%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT024-1 : 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 : n003.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 02:50:03 EDT 2024

% Result   : Unsatisfiable 14.30s 2.44s
% Output   : Refutation 14.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      : 1342
% Syntax   : Number of formulae    : 2533 ( 783 unt;   0 def)
%            Number of atoms       : 5809 ( 744 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 5724 (2448   ~;2523   |;   0   &)
%                                         ( 753 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :  783 ( 781 usr; 754 prp; 0-5 aty)
%            Number of functors    :   90 (  90 usr;   8 con; 0-7 aty)
%            Number of variables   : 4908 (4908   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f32370,plain,
    $false,
    inference(avatar_sat_refutation,[],[f803,f807,f812,f817,f822,f827,f832,f837,f842,f847,f852,f857,f862,f867,f871,f876,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f921,f925,f929,f933,f937,f941,f945,f949,f953,f957,f961,f965,f969,f973,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1034,f1038,f1052,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1111,f1115,f1119,f1123,f1127,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1214,f1218,f1245,f1274,f1278,f1282,f1287,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1372,f1404,f1427,f1431,f1435,f1439,f1443,f1447,f1451,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1495,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1605,f1609,f1613,f1682,f1692,f1718,f1722,f1726,f1730,f1734,f1738,f1748,f1752,f1756,f1760,f1764,f1768,f1772,f1776,f1780,f1784,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1967,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2050,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2102,f2106,f2110,f2114,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2166,f2170,f2175,f2181,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2504,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2785,f2789,f2793,f2797,f2801,f2805,f3233,f3255,f3259,f3263,f3267,f3272,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3324,f3328,f3332,f3336,f3340,f3344,f3348,f3352,f3357,f3361,f3365,f3502,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3836,f3840,f3844,f3848,f3852,f3856,f3860,f3864,f3868,f3872,f3876,f3962,f4056,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4425,f4562,f4687,f4691,f4695,f4699,f4703,f4707,f4864,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f5007,f5329,f5333,f5337,f5341,f5345,f5349,f5353,f5357,f5361,f5365,f5369,f5373,f5377,f5381,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5453,f5457,f5461,f5465,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5497,f5501,f6394,f6398,f6402,f6406,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6513,f6717,f6722,f6726,f6730,f6734,f6738,f6742,f6746,f6750,f6754,f7213,f7217,f7221,f7226,f7230,f7234,f7238,f7242,f7246,f7250,f7254,f7258,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7722,f7789,f7793,f7797,f7807,f7811,f7815,f7819,f7823,f7827,f7831,f7835,f7844,f8155,f8159,f8163,f8167,f8171,f8175,f8221,f8225,f8229,f8233,f8237,f8241,f8245,f8249,f8253,f8257,f8266,f8270,f9295,f9299,f9304,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9336,f9340,f9345,f9349,f9353,f9357,f9361,f9365,f10581,f10656,f10660,f10664,f10668,f10672,f10676,f10680,f10684,f10688,f10692,f10696,f10700,f11242,f11246,f11250,f11254,f11258,f11262,f11267,f11271,f11275,f11279,f11283,f11287,f11676,f11680,f11684,f11688,f11698,f11702,f11706,f11710,f11714,f11718,f11722,f11726,f11730,f11734,f11743,f11747,f11751,f11755,f11759,f11764,f11804,f12816,f12930,f12934,f12938,f12942,f12946,f12950,f12954,f13123,f13127,f13140,f13144,f13376,f13380,f13384,f13388,f13455,f13459,f13463,f13468,f13614,f13618,f13622,f13626,f13630,f13635,f13639,f13643,f13647,f13651,f13655,f13659,f14044,f15490,f15494,f15498,f15502,f15506,f15510,f15514,f15599,f16056,f16060,f16064,f16068,f16072,f16076,f16080,f16467,f16471,f16577,f16581,f16585,f16589,f16593,f16597,f16760,f16764,f16768,f16772,f16935,f16939,f17044,f17075,f17080,f17129,f17133,f17234,f17283,f17287,f17338,f17389,f17393,f17457,f17461,f17465,f17534,f17592,f17596,f17705,f17709,f17713,f17884,f17888,f18048,f18117,f18121,f18149,f18193,f18199,f18579,f18665,f18676,f18685,f18701,f18711,f18728,f18732,f18736,f18776,f18780,f18804,f18812,f18816,f18820,f18824,f18838,f18887,f18891,f18896,f18900,f18976,f18980,f19101,f19105,f19113,f19115,f19319,f19323,f19327,f19331,f19335,f19339,f19343,f19347,f19351,f19355,f19359,f19363,f19367,f19371,f19375,f19379,f19383,f19581,f19602,f19606,f19610,f19614,f19618,f19622,f19626,f19688,f19692,f19904,f19908,f19912,f19916,f19920,f19924,f19929,f19934,f19939,f19944,f19948,f19952,f19956,f19960,f19964,f19968,f19972,f20230,f20232,f20234,f20236,f20266,f20270,f20274,f20282,f20295,f20300,f20304,f20309,f20315,f20321,f20326,f20333,f20378,f20379,f20380,f20381,f20382,f20383,f20384,f20385,f20386,f20387,f20388,f20389,f20390,f20391,f20392,f20393,f20394,f20715,f20956,f21754,f21977,f22857,f23243,f23403,f23673,f23986,f24681,f24877,f26035,f29045,f29978,f31667,f32369]) ).

fof(f32369,plain,
    ( ~ spl0_2
    | spl0_753 ),
    inference(avatar_contradiction_clause,[],[f32368]) ).

fof(f32368,plain,
    ( $false
    | ~ spl0_2
    | spl0_753 ),
    inference(resolution,[],[f31666,f806]) ).

fof(f806,plain,
    ( ! [X1] : c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f805]) ).

fof(f805,plain,
    ( spl0_2
  <=> ! [X1] : c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f31666,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_753 ),
    inference(avatar_component_clause,[],[f31664]) ).

fof(f31664,plain,
    ( spl0_753
  <=> c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f31667,plain,
    ( ~ spl0_753
    | ~ spl0_234
    | ~ spl0_752 ),
    inference(avatar_split_clause,[],[f30434,f29975,f2204,f31664]) ).

fof(f2204,plain,
    ( spl0_234
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Oirrefl(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f29975,plain,
    ( spl0_752
  <=> hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f30434,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_234
    | ~ spl0_752 ),
    inference(resolution,[],[f29977,f2205]) ).

fof(f2205,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Relation_Oirrefl(X2,X0) )
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2204]) ).

fof(f29977,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_752 ),
    inference(avatar_component_clause,[],[f29975]) ).

fof(f29978,plain,
    ( spl0_752
    | ~ spl0_17
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20238,f20215,f878,f29975]) ).

fof(f878,plain,
    ( spl0_17
  <=> hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f20215,plain,
    ( spl0_725
  <=> v_a = v_b ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f20238,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_17
    | ~ spl0_725 ),
    inference(superposition,[],[f880,f20217]) ).

fof(f20217,plain,
    ( v_a = v_b
    | ~ spl0_725 ),
    inference(avatar_component_clause,[],[f20215]) ).

fof(f880,plain,
    ( hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f878]) ).

fof(f29045,plain,
    ( ~ spl0_751
    | ~ spl0_32
    | ~ spl0_722 ),
    inference(avatar_split_clause,[],[f28444,f19962,f939,f29042]) ).

fof(f29042,plain,
    ( spl0_751
  <=> c_Wellfounded_Owf(c_Relation_OId__on(hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f939,plain,
    ( spl0_32
  <=> ! [X4,X0] : c_Relation_Orefl__on(X4,c_Relation_OId__on(X4,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f19962,plain,
    ( spl0_722
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f28444,plain,
    ( ~ c_Wellfounded_Owf(c_Relation_OId__on(hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_32
    | ~ spl0_722 ),
    inference(resolution,[],[f19963,f940]) ).

fof(f940,plain,
    ( ! [X0,X4] : c_Relation_Orefl__on(X4,c_Relation_OId__on(X4,X0),X0)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f939]) ).

fof(f19963,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_722 ),
    inference(avatar_component_clause,[],[f19962]) ).

fof(f26035,plain,
    ( spl0_750
    | ~ spl0_53
    | ~ spl0_717 ),
    inference(avatar_split_clause,[],[f20175,f19941,f1023,f26032]) ).

fof(f26032,plain,
    ( spl0_750
  <=> hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1023,plain,
    ( spl0_53
  <=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f19941,plain,
    ( spl0_717
  <=> 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_717])]) ).

fof(f20175,plain,
    ( hBOOL(c_Orderings_Otop__class_Otop(tc_bool))
    | ~ spl0_53
    | ~ spl0_717 ),
    inference(superposition,[],[f1024,f19943]) ).

fof(f19943,plain,
    ( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
    | ~ spl0_717 ),
    inference(avatar_component_clause,[],[f19941]) ).

fof(f1024,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1))
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f24877,plain,
    ( ~ spl0_749
    | ~ spl0_32
    | ~ spl0_711 ),
    inference(avatar_split_clause,[],[f20173,f19914,f939,f24874]) ).

fof(f24874,plain,
    ( spl0_749
  <=> c_Relation_Oirrefl(c_Relation_OId__on(hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f19914,plain,
    ( spl0_711
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Oirrefl(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f20173,plain,
    ( ~ c_Relation_Oirrefl(c_Relation_OId__on(hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_32
    | ~ spl0_711 ),
    inference(resolution,[],[f19915,f940]) ).

fof(f19915,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Oirrefl(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_711 ),
    inference(avatar_component_clause,[],[f19914]) ).

