <=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X8) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2540,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f612,f2538]) ).

fof(f2536,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f601,f2534]) ).

fof(f2534,plain,
    ( spl0_224
  <=> ! [X20,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X0,X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f601,axiom,
    ! [X0,X25,X20] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X25,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X0,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

fof(f2532,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f587,f2530]) ).

fof(f2530,plain,
    ( spl0_223
  <=> ! [X0,X44,X33] :
        ( c_Finite__Set_Ofinite(X33,X0)
        | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f587,axiom,
    ! [X0,X44,X33] :
      ( c_Finite__Set_Ofinite(X33,X0)
      | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

fof(f2528,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f586,f2526]) ).

fof(f2526,plain,
    ( spl0_222
  <=> ! [X0,X44,X33] :
        ( c_Finite__Set_Ofinite(X44,X0)
        | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f586,axiom,
    ! [X0,X44,X33] :
      ( c_Finite__Set_Ofinite(X44,X0)
      | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X33),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

fof(f2524,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f534,f2522]) ).

fof(f534,axiom,
    ! [X0,X8,X6] : c_lessequals(X8,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

fof(f2520,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f533,f2518]) ).

fof(f533,axiom,
    ! [X0,X8,X6] : c_lessequals(X6,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X8),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

fof(f2516,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f505,f2514]) ).

fof(f2514,plain,
    ( spl0_219
  <=> ! [X20,X0,X25,X2,X1] :
        ( hAPP(X25,X1) = X2
        | c_Fun_Ofun__upd(X25,X1,X2,X0,X20) != X25 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f505,axiom,
    ! [X2,X0,X1,X25,X20] :
      ( hAPP(X25,X1) = X2
      | c_Fun_Ofun__upd(X25,X1,X2,X0,X20) != X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

fof(f2512,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f429,f2510]) ).

fof(f2510,plain,
    ( spl0_218
  <=> ! [X0,X44,X33] :
        ( ~ c_Finite__Set_Ofinite(X33,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f429,axiom,
    ! [X0,X44,X33] :
      ( ~ c_Finite__Set_Ofinite(X33,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

fof(f2508,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f428,f2506]) ).

fof(f2506,plain,
    ( spl0_217
  <=> ! [X0,X44,X33] :
        ( ~ c_Finite__Set_Ofinite(X44,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f428,axiom,
    ! [X0,X44,X33] :
      ( ~ c_Finite__Set_Ofinite(X44,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X33),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

fof(f2504,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f400,f2502]) ).

fof(f400,axiom,
    ! [X4,X13] :
      ( c_Suc(X13) = X4
      | c_lessequals(X4,X13,tc_nat)
      | ~ c_lessequals(X4,c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

fof(f2500,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f372,f2498]) ).

fof(f372,axiom,
    ! [X4,X13] :
      ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | c_Suc(X4) = X13
      | c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f2496,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f273,f2494]) ).

fof(f273,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | X1 = X2
      | ~ c_lessequals(X1,X2,X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

fof(f2492,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f271,f2490]) ).

fof(f271,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | X14 = X16
      | ~ c_lessequals(X14,X16,X0)
      | c_HOL_Oord__class_Oless(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

fof(f2488,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f111,f2486]) ).

fof(f111,axiom,
    ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X8,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

fof(f2484,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f110,f2482]) ).

fof(f110,axiom,
    ! [X0,X8,X6] : c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X8),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

fof(f2480,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f95,f2478]) ).

fof(f95,axiom,
    ! [X28,X29,X27] :
      ( ~ c_HOL_Oord__class_Oless(X27,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X29,X28,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X27),X28,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f2476,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f80,f2474]) ).

fof(f2474,plain,
    ( spl0_209
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | X1 = X2
        | c_HOL_Oord__class_Oless(X2,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f80,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | X1 = X2
      | c_HOL_Oord__class_Oless(X2,X1,X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

fof(f2472,plain,
    ( spl0_208
    | ~ spl0_51
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2421,f2311,f1243,f2470]) ).

fof(f2470,plain,
    ( spl0_208
  <=> ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f2421,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(v_P,X0),X0))
    | ~ spl0_51
    | ~ spl0_201 ),
    inference(resolution,[],[f2312,f1244]) ).

fof(f2468,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f5,f2466]) ).

fof(f2466,plain,
    ( spl0_207
  <=> ! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f5,axiom,
    ! [X0,X8] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X8) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

fof(f2464,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f4,f2462]) ).

fof(f2462,plain,
    ( spl0_206
  <=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f4,axiom,
    ! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

fof(f2335,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f950,f2333]) ).

fof(f2333,plain,
    ( spl0_205
  <=> ! [X0,X14,X16,X25] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X14,X0),X0),X16))
        | X14 = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f950,plain,
    ! [X0,X16,X14,X25] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X14,X0),X0),X16))
      | X14 = X16 ),
    inference(forward_demodulation,[],[f788,f926]) ).

fof(f788,axiom,
    ! [X0,X16,X14,X25] :
      ( X14 = X16
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

fof(f2331,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f835,f2329]) ).

fof(f835,axiom,
    ! [X0,X1,X6] : c_Set_Oinsert(X1,X6,X0) = c_Set_Oinsert(X1,c_Set_Oinsert(X1,X6,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f2321,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f669,f2319]) ).