fof(f24681,plain,
    ( ~ spl0_747
    | spl0_698
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20259,f20215,f19578,f23670]) ).

fof(f23670,plain,
    ( spl0_747
  <=> hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f19578,plain,
    ( spl0_698
  <=> hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f20259,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_698
    | ~ spl0_725 ),
    inference(superposition,[],[f19580,f20217]) ).

fof(f19580,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_698 ),
    inference(avatar_component_clause,[],[f19578]) ).

fof(f23986,plain,
    ( spl0_748
    | ~ spl0_358
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20244,f20215,f4861,f23983]) ).

fof(f23983,plain,
    ( spl0_748
  <=> hBOOL(c_in(v_a,c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f4861,plain,
    ( spl0_358
  <=> hBOOL(c_in(v_b,c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f20244,plain,
    ( hBOOL(c_in(v_a,c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_358
    | ~ spl0_725 ),
    inference(superposition,[],[f4863,f20217]) ).

fof(f4863,plain,
    ( hBOOL(c_in(v_b,c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_358 ),
    inference(avatar_component_clause,[],[f4861]) ).

fof(f23673,plain,
    ( spl0_747
    | ~ spl0_124
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20240,f20215,f1369,f23670]) ).

fof(f1369,plain,
    ( spl0_124
  <=> hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f20240,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_124
    | ~ spl0_725 ),
    inference(superposition,[],[f1371,f20217]) ).

fof(f1371,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1369]) ).

fof(f23403,plain,
    ( spl0_746
    | ~ spl0_376
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20245,f20215,f5004,f23400]) ).

fof(f23400,plain,
    ( spl0_746
  <=> hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f5004,plain,
    ( spl0_376
  <=> hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f20245,plain,
    ( hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a))
    | ~ spl0_376
    | ~ spl0_725 ),
    inference(superposition,[],[f5006,f20217]) ).

fof(f5006,plain,
    ( hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b))
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f5004]) ).

fof(f23243,plain,
    ( ~ spl0_745
    | spl0_103
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20507,f20215,f1284,f23240]) ).

fof(f23240,plain,
    ( spl0_745
  <=> hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f1284,plain,
    ( spl0_103
  <=> hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f20507,plain,
    ( ~ hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_103
    | ~ spl0_725 ),
    inference(forward_demodulation,[],[f1286,f20217]) ).

fof(f1286,plain,
    ( ~ hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_103 ),
    inference(avatar_component_clause,[],[f1284]) ).

fof(f22857,plain,
    ( ~ spl0_743
    | spl0_659
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20252,f20215,f18725,f21751]) ).

fof(f21751,plain,
    ( spl0_743
  <=> c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f18725,plain,
    ( spl0_659
  <=> c_FunDef_Oin__rel(hAPP(v_P,v_i),v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f20252,plain,
    ( ~ c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_659
    | ~ spl0_725 ),
    inference(superposition,[],[f18727,f20217]) ).

fof(f18727,plain,
    ( ~ c_FunDef_Oin__rel(hAPP(v_P,v_i),v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_659 ),
    inference(avatar_component_clause,[],[f18725]) ).

fof(f21977,plain,
    ( ~ spl0_744
    | ~ spl0_225
    | spl0_742 ),
    inference(avatar_split_clause,[],[f21959,f20712,f2160,f21974]) ).

fof(f21974,plain,
    ( spl0_744
  <=> c_Nitpick_Orefl_H(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f2160,plain,
    ( spl0_225
  <=> ! [X2,X0,X1] :
        ( ~ c_Nitpick_Orefl_H(X2,X0)
        | hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f20712,plain,
    ( spl0_742
  <=> hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f21959,plain,
    ( ~ c_Nitpick_Orefl_H(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_225
    | spl0_742 ),
    inference(resolution,[],[f2161,f20714]) ).

fof(f20714,plain,
    ( ~ hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_742 ),
    inference(avatar_component_clause,[],[f20712]) ).

fof(f2161,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Nitpick_Orefl_H(X2,X0) )
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2160]) ).

fof(f21754,plain,
    ( spl0_743
    | ~ spl0_339
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20243,f20215,f4144,f21751]) ).

fof(f4144,plain,
    ( spl0_339
  <=> c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f20243,plain,
    ( c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_339
    | ~ spl0_725 ),
    inference(superposition,[],[f4146,f20217]) ).

fof(f4146,plain,
    ( c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_339 ),
    inference(avatar_component_clause,[],[f4144]) ).

fof(f20956,plain,
    ( ~ spl0_735
    | spl0_319
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20418,f20215,f4053,f20297]) ).

fof(f20297,plain,
    ( spl0_735
  <=> c_FunDef_Oin__rel(v_F(v_P),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f4053,plain,
    ( spl0_319
  <=> c_FunDef_Oin__rel(v_F(v_P),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f20418,plain,
    ( ~ c_FunDef_Oin__rel(v_F(v_P),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_319
    | ~ spl0_725 ),
    inference(forward_demodulation,[],[f4055,f20217]) ).

fof(f4055,plain,
    ( ~ c_FunDef_Oin__rel(v_F(v_P),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_319 ),
    inference(avatar_component_clause,[],[f4053]) ).

fof(f20715,plain,
    ( ~ spl0_742
    | spl0_16
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20665,f20215,f873,f20712]) ).

fof(f873,plain,
    ( spl0_16
  <=> hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f20665,plain,
    ( ~ hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_16
    | ~ spl0_725 ),
    inference(forward_demodulation,[],[f875,f20217]) ).

fof(f875,plain,
    ( ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_16 ),
    inference(avatar_component_clause,[],[f873]) ).

fof(f20394,plain,
    ( ~ spl0_70
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20334]) ).

fof(f20334,plain,
    ( $false
    | ~ spl0_70
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1096]) ).

fof(f1096,plain,
    ( ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f1095]) ).

fof(f1095,plain,
    ( spl0_70
  <=> ! [X0,X1] : hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f20329,plain,
    ( ! [X1] : ~ hBOOL(X1)
    | ~ spl0_740 ),
    inference(avatar_component_clause,[],[f20328]) ).

fof(f20328,plain,
    ( spl0_740
  <=> ! [X1] : ~ hBOOL(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f20393,plain,
    ( ~ spl0_79
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20335]) ).

fof(f20335,plain,
    ( $false
    | ~ spl0_79
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1140]) ).

fof(f1140,plain,
    ( ! [X0,X7,X5] : hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X5,X0),X7),X0))
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f1139]) ).

fof(f1139,plain,
    ( spl0_79
  <=> ! [X5,X0,X7] : hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X5,X0),X7),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f20392,plain,
    ( ~ spl0_723
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20341]) ).

fof(f20341,plain,
    ( $false
    | ~ spl0_723
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f19967]) ).

fof(f19967,plain,
    ( ! [X0,X1] : hBOOL(c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_723 ),
    inference(avatar_component_clause,[],[f19966]) ).

fof(f19966,plain,
    ( spl0_723
  <=> ! [X0,X1] : hBOOL(c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f20391,plain,
    ( ~ spl0_227
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20342]) ).

fof(f20342,plain,
    ( $false
    | ~ spl0_227
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f2169]) ).

fof(f2169,plain,
    ( ! [X0,X1,X6,X16] : hBOOL(c_in(hAPP(X16,X1),c_Set_Oimage(X16,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X0),X0))
    | ~ spl0_227 ),
    inference(avatar_component_clause,[],[f2168]) ).

fof(f2168,plain,
    ( spl0_227
  <=> ! [X16,X0,X6,X1] : hBOOL(c_in(hAPP(X16,X1),c_Set_Oimage(X16,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f20390,plain,
    ( ~ spl0_17
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20354]) ).

fof(f20354,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f880]) ).

fof(f20389,plain,
    ( ~ spl0_183
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20355]) ).

fof(f20355,plain,
    ( $false
    | ~ spl0_183
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1796]) ).

fof(f1796,plain,
    ( ! [X0,X1,X12] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1795]) ).

fof(f1795,plain,
    ( spl0_183
  <=> ! [X0,X12,X1] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f20388,plain,
    ( ~ spl0_160
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20358]) ).

fof(f20358,plain,
    ( $false
    | ~ spl0_160
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1604]) ).

fof(f1604,plain,
    ( ! [X0,X5] : hBOOL(c_in(c_Pair(X5,X5,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0)))
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1603]) ).

fof(f1603,plain,
    ( spl0_160
  <=> ! [X5,X0] : hBOOL(c_in(c_Pair(X5,X5,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f20387,plain,
    ( ~ spl0_436
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20367]) ).

fof(f20367,plain,
    ( $false
    | ~ spl0_436
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f6721]) ).

fof(f6721,plain,
    ( hBOOL(c_in(v_a,c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f6719]) ).

fof(f6719,plain,
    ( spl0_436
  <=> hBOOL(c_in(v_a,c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f20386,plain,
    ( ~ spl0_358
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20368]) ).

fof(f20368,plain,
    ( $false
    | ~ spl0_358
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f4863]) ).

fof(f20385,plain,
    ( ~ spl0_61
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20369]) ).

fof(f20369,plain,
    ( $false
    | ~ spl0_61
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1060]) ).

fof(f1060,plain,
    ( ! [X0,X1,X4] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X4),X1))
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1059]) ).

fof(f1059,plain,
    ( spl0_61
  <=> ! [X4,X0,X1] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X4),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f20384,plain,
    ( ~ spl0_124
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20370]) ).

fof(f20370,plain,
    ( $false
    | ~ spl0_124
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1371]) ).

fof(f20383,plain,
    ( ~ spl0_125
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20371]) ).

fof(f20371,plain,
    ( $false
    | ~ spl0_125
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1403]) ).

fof(f1403,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(v_P,v_i),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(v_P,v_i),X0)))
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1402]) ).

fof(f1402,plain,
    ( spl0_125
  <=> ! [X0] : hBOOL(hAPP(hAPP(v_P,v_i),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(v_P,v_i),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f20382,plain,
    ( ~ spl0_376
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20372]) ).

fof(f20372,plain,
    ( $false
    | ~ spl0_376
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f5006]) ).

fof(f20381,plain,
    ( ~ spl0_448
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20373]) ).

fof(f20373,plain,
    ( $false
    | ~ spl0_448
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f7225]) ).

fof(f7225,plain,
    ( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a))
    | ~ spl0_448 ),
    inference(avatar_component_clause,[],[f7223]) ).

fof(f7223,plain,
    ( spl0_448
  <=> hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f20380,plain,
    ( ~ spl0_426
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20374]) ).

fof(f20374,plain,
    ( $false
    | ~ spl0_426
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f6413]) ).

fof(f6413,plain,
    ( ! [X0] : hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)))
    | ~ spl0_426 ),
    inference(avatar_component_clause,[],[f6412]) ).

fof(f6412,plain,
    ( spl0_426
  <=> ! [X0] : hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f20379,plain,
    ( ~ spl0_53
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20376]) ).

fof(f20376,plain,
    ( $false
    | ~ spl0_53
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f1024]) ).

fof(f20378,plain,
    ( ~ spl0_718
    | ~ spl0_740 ),
    inference(avatar_contradiction_clause,[],[f20377]) ).

fof(f20377,plain,
    ( $false
    | ~ spl0_718
    | ~ spl0_740 ),
    inference(resolution,[],[f20329,f19947]) ).

fof(f19947,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0)))
    | ~ spl0_718 ),
    inference(avatar_component_clause,[],[f19946]) ).

fof(f19946,plain,
    ( spl0_718
  <=> ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f20333,plain,
    ( spl0_740
    | spl0_741
    | ~ spl0_88
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f1397,f1341,f1175,f20331,f20328]) ).

fof(f20331,plain,
    ( spl0_741
  <=> ! [X2,X0] : hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f1175,plain,
    ( spl0_88
  <=> ! [X4,X0] : hAPP(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X4) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f1341,plain,
    ( spl0_117
  <=> ! [X0,X1,X15] :
        ( ~ hBOOL(hAPP(X15,X1))
        | hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X15,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f1397,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X2))
        | ~ hBOOL(X1) )
    | ~ spl0_88
    | ~ spl0_117 ),
    inference(forward_demodulation,[],[f1395,f1176]) ).

fof(f1176,plain,
    ( ! [X0,X4] : hAPP(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X4) = X4
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f1175]) ).

fof(f1395,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(X1)
        | hBOOL(hAPP(c_Relation_OImage(c_Relation_OId(X0),X0,X0),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X2))) )
    | ~ spl0_88
    | ~ spl0_117 ),
    inference(superposition,[],[f1342,f1176]) ).

fof(f1342,plain,
    ( ! [X0,X1,X15] :
        ( ~ hBOOL(hAPP(X15,X1))
        | hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X15,X0))) )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f1341]) ).

fof(f20326,plain,
    ( spl0_739
    | ~ spl0_62
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f1263,f1203,f1063,f20324]) ).

fof(f20324,plain,
    ( spl0_739
  <=> ! [X0,X1] :
        ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)
        | ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f1063,plain,
    ( spl0_62
  <=> ! [X2,X0] :
        ( ~ c_Wellfounded_Oacyclic(X2,X0)
        | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1203,plain,
    ( spl0_95
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1263,plain,
    ( ! [X0,X1] :
        ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X0,X1),X1)
        | ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X0,X1),X1) )
    | ~ spl0_62
    | ~ spl0_95 ),
    inference(superposition,[],[f1064,f1204]) ).

fof(f1204,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X0),X0)
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f1203]) ).

fof(f1064,plain,
    ( ! [X2,X0] :
        ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X2,X0),X0)
        | ~ c_Wellfounded_Oacyclic(X2,X0) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1063]) ).

fof(f20321,plain,
    ( ~ spl0_28
    | spl0_738 ),
    inference(avatar_contradiction_clause,[],[f20317]) ).

fof(f20317,plain,
    ( $false
    | ~ spl0_28
    | spl0_738 ),
    inference(resolution,[],[f20314,f924]) ).

fof(f924,plain,
    ( ! [X0,X4] : c_lessequals(X4,X4,tc_fun(X0,tc_bool))
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f923]) ).

fof(f923,plain,
    ( spl0_28
  <=> ! [X4,X0] : c_lessequals(X4,X4,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f20314,plain,
    ( ~ c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | spl0_738 ),
    inference(avatar_component_clause,[],[f20312]) ).

fof(f20312,plain,
    ( spl0_738
  <=> c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f20315,plain,
    ( ~ spl0_738
    | ~ spl0_725
    | spl0_737 ),
    inference(avatar_split_clause,[],[f20310,f20306,f20215,f20312]) ).

fof(f20306,plain,
    ( spl0_737
  <=> c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f20310,plain,
    ( ~ c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | ~ spl0_725
    | spl0_737 ),
    inference(forward_demodulation,[],[f20307,f20217]) ).

fof(f20307,plain,
    ( ~ c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | spl0_737 ),
    inference(avatar_component_clause,[],[f20306]) ).

fof(f20309,plain,
    ( spl0_737
    | spl0_733
    | ~ spl0_17
    | ~ spl0_632 ),
    inference(avatar_split_clause,[],[f17411,f17387,f878,f20280,f20306]) ).

fof(f20280,plain,
    ( spl0_733
  <=> ! [X0] : ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f17387,plain,
    ( spl0_632
  <=> ! [X5,X4,X0,X9,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | c_lessequals(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f17411,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
        | c_lessequals(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) )
    | ~ spl0_17
    | ~ spl0_632 ),
    inference(resolution,[],[f17388,f880]) ).

fof(f17388,plain,
    ( ! [X2,X0,X9,X4,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | c_lessequals(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)) )
    | ~ spl0_632 ),
    inference(avatar_component_clause,[],[f17387]) ).

fof(f20304,plain,
    ( spl0_736
    | ~ spl0_55
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f1234,f1175,f1032,f20302]) ).

fof(f20302,plain,
    ( spl0_736
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f1032,plain,
    ( spl0_55
  <=> ! [X23] :
        ( c_Relation_Otrans(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f1234,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55
    | ~ spl0_88 ),
    inference(superposition,[],[f1033,f1176]) ).

fof(f1033,plain,
    ( ! [X23] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1032]) ).

fof(f20300,plain,
    ( ~ spl0_735
    | spl0_319
    | ~ spl0_725 ),
    inference(avatar_split_clause,[],[f20242,f20215,f4053,f20297]) ).

fof(f20242,plain,
    ( ~ c_FunDef_Oin__rel(v_F(v_P),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_319
    | ~ spl0_725 ),
    inference(superposition,[],[f4055,f20217]) ).

fof(f20295,plain,
    ( spl0_734
    | ~ spl0_56
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f1233,f1175,f1036,f20293]) ).

fof(f20293,plain,
    ( spl0_734
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f1036,plain,
    ( spl0_56
  <=> ! [X23] :
        ( c_Relation_Oirrefl(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1233,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_x,c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Relation_OImage(c_Relation_OId(X0),X0,X0)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56
    | ~ spl0_88 ),
    inference(superposition,[],[f1037,f1176]) ).

fof(f1037,plain,
    ( ! [X23] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f1036]) ).

fof(f20282,plain,
    ( spl0_732
    | spl0_733
    | ~ spl0_17
    | ~ spl0_626 ),
    inference(avatar_split_clause,[],[f17151,f17127,f878,f20280,f20276]) ).

fof(f20276,plain,
    ( spl0_732
  <=> hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))) = hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f17127,plain,
    ( spl0_626
  <=> ! [X4,X0,X10,X2,X1] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X10,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f17151,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
        | hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_a,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))) = hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)))) )
    | ~ spl0_17
    | ~ spl0_626 ),
    inference(resolution,[],[f17128,f880]) ).

fof(f17128,plain,
    ( ! [X2,X10,X0,X1,X4] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X10,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) )
    | ~ spl0_626 ),
    inference(avatar_component_clause,[],[f17127]) ).

fof(f20274,plain,
    ( spl0_731
    | ~ spl0_71
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3207,f2771,f1103,f20272]) ).

fof(f20272,plain,
    ( spl0_731
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f1103,plain,
    ( spl0_71
  <=> ! [X23] :
        ( ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f2771,plain,
    ( spl0_256
  <=> ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f3207,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_71
    | ~ spl0_256 ),
    inference(superposition,[],[f1104,f2772]) ).

fof(f2772,plain,
    ( ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7)
    | ~ spl0_256 ),
    inference(avatar_component_clause,[],[f2771]) ).

fof(f1104,plain,
    ( ! [X23] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f1103]) ).

fof(f20270,plain,
    ( spl0_730
    | ~ spl0_71
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2980,f2731,f1103,f20268]) ).

fof(f20268,plain,
    ( spl0_730
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f2731,plain,
    ( spl0_246
  <=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2980,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_71
    | ~ spl0_246 ),
    inference(superposition,[],[f1104,f2732]) ).

fof(f2732,plain,
    ( ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X4)
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2731]) ).