fof(f669,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

fof(f2317,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f668,f2315]) ).

fof(f668,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Otop__class_Otop(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

fof(f2313,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f640,f2311]) ).

fof(f640,axiom,
    ! [X44,X52] :
      ( ~ c_lessequals(X52,X44,tc_fun(t_a,tc_bool))
      | hBOOL(hAPP(hAPP(v_P,X44),X52)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I1_J_0) ).

fof(f2309,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f583,f2307]) ).

fof(f583,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X8,X0)
      | c_Finite__Set_Ofinite(X6,X0)
      | ~ c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

fof(f2305,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f556,f2303]) ).

fof(f2303,plain,
    ( spl0_199
  <=> ! [X6,X25,X0] : hAPP(c_Finite__Set_Ofold1(X25,X0),X6) = c_The(c_Finite__Set_Ofold1Set(X25,X6,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f556,axiom,
    ! [X0,X6,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),X6) = c_The(c_Finite__Set_Ofold1Set(X25,X6,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).

fof(f2301,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f437,f2299]) ).

fof(f2299,plain,
    ( spl0_198
  <=> ! [X20,X0,X19,X25] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X19)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f437,axiom,
    ! [X0,X19,X25,X20] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),X19)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

fof(f2297,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f431,f2295]) ).

fof(f431,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Obot__class_Obot(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f2293,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f430,f2291]) ).

fof(f430,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f2289,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f427,f2287]) ).

fof(f2287,plain,
    ( spl0_195
  <=> ! [X19,X20,X0,X6,X25,X1] :
        ( c_Finite__Set_Ofinite(X6,X0)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f427,axiom,
    ! [X0,X1,X6,X19,X25,X20] :
      ( c_Finite__Set_Ofinite(X6,X0)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X25,X19,X6,X0,X20),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

fof(f2285,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f337,f2283]) ).

fof(f337,axiom,
    ! [X0,X25,X20] :
      ( ~ c_Fun_Obij(X25,X0,X20)
      | c_Fun_Oinj__on(X25,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_0) ).

fof(f2281,plain,
    ( spl0_193
    | ~ spl0_2
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2250,f2028,f1008,f2278]) ).

fof(f2250,plain,
    ( v_U = c_Set_Oinsert(v_x,v_U,tc_Com_Opname)
    | ~ spl0_2
    | ~ spl0_185 ),
    inference(resolution,[],[f2029,f1010]) ).

fof(f2276,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f153,f2274]) ).

fof(f2274,plain,
    ( spl0_192
  <=> ! [X13,X4] :
        ( X4 = X13
        | ~ c_lessequals(X4,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f153,axiom,
    ! [X4,X13] :
      ( X4 = X13
      | ~ c_lessequals(X4,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

fof(f2272,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f139,f2270]) ).

fof(f139,axiom,
    ! [X28,X29,X27] :
      ( ~ c_lessequals(X27,X29,tc_nat)
      | ~ c_lessequals(X29,X28,tc_nat)
      | c_lessequals(X27,X28,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

fof(f2268,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f87,f2266]) ).

fof(f2266,plain,
    ( spl0_190
  <=> ! [X6,X0,X8] :
        ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
        | c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f87,axiom,
    ! [X0,X8,X6] :
      ( ~ c_HOL_Oord__class_Oless(X6,X8,tc_fun(X0,tc_bool))
      | c_lessequals(X6,X8,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

fof(f2264,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f16,f2262]) ).

fof(f2262,plain,
    ( spl0_189
  <=> ! [X13,X4] :
        ( X4 = X13
        | c_HOL_Oord__class_Oless(X13,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f16,axiom,
    ! [X4,X13] :
      ( X4 = X13
      | c_HOL_Oord__class_Oless(X13,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

fof(f2242,plain,
    ( spl0_188
    | ~ spl0_89
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f1685,f1583,f1402,f2240]) ).

fof(f2240,plain,
    ( spl0_188
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f1583,plain,
    ( spl0_117
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f1685,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
    | ~ spl0_89
    | ~ spl0_117 ),
    inference(resolution,[],[f1584,f1403]) ).

fof(f1584,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f1583]) ).

fof(f2178,plain,
    ( spl0_187
    | ~ spl0_85
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1523,f1390,f1386,f2176]) ).

fof(f2176,plain,
    ( spl0_187
  <=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f1386,plain,
    ( spl0_85
  <=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1523,plain,
    ( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_85
    | ~ spl0_86 ),
    inference(resolution,[],[f1391,f1387]) ).

fof(f1387,plain,
    ( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f1386]) ).

fof(f2034,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f926,f2032]) ).

fof(f2030,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f854,f2028]) ).

fof(f854,axiom,
    ! [X0,X6,X14] :
      ( ~ hBOOL(c_in(X14,X6,X0))
      | c_Set_Oinsert(X14,X6,X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f2026,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f851,f2024]) ).

fof(f2024,plain,
    ( spl0_184
  <=> ! [X6,X2,X0,X1] :
        ( ~ hBOOL(hAPP(X6,X1))
        | hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f851,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ hBOOL(hAPP(X6,X1))
      | hBOOL(hAPP(c_Set_Oinsert(X2,X6,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f2022,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f838,f2020]) ).