fof(f20266,plain,
    ( spl0_729
    | ~ spl0_71
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2937,f2723,f1103,f20264]) ).

fof(f20264,plain,
    ( spl0_729
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f2723,plain,
    ( spl0_244
  <=> ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2937,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_71
    | ~ spl0_244 ),
    inference(superposition,[],[f1104,f2724]) ).

fof(f2724,plain,
    ( ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7)
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2723]) ).

fof(f20236,plain,
    ( ~ spl0_15
    | spl0_726 ),
    inference(avatar_contradiction_clause,[],[f20235]) ).

fof(f20235,plain,
    ( $false
    | ~ spl0_15
    | spl0_726 ),
    inference(resolution,[],[f20221,f870]) ).

fof(f870,plain,
    ( ! [X1] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f869]) ).

fof(f869,plain,
    ( spl0_15
  <=> ! [X1] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f20221,plain,
    ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_726 ),
    inference(avatar_component_clause,[],[f20219]) ).

fof(f20219,plain,
    ( spl0_726
  <=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f20234,plain,
    ( ~ spl0_2
    | spl0_728 ),
    inference(avatar_contradiction_clause,[],[f20233]) ).

fof(f20233,plain,
    ( $false
    | ~ spl0_2
    | spl0_728 ),
    inference(resolution,[],[f20229,f806]) ).

fof(f20229,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_728 ),
    inference(avatar_component_clause,[],[f20227]) ).

fof(f20227,plain,
    ( spl0_728
  <=> c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f20232,plain,
    ( ~ spl0_1
    | spl0_727 ),
    inference(avatar_contradiction_clause,[],[f20231]) ).

fof(f20231,plain,
    ( $false
    | ~ spl0_1
    | spl0_727 ),
    inference(resolution,[],[f20225,f802]) ).

fof(f802,plain,
    ( ! [X1] : c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f801]) ).

fof(f801,plain,
    ( spl0_1
  <=> ! [X1] : c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f20225,plain,
    ( ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_727 ),
    inference(avatar_component_clause,[],[f20223]) ).

fof(f20223,plain,
    ( spl0_727
  <=> c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f20230,plain,
    ( spl0_725
    | spl0_16
    | ~ spl0_726
    | ~ spl0_727
    | ~ spl0_728
    | ~ spl0_17
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1693,f1690,f878,f20227,f20223,f20219,f873,f20215]) ).

fof(f1690,plain,
    ( spl0_164
  <=> ! [X9,X5,X15] :
        ( X5 = X9
        | ~ c_Relation_Oirrefl(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X15,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f1693,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,v_Pa(v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | v_a = v_b
    | ~ spl0_17
    | ~ spl0_164 ),
    inference(resolution,[],[f1691,f880]) ).

fof(f1691,plain,
    ( ! [X9,X15,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X15,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ c_Relation_Oirrefl(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X5 = X9 )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1690]) ).

fof(f19972,plain,
    ( spl0_724
    | ~ spl0_70
    | ~ spl0_413 ),
    inference(avatar_split_clause,[],[f6198,f5471,f1095,f19970]) ).

fof(f19970,plain,
    ( spl0_724
  <=> ! [X0,X1] : c_Relation_Ototal__on(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f5471,plain,
    ( spl0_413
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f6198,plain,
    ( ! [X0,X1] : c_Relation_Ototal__on(X0,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_bool)),X1)
    | ~ spl0_70
    | ~ spl0_413 ),
    inference(resolution,[],[f5472,f1096]) ).

fof(f5472,plain,
    ( ! [X2,X0,X4] :
        ( ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),X0,X0),X2,tc_prod(X0,X0)))
        | c_Relation_Ototal__on(X4,X2,X0) )
    | ~ spl0_413 ),
    inference(avatar_component_clause,[],[f5471]) ).

fof(f19968,plain,
    ( spl0_723
    | ~ spl0_186
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f6128,f5459,f1807,f19966]) ).

fof(f1807,plain,
    ( spl0_186
  <=> ! [X53,X1,X23] : ~ hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f5459,plain,
    ( spl0_410
  <=> ! [X0,X12,X1] :
        ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X12,X0),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X1,X0),X1,X0,X0),X12,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f6128,plain,
    ( ! [X0,X1] : hBOOL(c_in(X0,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X1,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_186
    | ~ spl0_410 ),
    inference(resolution,[],[f5460,f1808]) ).

fof(f1808,plain,
    ( ! [X1,X53,X23] : ~ hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1807]) ).

fof(f5460,plain,
    ( ! [X0,X1,X12] :
        ( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X1,X0),X1,X0,X0),X12,tc_prod(X0,X0)))
        | hBOOL(c_in(X1,c_Wellfounded_Oacc(X12,X0),X0)) )
    | ~ spl0_410 ),
    inference(avatar_component_clause,[],[f5459]) ).

fof(f19964,plain,
    ( spl0_722
    | ~ spl0_226
    | ~ spl0_706 ),
    inference(avatar_split_clause,[],[f19695,f19686,f2164,f19962]) ).

fof(f2164,plain,
    ( spl0_226
  <=> ! [X5,X2,X0] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f19686,plain,
    ( spl0_706
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f19695,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_226
    | ~ spl0_706 ),
    inference(resolution,[],[f19687,f2165]) ).

fof(f2165,plain,
    ( ! [X2,X0,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Wellfounded_Owf(X2,X0) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2164]) ).

fof(f19687,plain,
    ( ! [X0] :
        ( hBOOL(c_in(c_Pair(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))))
        | ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_706 ),
    inference(avatar_component_clause,[],[f19686]) ).

fof(f19960,plain,
    ( spl0_721
    | ~ spl0_226
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4036,f3866,f2164,f19958]) ).

fof(f19958,plain,
    ( spl0_721
  <=> ! [X2,X0,X1] :
        ( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Wellfounded_Owf(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f3866,plain,
    ( spl0_315
  <=> ! [X10,X0,X12,X6,X1] :
        ( ~ c_FunDef_Oin__rel(X12,X1,X10,X0,X6)
        | hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f4036,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Wellfounded_Owf(X0,X2) )
    | ~ spl0_226
    | ~ spl0_315 ),
    inference(resolution,[],[f3867,f2165]) ).

fof(f3867,plain,
    ( ! [X10,X0,X1,X6,X12] :
        ( hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6)))
        | ~ c_FunDef_Oin__rel(X12,X1,X10,X0,X6) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3866]) ).

fof(f19956,plain,
    ( spl0_720
    | ~ spl0_234
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4035,f3866,f2204,f19954]) ).

fof(f19954,plain,
    ( spl0_720
  <=> ! [X2,X0,X1] :
        ( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Relation_Oirrefl(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f4035,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Relation_Oirrefl(X0,X2) )
    | ~ spl0_234
    | ~ spl0_315 ),
    inference(resolution,[],[f3867,f2205]) ).

fof(f19952,plain,
    ( spl0_719
    | ~ spl0_225
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f4017,f3862,f2160,f19950]) ).

fof(f19950,plain,
    ( spl0_719
  <=> ! [X2,X0,X1] :
        ( c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Nitpick_Orefl_H(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f3862,plain,
    ( spl0_314
  <=> ! [X10,X0,X12,X6,X1] :
        ( c_FunDef_Oin__rel(X12,X1,X10,X0,X6)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f4017,plain,
    ( ! [X2,X0,X1] :
        ( c_FunDef_Oin__rel(X0,X1,X1,X2,X2)
        | ~ c_Nitpick_Orefl_H(X0,X2) )
    | ~ spl0_225
    | ~ spl0_314 ),
    inference(resolution,[],[f3863,f2161]) ).

fof(f3863,plain,
    ( ! [X10,X0,X1,X6,X12] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6)))
        | c_FunDef_Oin__rel(X12,X1,X10,X0,X6) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3862]) ).

fof(f19948,plain,
    ( spl0_718
    | ~ spl0_98
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1677,f1603,f1216,f19946]) ).

fof(f1216,plain,
    ( spl0_98
  <=> ! [X13,X0,X1] :
        ( hBOOL(hAPP(X13,X1))
        | ~ hBOOL(c_in(X1,X13,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1677,plain,
    ( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0)))
    | ~ spl0_98
    | ~ spl0_160 ),
    inference(resolution,[],[f1604,f1217]) ).

fof(f1217,plain,
    ( ! [X0,X1,X13] :
        ( ~ hBOOL(c_in(X1,X13,X0))
        | hBOOL(hAPP(X13,X1)) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f1216]) ).

fof(f19944,plain,
    ( spl0_717
    | ~ spl0_11
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1532,f1482,f849,f19941]) ).

fof(f849,plain,
    ( spl0_11
  <=> class_Orderings_Otop(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f1482,plain,
    ( spl0_140
  <=> ! [X6] :
        ( ~ class_Orderings_Otop(X6)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X6)),v_x) = c_Orderings_Otop__class_Otop(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1532,plain,
    ( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x)
    | ~ spl0_11
    | ~ spl0_140 ),
    inference(resolution,[],[f1483,f851]) ).

fof(f851,plain,
    ( class_Orderings_Otop(tc_bool)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f849]) ).

fof(f1483,plain,
    ( ! [X6] :
        ( ~ class_Orderings_Otop(X6)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X6)),v_x) = c_Orderings_Otop__class_Otop(X6) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1482]) ).

fof(f19939,plain,
    ( spl0_716
    | ~ spl0_3
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1530,f1478,f809,f19936]) ).

fof(f19936,plain,
    ( spl0_716
  <=> 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_716])]) ).

fof(f809,plain,
    ( spl0_3
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1478,plain,
    ( spl0_139
  <=> ! [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_139])]) ).

fof(f1530,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_3
    | ~ spl0_139 ),
    inference(resolution,[],[f1479,f811]) ).

fof(f811,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f809]) ).

fof(f1479,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_139 ),
    inference(avatar_component_clause,[],[f1478]) ).

fof(f19934,plain,
    ( spl0_715
    | ~ spl0_3
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1527,f1470,f809,f19931]) ).

fof(f19931,plain,
    ( spl0_715
  <=> 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_715])]) ).

fof(f1470,plain,
    ( spl0_137
  <=> ! [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_137])]) ).

fof(f1527,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_3
    | ~ spl0_137 ),
    inference(resolution,[],[f1471,f811]) ).

fof(f1471,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_137 ),
    inference(avatar_component_clause,[],[f1470]) ).

fof(f19929,plain,
    ( spl0_714
    | ~ spl0_12
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1523,f1466,f854,f19926]) ).

fof(f19926,plain,
    ( spl0_714
  <=> 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_714])]) ).

fof(f854,plain,
    ( spl0_12
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1466,plain,
    ( spl0_136
  <=> ! [X6] :
        ( ~ class_Orderings_Obot(X6)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X6)),v_x) = c_Orderings_Obot__class_Obot(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1523,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_12
    | ~ spl0_136 ),
    inference(resolution,[],[f1467,f856]) ).

fof(f856,plain,
    ( class_Orderings_Obot(tc_bool)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f854]) ).

fof(f1467,plain,
    ( ! [X6] :
        ( ~ class_Orderings_Obot(X6)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X6)),v_x) = c_Orderings_Obot__class_Obot(X6) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1466]) ).

fof(f19924,plain,
    ( spl0_713
    | ~ spl0_7
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1500,f1437,f829,f19922]) ).

fof(f19922,plain,
    ( spl0_713
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f829,plain,
    ( spl0_7
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1437,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Otop__class_Otop(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1500,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
    | ~ spl0_7
    | ~ spl0_129 ),
    inference(resolution,[],[f1438,f831]) ).

fof(f831,plain,
    ( class_Lattices_Obounded__lattice(tc_bool)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f829]) ).

fof(f1438,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Otop__class_Otop(X0)) )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1437]) ).

fof(f19920,plain,
    ( spl0_712
    | ~ spl0_7
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1498,f1433,f829,f19918]) ).

fof(f19918,plain,
    ( spl0_712
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f1433,plain,
    ( spl0_128
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1498,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X0)
    | ~ spl0_7
    | ~ spl0_128 ),
    inference(resolution,[],[f1434,f831]) ).

fof(f1434,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X0),X1) )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1433]) ).

fof(f19916,plain,
    ( spl0_711
    | ~ spl0_234
    | ~ spl0_706 ),
    inference(avatar_split_clause,[],[f19694,f19686,f2204,f19914]) ).

fof(f19694,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Oirrefl(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_234
    | ~ spl0_706 ),
    inference(resolution,[],[f19687,f2205]) ).

fof(f19912,plain,
    ( spl0_710
    | ~ spl0_7
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1496,f1429,f829,f19910]) ).

fof(f19910,plain,
    ( spl0_710
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f1429,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1496,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X0)
    | ~ spl0_7
    | ~ spl0_127 ),
    inference(resolution,[],[f1430,f831]) ).

fof(f1430,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X0),X1) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1429]) ).

fof(f19908,plain,
    ( spl0_709
    | ~ spl0_7
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1490,f1425,f829,f19906]) ).

fof(f19906,plain,
    ( spl0_709
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f1425,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Obot__class_Obot(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1490,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))
    | ~ spl0_7
    | ~ spl0_126 ),
    inference(resolution,[],[f1426,f831]) ).

fof(f1426,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Obot__class_Obot(X0)) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f1425]) ).

fof(f19904,plain,
    ( spl0_708
    | ~ spl0_98
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f1389,f1337,f1216,f19902]) ).

fof(f19902,plain,
    ( spl0_708
  <=> ! [X2,X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f1337,plain,
    ( spl0_116
  <=> ! [X2,X0,X1] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1389,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
    | ~ spl0_98
    | ~ spl0_116 ),
    inference(resolution,[],[f1338,f1217]) ).

fof(f1338,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ c_Wellfounded_Owf(X2,X0) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1337]) ).

fof(f19692,plain,
    ( spl0_707
    | ~ spl0_17
    | ~ spl0_520 ),
    inference(avatar_split_clause,[],[f11026,f10674,f878,f19690]) ).

fof(f19690,plain,
    ( spl0_707
  <=> ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(X1,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X0,c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(X1,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f10674,plain,
    ( spl0_520
  <=> ! [X4,X40,X0,X6,X26] :
        ( ~ hBOOL(c_in(X40,X26,X0))
        | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X4,X40),tc_fun(X6,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f11026,plain,
    ( ! [X0,X1] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(X1,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X0,c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(X1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(X1,tc_bool)))
    | ~ spl0_17
    | ~ spl0_520 ),
    inference(resolution,[],[f10675,f880]) ).

fof(f10675,plain,
    ( ! [X40,X0,X6,X26,X4] :
        ( ~ hBOOL(c_in(X40,X26,X0))
        | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X4,X40),tc_fun(X6,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool))) )
    | ~ spl0_520 ),
    inference(avatar_component_clause,[],[f10674]) ).

fof(f19688,plain,
    ( spl0_706
    | ~ spl0_17
    | ~ spl0_375 ),
    inference(avatar_split_clause,[],[f5316,f4953,f878,f19686]) ).

fof(f4953,plain,
    ( spl0_375
  <=> ! [X4,X0,X5,X2] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | ~ hBOOL(c_in(X5,X4,X0))
        | hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f5316,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0,tc_prod(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) )
    | ~ spl0_17
    | ~ spl0_375 ),
    inference(resolution,[],[f4954,f880]) ).

fof(f4954,plain,
    ( ! [X2,X0,X4,X5] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | ~ c_Relation_Orefl__on(X4,X2,X0)
        | hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0))) )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f4953]) ).

fof(f19626,plain,
    ( spl0_705
    | ~ spl0_17
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f7283,f7211,f878,f19624]) ).

fof(f19624,plain,
    ( spl0_705
  <=> ! [X0] : hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_P,v_i)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_P,v_i)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f7211,plain,
    ( spl0_445
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(c_in(X1,X7,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f7283,plain,
    ( ! [X0] : hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_P,v_i)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_P,v_i))
    | ~ spl0_17
    | ~ spl0_445 ),
    inference(resolution,[],[f7212,f880]) ).

fof(f7212,plain,
    ( ! [X0,X1,X7,X4] :
        ( ~ hBOOL(c_in(X1,X7,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),X7) )
    | ~ spl0_445 ),
    inference(avatar_component_clause,[],[f7211]) ).

fof(f19622,plain,
    ( spl0_704
    | ~ spl0_55
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3209,f2771,f1032,f19620]) ).

fof(f19620,plain,
    ( spl0_704
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f3209,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55
    | ~ spl0_256 ),
    inference(superposition,[],[f1033,f2772]) ).

fof(f19618,plain,
    ( spl0_703
    | ~ spl0_56
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3208,f2771,f1036,f19616]) ).

fof(f19616,plain,
    ( spl0_703
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f3208,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56
    | ~ spl0_256 ),
    inference(superposition,[],[f1037,f2772]) ).

fof(f19614,plain,
    ( spl0_702
    | ~ spl0_55
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2982,f2731,f1032,f19612]) ).

fof(f19612,plain,
    ( spl0_702
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f2982,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55
    | ~ spl0_246 ),
    inference(superposition,[],[f1033,f2732]) ).

fof(f19610,plain,
    ( spl0_701
    | ~ spl0_56
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2981,f2731,f1036,f19608]) ).

fof(f19608,plain,
    ( spl0_701
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f2981,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56
    | ~ spl0_246 ),
    inference(superposition,[],[f1037,f2732]) ).

fof(f19606,plain,
    ( spl0_700
    | ~ spl0_55
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2939,f2723,f1032,f19604]) ).

fof(f19604,plain,
    ( spl0_700
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f2939,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55
    | ~ spl0_244 ),
    inference(superposition,[],[f1033,f2724]) ).

fof(f19602,plain,
    ( spl0_699
    | ~ spl0_56
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2938,f2723,f1036,f19600]) ).

fof(f19600,plain,
    ( spl0_699
  <=> ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f2938,plain,
    ( ! [X0] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56
    | ~ spl0_244 ),
    inference(superposition,[],[f1037,f2724]) ).

fof(f19581,plain,
    ( ~ spl0_698
    | ~ spl0_96
    | spl0_652 ),
    inference(avatar_split_clause,[],[f18671,f18658,f1207,f19578]) ).

fof(f1207,plain,
    ( spl0_96
  <=> ! [X13,X0,X1] :
        ( ~ hBOOL(hAPP(X13,X1))
        | hBOOL(c_in(X1,X13,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f18658,plain,
    ( spl0_652
  <=> hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f18671,plain,
    ( ~ hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_96
    | spl0_652 ),
    inference(resolution,[],[f18660,f1208]) ).

fof(f1208,plain,
    ( ! [X0,X1,X13] :
        ( hBOOL(c_in(X1,X13,X0))
        | ~ hBOOL(hAPP(X13,X1)) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f1207]) ).

fof(f18660,plain,
    ( ~ hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_652 ),
    inference(avatar_component_clause,[],[f18658]) ).