fof(f838,axiom,
    ! [X20] :
      ( ~ class_Orderings_Obot(X20)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X20)),v_x) = c_Orderings_Obot__class_Obot(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f2018,plain,
    ( spl0_182
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1862,f1691,f2016]) ).

fof(f2016,plain,
    ( spl0_182
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1862,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_140 ),
    inference(factoring,[],[f1692]) ).

fof(f2014,plain,
    ( spl0_181
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2010,f2007,f2012]) ).

fof(f2012,plain,
    ( spl0_181
  <=> ! [X0,X1] : c_Set_Ocontents(c_fequal(X1,X0),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f2007,plain,
    ( spl0_180
  <=> ! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f2010,plain,
    ( ! [X0,X1] : c_Set_Ocontents(c_fequal(X1,X0),X0) = X1
    | ~ spl0_180 ),
    inference(forward_demodulation,[],[f2008,f926]) ).

fof(f2008,plain,
    ( ! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f2007]) ).

fof(f2009,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f789,f2007]) ).

fof(f789,axiom,
    ! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).

fof(f2004,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f783,f2002]) ).

fof(f2002,plain,
    ( spl0_179
  <=> ! [X0,X1] : c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f783,axiom,
    ! [X0,X1] : c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).

fof(f2000,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f724,f1998]) ).

fof(f724,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).

fof(f1996,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f697,f1994]) ).

fof(f697,axiom,
    ! [X20] :
      ( ~ class_Orderings_Otop(X20)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X20)),v_x) = c_Orderings_Otop__class_Otop(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

fof(f1992,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f695,f1990]) ).

fof(f695,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).

fof(f1988,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f657,f1986]) ).

fof(f657,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

fof(f1984,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f615,f1982]) ).

fof(f615,axiom,
    ! [X0,X6] : c_HOL_Ominus__class_Ominus(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f1980,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f614,f1978]) ).

fof(f614,axiom,
    ! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X6,X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f1966,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f594,f1964]) ).

fof(f594,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1962,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f593,f1960]) ).

fof(f593,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1958,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f592,f1956]) ).

fof(f1956,plain,
    ( spl0_170
  <=> ! [X6,X0,X8] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f592,axiom,
    ! [X0,X8,X6] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

fof(f1954,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f530,f1952]) ).

fof(f530,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1950,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f529,f1948]) ).

fof(f529,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1946,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f526,f1944]) ).

fof(f526,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1942,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f525,f1940]) ).

fof(f525,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1938,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f523,f1936]) ).

fof(f523,axiom,
    ! [X0,X8,X6] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X8,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f1934,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f501,f1932]) ).

fof(f501,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).

fof(f1930,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f266,f1928]) ).

fof(f266,axiom,
    ! [X4,X13] :
      ( X4 = X13
      | ~ c_lessequals(X4,X13,tc_nat)
      | c_HOL_Oord__class_Oless(X4,X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

fof(f1926,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f180,f1924]) ).

fof(f180,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

fof(f1922,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f179,f1920]) ).

fof(f179,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X2),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

fof(f1918,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f171,f1916]) ).

fof(f171,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).

fof(f1914,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f170,f1912]) ).

fof(f170,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X2,hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).

fof(f1910,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f109,f1908]) ).

fof(f109,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f1906,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f108,f1904]) ).

fof(f108,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f1902,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f104,f1900]) ).

fof(f104,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f1898,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f103,f1896]) ).

fof(f103,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X2),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f1894,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f77,f1892]) ).

fof(f77,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

fof(f1890,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f74,f1888]) ).

fof(f74,axiom,
    ! [X4,X13] :
      ( X4 = X13
      | ~ c_lessequals(X4,X13,tc_nat)
      | ~ c_lessequals(X13,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

fof(f1886,plain,
    ( ~ spl0_1
    | spl0_152
    | ~ spl0_3
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1865,f1695,f1013,f1883,f1003]) ).

fof(f1883,plain,
    ( spl0_152
  <=> c_Finite__Set_Ofinite(v_G,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1865,plain,
    ( c_Finite__Set_Ofinite(v_G,t_a)
    | ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname)
    | ~ spl0_3
    | ~ spl0_141 ),
    inference(superposition,[],[f1696,f1015]) ).

fof(f1881,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f7,f1879]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),c_Orderings_Otop__class_Otop(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

fof(f1877,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f6,f1875]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

fof(f1797,plain,
    ( spl0_149
    | ~ spl0_43
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f1526,f1398,f1211,f1795]) ).

fof(f1795,plain,
    ( spl0_149
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1526,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_43
    | ~ spl0_88 ),
    inference(resolution,[],[f1399,f1212]) ).

fof(f1726,plain,
    ( spl0_148
    | ~ spl0_44
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f1524,f1394,f1215,f1724]) ).

fof(f1524,plain,
    ( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
    | ~ spl0_44
    | ~ spl0_87 ),
    inference(resolution,[],[f1395,f1216]) ).

fof(f1721,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f952,f1719]) ).

fof(f1719,plain,
    ( spl0_147
  <=> ! [X0,X1,X26] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X26
        | ~ hBOOL(hAPP(X26,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f952,plain,
    ! [X0,X1,X26] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X26
      | ~ hBOOL(hAPP(X26,X1)) ),
    inference(forward_demodulation,[],[f608,f665]) ).

fof(f608,axiom,
    ! [X0,X1,X26] :
      ( ~ hBOOL(hAPP(X26,X1))
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X26,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).

fof(f1717,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f949,f1715]) ).

fof(f1715,plain,
    ( spl0_146
  <=> ! [X0,X16,X14] :
        ( ~ hBOOL(c_in(X16,c_fequal(X14,X0),X0))
        | X14 = X16 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f949,plain,
    ! [X0,X16,X14] :
      ( ~ hBOOL(c_in(X16,c_fequal(X14,X0),X0))
      | X14 = X16 ),
    inference(forward_demodulation,[],[f839,f926]) ).

fof(f839,axiom,
    ! [X0,X16,X14] :
      ( X14 = X16
      | ~ hBOOL(c_in(X16,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

fof(f1713,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f946,f1711]) ).

fof(f946,plain,
    ! [X0,X14] :
      ( c_fequal(X14,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0)
      | ~ class_Orderings_Oorder(X0) ),
    inference(forward_demodulation,[],[f794,f926]) ).

fof(f794,axiom,
    ! [X0,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X14,X14,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

fof(f1709,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f941,f1707]) ).

fof(f941,plain,
    ! [X0,X14] :
      ( hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_fequal(X14,X0)) = X14
      | ~ class_Orderings_Olinorder(X0) ),
    inference(forward_demodulation,[],[f792,f926]) ).

fof(f792,axiom,
    ! [X0,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(c_Finite__Set_Olinorder__class_OMax(X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

fof(f1705,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f940,f1703]) ).

fof(f940,plain,
    ! [X0,X14] :
      ( hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_fequal(X14,X0)) = X14
      | ~ class_Orderings_Olinorder(X0) ),
    inference(forward_demodulation,[],[f782,f926]) ).

fof(f782,axiom,
    ! [X0,X14] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(c_Finite__Set_Olinorder__class_OMin(X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

fof(f1701,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f930,f1699]) ).

fof(f930,plain,
    ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_fequal(X1,X0),X0))),
    inference(forward_demodulation,[],[f779,f926]) ).

fof(f779,axiom,
    ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

fof(f1697,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f828,f1695]) ).

fof(f828,axiom,
    ! [X0,X35,X33,X20] :
      ( ~ c_Finite__Set_Ofinite(X33,X0)
      | c_Finite__Set_Ofinite(c_Set_Oimage(X35,X33,X0,X20),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

fof(f1693,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f760,f1691]) ).

fof(f760,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X2,X0)
      | c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f1689,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f712,f1687]) ).

fof(f1687,plain,
    ( spl0_139
  <=> ! [X20,X0,X25,X2,X1] : hAPP(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f712,axiom,
    ! [X2,X0,X1,X25,X20] : hAPP(c_Fun_Ofun__upd(X25,X1,X2,X20,X0),X1) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

fof(f1682,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f711,f1680]) ).

fof(f711,axiom,
    ! [X0,X1,X25,X20] : c_Fun_Ofun__upd(X25,X1,hAPP(X25,X1),X20,X0) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

fof(f1678,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f609,f1676]) ).

fof(f1676,plain,
    ( spl0_137
  <=> ! [X25,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f609,axiom,
    ! [X0,X1,X25] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

fof(f1674,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f550,f1672]) ).

fof(f1672,plain,
    ( spl0_136
  <=> ! [X6,X0] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X6) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f550,axiom,
    ! [X0,X6] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X6),X6) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f1670,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f549,f1668]) ).

fof(f549,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X1),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1666,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f419,f1664]) ).

fof(f419,axiom,
    ! [X4,X13] :
      ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

fof(f1662,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f418,f1660]) ).

fof(f418,axiom,
    ! [X4,X13] :
      ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f1658,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f290,f1656]) ).

fof(f1656,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f290,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

fof(f1654,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f288,f1652]) ).

fof(f1652,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f288,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f1650,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f287,f1648]) ).

fof(f1648,plain,
    ( spl0_130
  <=> ! [X0,X16,X14] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X16,X14,X0)
        | ~ c_HOL_Oord__class_Oless(X14,X16,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f287,axiom,
    ! [X0,X16,X14] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X16,X14,X0)
      | ~ c_HOL_Oord__class_Oless(X14,X16,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f1646,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f277,f1644]) ).

fof(f277,axiom,
    ! [X4,X13] :
      ( ~ c_lessequals(X13,X4,tc_nat)
      | c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

fof(f1642,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f276,f1640]) ).

fof(f276,axiom,
    ! [X4,X13] :
      ( c_lessequals(X13,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X13),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

fof(f1638,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f240,f1636]) ).

fof(f240,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f1634,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f237,f1632]) ).

fof(f237,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_lessequals(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

fof(f1630,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f232,f1628]) ).

fof(f232,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_lessequals(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

fof(f1626,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f127,f1624]) ).

fof(f127,axiom,
    ! [X0,X6] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X6),X6) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1622,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f126,f1620]) ).

fof(f126,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X1),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1618,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f91,f1616]) ).

fof(f1616,plain,
    ( spl0_122
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_lessequals(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f91,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_lessequals(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

fof(f1614,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f90,f1612]) ).

fof(f1612,plain,
    ( spl0_121
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_lessequals(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f90,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_lessequals(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

fof(f1610,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f81,f1608]) ).

fof(f81,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X1),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).

fof(f1606,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f69,f1604]) ).