fof(f19383,plain,
    ( spl0_697
    | ~ spl0_66
    | ~ spl0_86
    | ~ spl0_119
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f6337,f5495,f1349,f1167,f1079,f19381]) ).

fof(f19381,plain,
    ( spl0_697
  <=> ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f1079,plain,
    ( spl0_66
  <=> ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1167,plain,
    ( spl0_86
  <=> ! [X6,X0,X12] : c_Relation_Orel__comp(c_Relation_OId(X0),X12,X0,X0,X6) = X12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1349,plain,
    ( spl0_119
  <=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f5495,plain,
    ( spl0_419
  <=> ! [X2,X0] :
        ( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0),X2,X0)
        | c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f6337,plain,
    ( ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0)
    | ~ spl0_66
    | ~ spl0_86
    | ~ spl0_119
    | ~ spl0_419 ),
    inference(forward_demodulation,[],[f6336,f1350]) ).

fof(f1350,plain,
    ( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0)
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f1349]) ).

fof(f6336,plain,
    ( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0)
    | ~ spl0_66
    | ~ spl0_86
    | ~ spl0_419 ),
    inference(trivial_inequality_removal,[],[f6335]) ).

fof(f6335,plain,
    ( ! [X0] :
        ( c_Relation_OId(X0) != c_Relation_OId(X0)
        | c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
    | ~ spl0_66
    | ~ spl0_86
    | ~ spl0_419 ),
    inference(forward_demodulation,[],[f6331,f1168]) ).

fof(f1168,plain,
    ( ! [X0,X6,X12] : c_Relation_Orel__comp(c_Relation_OId(X0),X12,X0,X0,X6) = X12
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f1167]) ).

fof(f6331,plain,
    ( ! [X0] :
        ( c_Relation_OId(X0) != c_Relation_Orel__comp(c_Relation_OId(X0),c_Relation_OId(X0),X0,X0,X0)
        | c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
    | ~ spl0_66
    | ~ spl0_419 ),
    inference(superposition,[],[f5496,f1080]) ).

fof(f1080,plain,
    ( ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0)
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1079]) ).

fof(f5496,plain,
    ( ! [X2,X0] :
        ( c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) != X2
        | c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0),X2,X0) )
    | ~ spl0_419 ),
    inference(avatar_component_clause,[],[f5495]) ).

fof(f19379,plain,
    ( spl0_696
    | ~ spl0_64
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f4549,f4149,f1071,f19377]) ).

fof(f19377,plain,
    ( spl0_696
  <=> ! [X0] : c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f1071,plain,
    ( spl0_64
  <=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f4149,plain,
    ( spl0_340
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__2(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f4549,plain,
    ( ! [X0] : c_Relation_Otrans(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_64
    | ~ spl0_340 ),
    inference(resolution,[],[f4150,f1072]) ).

fof(f1072,plain,
    ( ! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1071]) ).

fof(f4150,plain,
    ( ! [X2,X0] :
        ( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__2(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0)))
        | c_Relation_Otrans(X2,X0) )
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f4149]) ).

fof(f19375,plain,
    ( spl0_695
    | ~ spl0_70
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f4535,f4140,f1095,f19373]) ).

fof(f19373,plain,
    ( spl0_695
  <=> ! [X0] : c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f4140,plain,
    ( spl0_338
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f4535,plain,
    ( ! [X0] : c_Relation_Otrans(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_70
    | ~ spl0_338 ),
    inference(resolution,[],[f4141,f1096]) ).

fof(f4141,plain,
    ( ! [X2,X0] :
        ( ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0)))
        | c_Relation_Otrans(X2,X0) )
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f4140]) ).

fof(f19371,plain,
    ( spl0_694
    | ~ spl0_70
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f4527,f4136,f1095,f19369]) ).

fof(f19369,plain,
    ( spl0_694
  <=> ! [X0] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f4136,plain,
    ( spl0_337
  <=> ! [X2,X0] :
        ( c_Nitpick_Orefl_H(X2,X0)
        | ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f4527,plain,
    ( ! [X0] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_70
    | ~ spl0_337 ),
    inference(resolution,[],[f4137,f1096]) ).

fof(f4137,plain,
    ( ! [X2,X0] :
        ( ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0)))
        | c_Nitpick_Orefl_H(X2,X0) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f4136]) ).

fof(f19367,plain,
    ( spl0_693
    | ~ spl0_186
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4033,f3866,f1807,f19365]) ).

fof(f19365,plain,
    ( spl0_693
  <=> ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f4033,plain,
    ( ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_186
    | ~ spl0_315 ),
    inference(resolution,[],[f3867,f1808]) ).

fof(f19363,plain,
    ( spl0_692
    | ~ spl0_185
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4032,f3866,f1803,f19361]) ).

fof(f19361,plain,
    ( spl0_692
  <=> ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1803,plain,
    ( spl0_185
  <=> ! [X53,X1,X10] : ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f4032,plain,
    ( ! [X2,X0,X1] : ~ c_FunDef_Oin__rel(c_Arrow__Order__Mirabelle_Omktop(X0,X1),X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_185
    | ~ spl0_315 ),
    inference(resolution,[],[f3867,f1804]) ).

fof(f1804,plain,
    ( ! [X10,X1,X53] : ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1803]) ).

fof(f19359,plain,
    ( spl0_691
    | ~ spl0_183
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f4019,f3862,f1795,f19357]) ).

fof(f19357,plain,
    ( spl0_691
  <=> ! [X2,X0,X1] : c_FunDef_Oin__rel(c_Transitive__Closure_Ortrancl(X0,X1),X2,X2,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f4019,plain,
    ( ! [X2,X0,X1] : c_FunDef_Oin__rel(c_Transitive__Closure_Ortrancl(X0,X1),X2,X2,X1,X1)
    | ~ spl0_183
    | ~ spl0_314 ),
    inference(resolution,[],[f3863,f1796]) ).

fof(f19355,plain,
    ( spl0_690
    | ~ spl0_222
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3204,f2771,f2148,f19353]) ).

fof(f19353,plain,
    ( spl0_690
  <=> ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f2148,plain,
    ( spl0_222
  <=> ! [X2,X0] : c_Relation_Osym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Oconverse(X2,X0,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f3204,plain,
    ( ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_222
    | ~ spl0_256 ),
    inference(superposition,[],[f2149,f2772]) ).

fof(f2149,plain,
    ( ! [X2,X0] : c_Relation_Osym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Oconverse(X2,X0,X0)),X0)
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2148]) ).

fof(f19351,plain,
    ( spl0_689
    | ~ spl0_70
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2664,f2204,f1095,f19349]) ).

fof(f19349,plain,
    ( spl0_689
  <=> ! [X0] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f2664,plain,
    ( ! [X0] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_70
    | ~ spl0_234 ),
    inference(resolution,[],[f2205,f1096]) ).

fof(f19347,plain,
    ( spl0_688
    | ~ spl0_70
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2633,f2164,f1095,f19345]) ).

fof(f19345,plain,
    ( spl0_688
  <=> ! [X0] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f2633,plain,
    ( ! [X0] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_70
    | ~ spl0_226 ),
    inference(resolution,[],[f2165,f1096]) ).

fof(f19343,plain,
    ( spl0_687
    | ~ spl0_64
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2627,f2160,f1071,f19341]) ).

fof(f19341,plain,
    ( spl0_687
  <=> ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f2627,plain,
    ( ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_64
    | ~ spl0_225 ),
    inference(resolution,[],[f2161,f1072]) ).

fof(f19339,plain,
    ( spl0_686
    | ~ spl0_22
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f1978,f1791,f899,f19337]) ).

fof(f19337,plain,
    ( spl0_686
  <=> ! [X0,X1] : c_Relation_Otrans(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f899,plain,
    ( spl0_22
  <=> ! [X2,X0] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X2,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1791,plain,
    ( spl0_182
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1978,plain,
    ( ! [X0,X1] : c_Relation_Otrans(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
    | ~ spl0_22
    | ~ spl0_182 ),
    inference(superposition,[],[f900,f1792]) ).

fof(f1792,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X0),X0,X0)
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1791]) ).

fof(f900,plain,
    ( ! [X2,X0] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X2,X0),X0)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f899]) ).

fof(f19335,plain,
    ( spl0_685
    | ~ spl0_146
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1671,f1591,f1547,f19333]) ).

fof(f19333,plain,
    ( spl0_685
  <=> ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f1547,plain,
    ( spl0_146
  <=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1591,plain,
    ( spl0_157
  <=> ! [X2,X0] : c_Relation_Oirrefl(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f1671,plain,
    ( ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_146
    | ~ spl0_157 ),
    inference(superposition,[],[f1592,f1548]) ).

fof(f1548,plain,
    ( ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X4)
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1547]) ).

fof(f1592,plain,
    ( ! [X2,X0] : c_Relation_Oirrefl(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0)
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1591]) ).

fof(f19331,plain,
    ( spl0_684
    | ~ spl0_7
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1387,f1329,f829,f19329]) ).

fof(f19329,plain,
    ( spl0_684
  <=> ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f1329,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Otop__class_Otop(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1387,plain,
    ( ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = X0
    | ~ spl0_7
    | ~ spl0_114 ),
    inference(resolution,[],[f1330,f831]) ).

fof(f1330,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Otop__class_Otop(X0)) = X1 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f1329]) ).

fof(f19327,plain,
    ( spl0_683
    | ~ spl0_7
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1385,f1325,f829,f19325]) ).