fof(f69,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X1),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

fof(f1602,plain,
    ( spl0_118
    | ~ spl0_2
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f1589,f1486,f1008,f1599]) ).

fof(f1589,plain,
    ( hBOOL(hAPP(v_U,v_x))
    | ~ spl0_2
    | ~ spl0_110 ),
    inference(resolution,[],[f1487,f1010]) ).

fof(f1585,plain,
    ( spl0_117
    | ~ spl0_40
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f1527,f1402,f1199,f1583]) ).

fof(f1527,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
    | ~ spl0_40
    | ~ spl0_89 ),
    inference(resolution,[],[f1403,f1200]) ).

fof(f1516,plain,
    ( spl0_116
    | ~ spl0_19
    | ~ spl0_14
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f1509,f1382,f1068,f1093,f1513]) ).

fof(f1509,plain,
    ( ~ class_Orderings_Olinorder(tc_nat)
    | c_Lattices_Oupper__semilattice__class_Osup(tc_nat) = c_Orderings_Oord__class_Omax(tc_nat)
    | ~ spl0_14
    | ~ spl0_84 ),
    inference(resolution,[],[f1383,f1070]) ).

fof(f1070,plain,
    ( class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f1068]) ).

fof(f1508,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f943,f1506]) ).

fof(f943,plain,
    ! [X0,X14] :
      ( c_Complete__Lattice_OSup__class_OSup(c_fequal(X14,X0),X0) = X14
      | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
    inference(forward_demodulation,[],[f778,f926]) ).

fof(f778,axiom,
    ! [X0,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

fof(f1504,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f942,f1502]) ).

fof(f942,plain,
    ! [X0,X14] :
      ( c_Complete__Lattice_OInf__class_OInf(c_fequal(X14,X0),X0) = X14
      | ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
    inference(forward_demodulation,[],[f796,f926]) ).

fof(f796,axiom,
    ! [X0,X14] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

fof(f1500,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f928,f1498]) ).

fof(f1498,plain,
    ( spl0_113
  <=> ! [X25,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X1,X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f928,plain,
    ! [X0,X1,X25] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_fequal(X1,X0),X0),X1)),
    inference(forward_demodulation,[],[f781,f926]) ).

fof(f781,axiom,
    ! [X0,X1,X25] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X25,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

fof(f1496,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f927,f1494]) ).

fof(f927,plain,
    ! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_fequal(X14,X0)) = X14,
    inference(forward_demodulation,[],[f791,f926]) ).

fof(f791,axiom,
    ! [X0,X14,X25] : hAPP(c_Finite__Set_Ofold1(X25,X0),c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

fof(f1492,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f913,f1490]) ).

fof(f913,axiom,
    ! [X0,X47,X57] :
      ( X47 = X57
      | ~ hBOOL(hAPP(c_fequal(X47,X0),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1488,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f845,f1486]) ).

fof(f845,axiom,
    ! [X51,X0,X1] :
      ( hBOOL(hAPP(X51,X1))
      | ~ hBOOL(c_in(X1,X51,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1484,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f844,f1482]) ).

fof(f844,axiom,
    ! [X51,X0,X1] :
      ( ~ hBOOL(hAPP(X51,X1))
      | hBOOL(c_in(X1,X51,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1480,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f833,f1478]) ).

fof(f1478,plain,
    ( spl0_108
  <=> ! [X6,X0,X14] :
        ( c_Finite__Set_Ofinite(X6,X0)
        | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f833,axiom,
    ! [X0,X6,X14] :
      ( c_Finite__Set_Ofinite(X6,X0)
      | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

fof(f1476,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f832,f1474]) ).

fof(f1474,plain,
    ( spl0_107
  <=> ! [X6,X0,X14] :
        ( ~ c_Finite__Set_Ofinite(X6,X0)
        | c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f832,axiom,
    ! [X0,X6,X14] :
      ( ~ c_Finite__Set_Ofinite(X6,X0)
      | c_Finite__Set_Ofinite(c_Set_Oinsert(X14,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

fof(f1472,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f822,f1470]) ).

fof(f822,axiom,
    ! [X0,X6,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X14,X6,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

fof(f1468,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f722,f1466]) ).

fof(f722,axiom,
    ! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

fof(f1464,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f630,f1462]) ).

fof(f630,axiom,
    ! [X0,X8,X14] : c_lessequals(X8,c_Set_Oinsert(X14,X8,X0),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1460,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f616,f1458]) ).

fof(f616,axiom,
    ! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1456,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f610,f1454]) ).

fof(f1454,plain,
    ( spl0_102
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f610,axiom,
    ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

fof(f1452,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f433,f1450]) ).

fof(f1450,plain,
    ( spl0_101
  <=> ! [X6,X0] : ~ c_HOL_Oord__class_Oless(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f433,axiom,
    ! [X0,X6] : ~ c_HOL_Oord__class_Oless(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

fof(f1448,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f403,f1446]) ).

fof(f403,axiom,
    ! [X4,X13] :
      ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f1444,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f402,f1442]) ).

fof(f402,axiom,
    ! [X4,X13] :
      ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f1440,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f374,f1438]) ).

fof(f374,axiom,
    ! [X4,X13] :
      ( c_lessequals(X4,X13,tc_nat)
      | c_lessequals(c_Suc(X13),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

fof(f1436,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f373,f1434]) ).

fof(f373,axiom,
    ! [X4,X13] :
      ( ~ c_lessequals(X4,X13,tc_nat)
      | ~ c_lessequals(c_Suc(X13),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

fof(f1432,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f348,f1430]) ).

fof(f348,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).

fof(f1428,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f347,f1426]) ).

fof(f347,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).

fof(f1424,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f227,f1422]) ).

fof(f227,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X0) = c_Orderings_Oord__class_Omin(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).

fof(f1420,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f202,f1418]) ).

fof(f202,axiom,
    ! [X4,X13] :
      ( c_lessequals(X4,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

fof(f1416,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f201,f1414]) ).

fof(f201,axiom,
    ! [X4,X13] :
      ( ~ c_lessequals(X4,X13,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

fof(f1412,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f164,f1410]) ).

fof(f164,axiom,
    ! [X4,X13] :
      ( ~ c_HOL_Oord__class_Oless(X13,X4,tc_nat)
      | c_lessequals(c_Suc(X13),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

fof(f1408,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f163,f1406]) ).

fof(f163,axiom,
    ! [X4,X13] :
      ( c_HOL_Oord__class_Oless(X13,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X13),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

fof(f1404,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f155,f1402]) ).

fof(f155,axiom,
    ! [X4,X13] :
      ( ~ c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

fof(f1400,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f154,f1398]) ).

fof(f154,axiom,
    ! [X4,X13] :
      ( c_HOL_Oord__class_Oless(X4,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X4),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

fof(f1396,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f115,f1394]) ).

fof(f115,axiom,
    ! [X4,X13] :
      ( ~ c_lessequals(X4,X13,tc_nat)
      | c_lessequals(X4,c_Suc(X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

fof(f1392,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f114,f1390]) ).

fof(f114,axiom,
    ! [X4,X13] :
      ( c_lessequals(X4,X13,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

fof(f1388,plain,
    ( spl0_85
    | ~ spl0_43
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f1377,f1345,f1211,f1386]) ).

fof(f1377,plain,
    ( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
    | ~ spl0_43
    | ~ spl0_76 ),
    inference(resolution,[],[f1346,f1212]) ).

fof(f1384,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f21,f1382]) ).

fof(f21,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X0) = c_Orderings_Oord__class_Omax(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).

fof(f1375,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f870,f1373]) ).

fof(f1373,plain,
    ( spl0_83
  <=> ! [X55,X56] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X55)
        | ~ class_Finite__Set_Ofinite_Ofinite(X56)
        | class_Finite__Set_Ofinite_Ofinite(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f870,axiom,
    ! [X56,X55] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X55)
      | ~ class_Finite__Set_Ofinite_Ofinite(X56)
      | class_Finite__Set_Ofinite_Ofinite(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

fof(f1371,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f842,f1369]) ).

fof(f842,axiom,
    ! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

fof(f1367,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f820,f1365]) ).

fof(f820,axiom,
    ! [X0,X15] : ~ hBOOL(c_in(X15,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

fof(f1363,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f617,f1361]) ).

fof(f617,axiom,
    ! [X0,X25,X20] : c_Fun_Oinj__on(X25,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

fof(f1359,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f547,f1357]) ).

fof(f547,axiom,
    ! [X50,X0,X26,X20] : hAPP(c_COMBK(X26,X0,X20),X50) = X26,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1355,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f490,f1353]) ).

fof(f490,axiom,
    ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

fof(f1351,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f289,f1349]) ).

fof(f289,axiom,
    ! [X4,X13] :
      ( c_lessequals(X4,X13,tc_nat)
      | c_lessequals(X13,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

fof(f1347,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f86,f1345]) ).

fof(f86,axiom,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_lessequals(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

fof(f1343,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f43,f1341]) ).

fof(f1341,plain,
    ( spl0_75
  <=> ! [X24,X23] :
        ( X23 = X24
        | c_Suc(X23) != c_Suc(X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f43,axiom,
    ! [X24,X23] :
      ( X23 = X24
      | c_Suc(X23) != c_Suc(X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

fof(f1339,plain,
    ( ~ spl0_74
    | ~ spl0_44
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f1334,f1319,f1215,f1336]) ).

fof(f1336,plain,
    ( spl0_74
  <=> class_Orderings_Otop(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f1334,plain,
    ( ~ class_Orderings_Otop(tc_nat)
    | ~ spl0_44
    | ~ spl0_70 ),
    inference(resolution,[],[f1320,f1216]) ).

fof(f1333,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f830,f1331]) ).

fof(f1331,plain,
    ( spl0_73
  <=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f830,axiom,
    ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f1329,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f816,f1327]) ).

fof(f816,axiom,
    ! [X0,X1,X6] : hBOOL(hAPP(c_Set_Oinsert(X1,X6,X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f1325,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f751,f1323]) ).

fof(f1323,plain,
    ( spl0_71
  <=> ! [X0,X1] : c_The(c_fequal(X1,X0),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f751,axiom,
    ! [X0,X1] : c_The(c_fequal(X1,X0),X0) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

fof(f1321,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f723,f1319]) ).

fof(f723,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Otop(X0)
      | c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

fof(f1317,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f696,f1315]) ).

fof(f1315,plain,
    ( spl0_69
  <=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f696,axiom,
    ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

fof(f1313,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f595,f1311]) ).