fof(f19325,plain,
    ( spl0_683
  <=> ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f1325,plain,
    ( spl0_113
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1385,plain,
    ( ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X0) = X0
    | ~ spl0_7
    | ~ spl0_113 ),
    inference(resolution,[],[f1326,f831]) ).

fof(f1326,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X0),X1) = X1 )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f1325]) ).

fof(f19323,plain,
    ( spl0_682
    | ~ spl0_7
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f1379,f1301,f829,f19321]) ).

fof(f19321,plain,
    ( spl0_682
  <=> ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f1301,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1379,plain,
    ( ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X0) = X0
    | ~ spl0_7
    | ~ spl0_107 ),
    inference(resolution,[],[f1302,f831]) ).

fof(f1302,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X0),X1) = X1 )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1301]) ).

fof(f19319,plain,
    ( spl0_681
    | ~ spl0_7
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1377,f1297,f829,f19317]) ).

fof(f19317,plain,
    ( spl0_681
  <=> ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f1297,plain,
    ( spl0_106
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Obot__class_Obot(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1377,plain,
    ( ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = X0
    | ~ spl0_7
    | ~ spl0_106 ),
    inference(resolution,[],[f1298,f831]) ).

fof(f1298,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Obot__class_Obot(X0)) = X1 )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1297]) ).

fof(f19115,plain,
    ( ~ spl0_1
    | spl0_679 ),
    inference(avatar_contradiction_clause,[],[f19114]) ).

fof(f19114,plain,
    ( $false
    | ~ spl0_1
    | spl0_679 ),
    inference(resolution,[],[f19109,f802]) ).

fof(f19109,plain,
    ( ~ c_Relation_Otrans(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_679 ),
    inference(avatar_component_clause,[],[f19107]) ).

fof(f19107,plain,
    ( spl0_679
  <=> c_Relation_Otrans(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f19113,plain,
    ( ~ spl0_679
    | spl0_680
    | ~ spl0_17
    | ~ spl0_609 ),
    inference(avatar_split_clause,[],[f16489,f16465,f878,f19111,f19107]) ).

fof(f19111,plain,
    ( spl0_680
  <=> ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f16465,plain,
    ( spl0_609
  <=> ! [X18,X0,X10,X2,X1] :
        ( ~ c_Relation_Otrans(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f16489,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ c_Relation_Otrans(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_17
    | ~ spl0_609 ),
    inference(resolution,[],[f16466,f880]) ).

fof(f16466,plain,
    ( ! [X2,X10,X0,X18,X1] :
        ( ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Relation_Otrans(X2,X0)
        | hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0))) )
    | ~ spl0_609 ),
    inference(avatar_component_clause,[],[f16465]) ).

fof(f19105,plain,
    ( spl0_678
    | spl0_16
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f7518,f7236,f873,f19103]) ).

fof(f19103,plain,
    ( spl0_678
  <=> ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f7236,plain,
    ( spl0_451
  <=> ! [X11,X0,X5,X7] :
        ( hBOOL(c_in(X5,X11,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f7518,plain,
    ( ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P))
    | spl0_16
    | ~ spl0_451 ),
    inference(resolution,[],[f7237,f875]) ).

fof(f7237,plain,
    ( ! [X0,X11,X7,X5] :
        ( hBOOL(c_in(X5,X11,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) )
    | ~ spl0_451 ),
    inference(avatar_component_clause,[],[f7236]) ).

fof(f19101,plain,
    ( spl0_677
    | spl0_16
    | ~ spl0_450 ),
    inference(avatar_split_clause,[],[f7453,f7232,f873,f19099]) ).

fof(f19099,plain,
    ( spl0_677
  <=> ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f7232,plain,
    ( spl0_450
  <=> ! [X4,X0,X5,X7] :
        ( hBOOL(c_in(X5,X4,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f7453,plain,
    ( ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X0))
    | spl0_16
    | ~ spl0_450 ),
    inference(resolution,[],[f7233,f875]) ).

fof(f7233,plain,
    ( ! [X0,X7,X4,X5] :
        ( hBOOL(c_in(X5,X4,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) )
    | ~ spl0_450 ),
    inference(avatar_component_clause,[],[f7232]) ).

fof(f18980,plain,
    ( spl0_676
    | ~ spl0_17
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f16816,f16762,f878,f18978]) ).

fof(f18978,plain,
    ( spl0_676
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_a,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_b,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,hAPP(v_P,v_i),X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f16762,plain,
    ( spl0_618
  <=> ! [X5,X3,X28,X9,X0,X14,X6,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X6,X14),X3,tc_prod(X6,X14)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X14),c_Relation_Orel__comp(X2,X3,X0,X6,X14),tc_prod(X0,X14))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f16816,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_a,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_b,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,hAPP(v_P,v_i),X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_17
    | ~ spl0_618 ),
    inference(resolution,[],[f16763,f880]) ).

fof(f16763,plain,
    ( ! [X2,X28,X3,X0,X6,X9,X14,X5] :
        ( ~ hBOOL(c_in(c_Pair(X9,X28,X6,X14),X3,tc_prod(X6,X14)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X14),c_Relation_Orel__comp(X2,X3,X0,X6,X14),tc_prod(X0,X14))) )
    | ~ spl0_618 ),
    inference(avatar_component_clause,[],[f16762]) ).

fof(f18976,plain,
    ( spl0_675
    | ~ spl0_17
    | ~ spl0_425 ),
    inference(avatar_split_clause,[],[f6549,f6408,f878,f18974]) ).

fof(f18974,plain,
    ( spl0_675
  <=> ! [X0,X1] : c_Set_Oimage(X0,hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = hAPP(c_Set_Oinsert(hAPP(X0,c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),c_Set_Oimage(X0,hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f6408,plain,
    ( spl0_425
  <=> ! [X16,X4,X0,X6,X1] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | c_Set_Oimage(X16,X4,X0,X6) = hAPP(c_Set_Oinsert(hAPP(X16,X1),X6),c_Set_Oimage(X16,X4,X0,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f6549,plain,
    ( ! [X0,X1] : c_Set_Oimage(X0,hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = hAPP(c_Set_Oinsert(hAPP(X0,c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),c_Set_Oimage(X0,hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1))
    | ~ spl0_17
    | ~ spl0_425 ),
    inference(resolution,[],[f6409,f880]) ).

fof(f6409,plain,
    ( ! [X0,X1,X6,X16,X4] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | c_Set_Oimage(X16,X4,X0,X6) = hAPP(c_Set_Oinsert(hAPP(X16,X1),X6),c_Set_Oimage(X16,X4,X0,X6)) )
    | ~ spl0_425 ),
    inference(avatar_component_clause,[],[f6408]) ).

fof(f18900,plain,
    ( spl0_674
    | ~ spl0_160
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f4020,f3862,f1603,f18898]) ).

fof(f18898,plain,
    ( spl0_674
  <=> ! [X0,X1] : c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X1,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f4020,plain,
    ( ! [X0,X1] : c_FunDef_Oin__rel(c_Relation_OId(X0),X1,X1,X0,X0)
    | ~ spl0_160
    | ~ spl0_314 ),
    inference(resolution,[],[f3863,f1604]) ).

fof(f18896,plain,
    ( ~ spl0_673
    | ~ spl0_96
    | spl0_656 ),
    inference(avatar_split_clause,[],[f18697,f18682,f1207,f18893]) ).

fof(f18893,plain,
    ( spl0_673
  <=> hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),v_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f18682,plain,
    ( spl0_656
  <=> hBOOL(c_in(v_a,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f18697,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),v_a))
    | ~ spl0_96
    | spl0_656 ),
    inference(resolution,[],[f18683,f1208]) ).

fof(f18683,plain,
    ( ~ hBOOL(c_in(v_a,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | spl0_656 ),
    inference(avatar_component_clause,[],[f18682]) ).

fof(f18891,plain,
    ( spl0_672
    | ~ spl0_5
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f1224,f1131,f819,f18889]) ).

fof(f18889,plain,
    ( spl0_672
  <=> ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f819,plain,
    ( spl0_5
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1131,plain,
    ( spl0_77
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1224,plain,
    ( ! [X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,tc_bool),X0) = X0
    | ~ spl0_5
    | ~ spl0_77 ),
    inference(resolution,[],[f1132,f821]) ).

fof(f821,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f819]) ).

fof(f1132,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X1) = X1 )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1131]) ).

fof(f18887,plain,
    ( spl0_671
    | ~ spl0_4
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f1219,f1117,f814,f18885]) ).

fof(f18885,plain,
    ( spl0_671
  <=> ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f814,plain,
    ( spl0_4
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1117,plain,
    ( spl0_74
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f1219,plain,
    ( ! [X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_bool),X0) = X0
    | ~ spl0_4
    | ~ spl0_74 ),
    inference(resolution,[],[f1118,f816]) ).

fof(f816,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f814]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X1) = X1 )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f1117]) ).

fof(f18838,plain,
    ( spl0_670
    | spl0_16
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f7754,f7720,f873,f18835]) ).

fof(f18835,plain,
    ( spl0_670
  <=> v_F(v_P) = hAPP(c_HOL_Ominus__class_Ominus(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f7720,plain,
    ( spl0_464
  <=> ! [X4,X0,X1] :
        ( hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4
        | hBOOL(c_in(X1,X4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f7754,plain,
    ( v_F(v_P) = hAPP(c_HOL_Ominus__class_Ominus(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
    | spl0_16
    | ~ spl0_464 ),
    inference(resolution,[],[f7721,f875]) ).