fof(f595,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Obot(X0)
      | c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f1309,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f912,f1307]) ).

fof(f1307,plain,
    ( spl0_67
  <=> ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f912,axiom,
    ! [X0,X1] : hBOOL(hAPP(c_fequal(X1,X0),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f1305,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f877,f1303]) ).

fof(f1303,plain,
    ( spl0_66
  <=> ! [X55,X56] :
        ( ~ class_HOL_Oord(X56)
        | class_HOL_Oord(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f877,axiom,
    ! [X56,X55] :
      ( ~ class_HOL_Oord(X56)
      | class_HOL_Oord(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f1301,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f876,f1299]) ).

fof(f1299,plain,
    ( spl0_65
  <=> ! [X55,X56] :
        ( ~ class_HOL_Ominus(X56)
        | class_HOL_Ominus(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f876,axiom,
    ! [X56,X55] :
      ( ~ class_HOL_Ominus(X56)
      | class_HOL_Ominus(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f1297,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f875,f1295]) ).

fof(f875,axiom,
    ! [X56,X55] :
      ( ~ class_Orderings_Obot(X56)
      | class_Orderings_Obot(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f1293,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f874,f1291]) ).

fof(f874,axiom,
    ! [X56,X55] :
      ( ~ class_Orderings_Otop(X56)
      | class_Orderings_Otop(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

fof(f1289,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f873,f1287]) ).

fof(f873,axiom,
    ! [X56,X55] :
      ( ~ class_Orderings_Oorder(X56)
      | class_Orderings_Oorder(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f1285,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f872,f1283]) ).

fof(f1283,plain,
    ( spl0_61
  <=> ! [X55,X56] :
        ( ~ class_Lattices_Olattice(X56)
        | class_Lattices_Olattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f872,axiom,
    ! [X56,X55] :
      ( ~ class_Lattices_Olattice(X56)
      | class_Lattices_Olattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f1281,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f871,f1279]) ).

fof(f1279,plain,
    ( spl0_60
  <=> ! [X55,X56] :
        ( ~ class_Orderings_Opreorder(X56)
        | class_Orderings_Opreorder(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f871,axiom,
    ! [X56,X55] :
      ( ~ class_Orderings_Opreorder(X56)
      | class_Orderings_Opreorder(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f1277,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f869,f1275]) ).

fof(f869,axiom,
    ! [X56,X55] :
      ( ~ class_Lattices_Obounded__lattice(X56)
      | class_Lattices_Obounded__lattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f1273,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f868,f1271]) ).

fof(f1271,plain,
    ( spl0_58
  <=> ! [X55,X56] :
        ( ~ class_Lattices_Odistrib__lattice(X56)
        | class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f868,axiom,
    ! [X56,X55] :
      ( ~ class_Lattices_Odistrib__lattice(X56)
      | class_Lattices_Odistrib__lattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f1269,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f867,f1267]) ).

fof(f867,axiom,
    ! [X56,X55] :
      ( ~ class_Lattices_Olattice(X56)
      | class_Lattices_Olower__semilattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f1265,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f866,f1263]) ).

fof(f866,axiom,
    ! [X56,X55] :
      ( ~ class_Lattices_Olattice(X56)
      | class_Lattices_Oupper__semilattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f1261,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f865,f1259]) ).

fof(f865,axiom,
    ! [X56,X55] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X56)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X55,X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(f1257,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f831,f1255]) ).

fof(f831,axiom,
    ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

fof(f1253,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f741,f1251]) ).

fof(f741,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | c_lessequals(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f1249,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f740,f1247]) ).

fof(f740,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f1245,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f735,f1243]) ).

fof(f735,axiom,
    ! [X0,X1] : c_lessequals(X1,X1,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

fof(f1241,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f67,f1239]) ).

fof(f1239,plain,
    ( spl0_50
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f67,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1237,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f66,f1235]) ).

fof(f1235,plain,
    ( spl0_49
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f66,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1233,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f65,f1231]) ).

fof(f65,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1229,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f61,f1227]) ).

fof(f1227,plain,
    ( spl0_47
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f61,axiom,
    ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

fof(f1225,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f856,f1223]) ).

fof(f856,axiom,
    ! [X0,X6] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X0)
      | c_Finite__Set_Ofinite(X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

fof(f1221,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f665,f1219]) ).

fof(f1219,plain,
    ( spl0_45
  <=> ! [X0,X26] : c_Collect(X26,X0) = X26 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1217,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f120,f1215]) ).

fof(f120,axiom,
    ! [X13] : ~ c_lessequals(c_Suc(X13),X13,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

fof(f1213,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f94,f1211]) ).

fof(f94,axiom,
    ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f1209,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f138,f1207]) ).

fof(f138,axiom,
    ! [X13] : c_lessequals(X13,X13,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

fof(f1205,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f124,f1203]) ).

fof(f1203,plain,
    ( spl0_41
  <=> ! [X13] : c_Suc(X13) != X13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f124,axiom,
    ! [X13] : c_Suc(X13) != X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

fof(f1201,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f62,f1199]) ).

fof(f62,axiom,
    ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f1197,plain,
    ( ~ spl0_39
    | spl0_38 ),
    inference(avatar_split_clause,[],[f1192,f1188,f1194]) ).

fof(f1188,plain,
    ( spl0_38
  <=> hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1192,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_fequal(hAPP(v_mgt__call,v_x),t_a)))
    | spl0_38 ),
    inference(forward_demodulation,[],[f1190,f926]) ).

fof(f1190,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)))
    | spl0_38 ),
    inference(avatar_component_clause,[],[f1188]) ).

fof(f1191,plain,
    ~ spl0_38,
    inference(avatar_split_clause,[],[f925,f1188]) ).

fof(f925,plain,
    ~ hBOOL(hAPP(hAPP(v_P,v_G),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    inference(forward_demodulation,[],[f864,f862]) ).

fof(f862,axiom,
    v_G = c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f864,axiom,
    ~ hBOOL(hAPP(hAPP(v_P,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a)),c_Set_Oinsert(hAPP(v_mgt__call,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f1186,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f911,f1183]) ).

fof(f911,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f1181,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f910,f1178]) ).

fof(f1178,plain,
    ( spl0_36
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f910,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f1176,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f909,f1173]) ).

fof(f909,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f1171,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f908,f1168]) ).

fof(f908,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

fof(f1166,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f907,f1163]) ).

fof(f907,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f1161,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f906,f1158]) ).

fof(f906,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f1156,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f905,f1153]) ).

fof(f905,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f1151,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f904,f1148]) ).

fof(f1148,plain,
    ( spl0_30
  <=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f904,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

fof(f1146,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f903,f1143]) ).

fof(f903,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f1141,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f902,f1138]) ).

fof(f1138,plain,
    ( spl0_28
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f902,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f1136,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f901,f1133]) ).

fof(f901,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f1131,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f900,f1128]) ).

fof(f900,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f1126,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f899,f1123]) ).

fof(f899,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

fof(f1121,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f898,f1118]) ).

fof(f1118,plain,
    ( spl0_24
  <=> class_HOL_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f898,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

fof(f1116,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f897,f1113]) ).

fof(f1113,plain,
    ( spl0_23
  <=> class_HOL_Ominus(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f897,axiom,
    class_HOL_Ominus(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

fof(f1111,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f896,f1108]) ).

fof(f896,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

fof(f1106,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f895,f1103]) ).

fof(f895,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f1101,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f894,f1098]) ).

fof(f894,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f1096,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f893,f1093]) ).

fof(f893,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f1091,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f892,f1088]) ).

fof(f1088,plain,
    ( spl0_18
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f892,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f1086,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f891,f1083]) ).

fof(f1083,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f891,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f1081,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f890,f1078]) ).

fof(f1078,plain,
    ( spl0_16
  <=> class_Lattices_Odistrib__lattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f890,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

fof(f1076,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f889,f1073]) ).

fof(f889,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

fof(f1071,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f888,f1068]) ).

fof(f888,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

fof(f1066,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f887,f1063]) ).

fof(f887,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f1061,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f886,f1058]) ).

fof(f1058,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f886,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f1056,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f885,f1053]) ).

fof(f1053,plain,
    ( spl0_11
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f885,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f1051,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f884,f1048]) ).

fof(f1048,plain,
    ( spl0_10
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f884,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f1046,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f883,f1043]) ).

fof(f883,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1041,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f882,f1038]) ).

fof(f1038,plain,
    ( spl0_8
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f882,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1036,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f881,f1033]) ).

fof(f1033,plain,
    ( spl0_7
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f881,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1031,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f880,f1028]) ).

fof(f1028,plain,
    ( spl0_6
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f880,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f1026,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f879,f1023]) ).

fof(f1023,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f879,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f1021,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f878,f1018]) ).

fof(f1018,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f878,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f1016,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f862,f1013]) ).

fof(f1011,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f863,f1008]) ).

fof(f863,axiom,
    hBOOL(c_in(v_x,v_U,tc_Com_Opname)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f1006,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f861,f1003]) ).

fof(f861,axiom,
    c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV879-1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 07:09:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (11502)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (11506)WARNING: value z3 for option sas not known
% 0.20/0.43  % (11505)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.43  % (11508)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.43  % (11507)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.43  % (11509)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.43  % (11504)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.43  % (11506)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.43  % (11510)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)
% 1.71/0.68  TRYING [1]
% 1.71/0.72  TRYING [2]
% 6.90/1.40  TRYING [3]
% 8.01/1.54  TRYING [1]
% 8.57/1.69  TRYING [2]
% 9.12/1.77  TRYING [1]
% 9.87/1.81  TRYING [2]
% 14.04/2.42  TRYING [3]
% 20.88/3.42  % (11508)First to succeed.
% 21.63/3.49  % (11508)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11502"
% 21.63/3.50  % (11508)Refutation found. Thanks to Tanya!
% 21.63/3.50  % SZS status Unsatisfiable for theBenchmark
% 21.63/3.50  % SZS output start Proof for theBenchmark
% See solution above
% 21.84/3.54  % (11508)------------------------------
% 21.84/3.54  % (11508)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 21.84/3.54  % (11508)Termination reason: Refutation
% 21.84/3.54  
% 21.84/3.54  % (11508)Memory used [KB]: 21635
% 21.84/3.54  % (11508)Time elapsed: 3.051 s
% 21.84/3.54  % (11508)Instructions burned: 4311 (million)
% 21.84/3.54  % (11502)Success in time 3.172 s
%------------------------------------------------------------------------------