fof(f7721,plain,
    ( ! [X0,X1,X4] :
        ( hBOOL(c_in(X1,X4,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4 )
    | ~ spl0_464 ),
    inference(avatar_component_clause,[],[f7720]) ).

fof(f18824,plain,
    ( spl0_669
    | ~ spl0_226
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f4665,f4185,f2164,f18822]) ).

fof(f18822,plain,
    ( spl0_669
  <=> ! [X0,X1] :
        ( c_Relation_Oirrefl(X0,X1)
        | ~ c_Wellfounded_Owf(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f4185,plain,
    ( spl0_349
  <=> ! [X2,X0] :
        ( c_Relation_Oirrefl(X2,X0)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f4665,plain,
    ( ! [X0,X1] :
        ( c_Relation_Oirrefl(X0,X1)
        | ~ c_Wellfounded_Owf(X0,X1) )
    | ~ spl0_226
    | ~ spl0_349 ),
    inference(resolution,[],[f4186,f2165]) ).

fof(f4186,plain,
    ( ! [X2,X0] :
        ( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0)))
        | c_Relation_Oirrefl(X2,X0) )
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f4185]) ).

fof(f18820,plain,
    ( spl0_668
    | ~ spl0_225
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2661,f2204,f2160,f18818]) ).

fof(f18818,plain,
    ( spl0_668
  <=> ! [X0,X1] :
        ( ~ c_Relation_Oirrefl(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f2661,plain,
    ( ! [X0,X1] :
        ( ~ c_Relation_Oirrefl(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) )
    | ~ spl0_225
    | ~ spl0_234 ),
    inference(resolution,[],[f2205,f2161]) ).

fof(f18816,plain,
    ( spl0_667
    | ~ spl0_225
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2630,f2164,f2160,f18814]) ).

fof(f18814,plain,
    ( spl0_667
  <=> ! [X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f2630,plain,
    ( ! [X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) )
    | ~ spl0_225
    | ~ spl0_226 ),
    inference(resolution,[],[f2165,f2161]) ).

fof(f18812,plain,
    ( ~ spl0_666
    | ~ spl0_96
    | spl0_655 ),
    inference(avatar_split_clause,[],[f18691,f18678,f1207,f18809]) ).

fof(f18809,plain,
    ( spl0_666
  <=> hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),v_b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f18678,plain,
    ( spl0_655
  <=> hBOOL(c_in(v_b,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f18691,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),v_b))
    | ~ spl0_96
    | spl0_655 ),
    inference(resolution,[],[f18680,f1208]) ).

fof(f18680,plain,
    ( ~ hBOOL(c_in(v_b,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | spl0_655 ),
    inference(avatar_component_clause,[],[f18678]) ).

fof(f18804,plain,
    ( spl0_665
    | ~ spl0_60
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f1107,f1103,f1055,f18802]) ).

fof(f18802,plain,
    ( spl0_665
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f1055,plain,
    ( spl0_60
  <=> ! [X15,X0,X6,X22] : hAPP(c_COMBK(X15,X0,X6),X22) = X15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f1107,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_60
    | ~ spl0_71 ),
    inference(superposition,[],[f1104,f1056]) ).

fof(f1056,plain,
    ( ! [X0,X6,X15,X22] : hAPP(c_COMBK(X15,X0,X6),X22) = X15
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f1055]) ).

fof(f18780,plain,
    ( spl0_664
    | ~ spl0_17
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f6497,f6400,f878,f18778]) ).

fof(f18778,plain,
    ( spl0_664
  <=> ! [X0,X1] : hAPP(c_Set_Oinsert(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f6400,plain,
    ( spl0_423
  <=> ! [X28,X4,X0,X6,X1] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | c_Set_Oimage(c_COMBK(X28,X6,X0),X4,X0,X6) = hAPP(c_Set_Oinsert(X28,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f6497,plain,
    ( ! [X0,X1] : hAPP(c_Set_Oinsert(X0,X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)
    | ~ spl0_17
    | ~ spl0_423 ),
    inference(resolution,[],[f6401,f880]) ).

fof(f6401,plain,
    ( ! [X28,X0,X1,X6,X4] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | c_Set_Oimage(c_COMBK(X28,X6,X0),X4,X0,X6) = hAPP(c_Set_Oinsert(X28,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))) )
    | ~ spl0_423 ),
    inference(avatar_component_clause,[],[f6400]) ).

fof(f18776,plain,
    ( spl0_662
    | ~ spl0_663
    | ~ spl0_17
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f11627,f11281,f878,f18773,f18770]) ).

fof(f18770,plain,
    ( spl0_662
  <=> ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | v_b = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f18773,plain,
    ( spl0_663
  <=> c_Relation_Osingle__valued(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f11281,plain,
    ( spl0_537
  <=> ! [X18,X10,X0,X6,X2,X1] :
        ( X10 = X18
        | ~ c_Relation_Osingle__valued(X2,X0,X6)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X2,tc_prod(X0,X6)))
        | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f11627,plain,
    ( ! [X0] :
        ( ~ c_Relation_Osingle__valued(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ hBOOL(c_in(c_Pair(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | v_b = X0 )
    | ~ spl0_17
    | ~ spl0_537 ),
    inference(resolution,[],[f11282,f880]) ).

fof(f11282,plain,
    ( ! [X2,X10,X0,X1,X18,X6] :
        ( ~ hBOOL(c_in(c_Pair(X1,X18,X0,X6),X2,tc_prod(X0,X6)))
        | ~ c_Relation_Osingle__valued(X2,X0,X6)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X2,tc_prod(X0,X6)))
        | X10 = X18 )
    | ~ spl0_537 ),
    inference(avatar_component_clause,[],[f11281]) ).

fof(f18736,plain,
    ( spl0_661
    | ~ spl0_17
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f3584,f3302,f878,f18734]) ).

fof(f18734,plain,
    ( spl0_661
  <=> ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f3302,plain,
    ( spl0_278
  <=> ! [X0,X12,X22,X1] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | ~ hBOOL(c_in(X1,X22,X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X22,X12,X0),X22,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f3584,plain,
    ( ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_17
    | ~ spl0_278 ),
    inference(resolution,[],[f3303,f880]) ).

fof(f3303,plain,
    ( ! [X0,X1,X22,X12] :
        ( ~ hBOOL(c_in(X1,X22,X0))
        | ~ c_Wellfounded_Owf(X12,X0)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X22,X12,X0),X22,X0)) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f3302]) ).

fof(f18732,plain,
    ( spl0_660
    | ~ spl0_17
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f3569,f3298,f878,f18730]) ).

fof(f18730,plain,
    ( spl0_660
  <=> ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f3298,plain,
    ( spl0_277
  <=> ! [X2,X0,X23,X22] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(X23,X22,X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X22,X2,X0),X22,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f3569,plain,
    ( ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(hAPP(v_P,v_i),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_17
    | ~ spl0_277 ),
    inference(resolution,[],[f3299,f880]) ).

fof(f3299,plain,
    ( ! [X2,X0,X22,X23] :
        ( ~ hBOOL(c_in(X23,X22,X0))
        | ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X22,X2,X0),X22,X0)) )
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f3298]) ).

fof(f18728,plain,
    ( ~ spl0_659
    | ~ spl0_315
    | spl0_652 ),
    inference(avatar_split_clause,[],[f18666,f18658,f3866,f18725]) ).

fof(f18666,plain,
    ( ~ c_FunDef_Oin__rel(hAPP(v_P,v_i),v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_315
    | spl0_652 ),
    inference(resolution,[],[f18660,f3867]) ).

fof(f18711,plain,
    ( spl0_658
    | ~ spl0_183
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f4524,f4136,f1795,f18709]) ).

fof(f18709,plain,
    ( spl0_658
  <=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f4524,plain,
    ( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_183
    | ~ spl0_337 ),
    inference(resolution,[],[f4137,f1796]) ).

fof(f18701,plain,
    ( spl0_657
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2662,f2204,f1795,f18699]) ).

fof(f18699,plain,
    ( spl0_657
  <=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f2662,plain,
    ( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_183
    | ~ spl0_234 ),
    inference(resolution,[],[f2205,f1796]) ).

fof(f18685,plain,
    ( ~ spl0_655
    | spl0_656
    | ~ spl0_17
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f8131,f7833,f878,f18682,f18678]) ).

fof(f7833,plain,
    ( spl0_475
  <=> ! [X10,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | hBOOL(c_in(X10,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X10,X5,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f8131,plain,
    ( hBOOL(c_in(v_a,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ hBOOL(c_in(v_b,c_Wellfounded_Oacc(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_17
    | ~ spl0_475 ),
    inference(resolution,[],[f7834,f880]) ).

fof(f7834,plain,
    ( ! [X2,X10,X0,X5] :
        ( ~ hBOOL(c_in(c_Pair(X10,X5,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X10,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0)) )
    | ~ spl0_475 ),
    inference(avatar_component_clause,[],[f7833]) ).

fof(f18676,plain,
    ( spl0_652
    | ~ spl0_654
    | ~ spl0_17
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f8095,f7825,f878,f18673,f18658]) ).

fof(f18673,plain,
    ( spl0_654
  <=> c_Relation_Osym(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f7825,plain,
    ( spl0_473
  <=> ! [X0,X10,X2,X1] :
        ( ~ c_Relation_Osym(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f8095,plain,
    ( ~ c_Relation_Osym(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_17
    | ~ spl0_473 ),
    inference(resolution,[],[f7826,f880]) ).

fof(f7826,plain,
    ( ! [X2,X10,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Relation_Osym(X2,X0)
        | hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0))) )
    | ~ spl0_473 ),
    inference(avatar_component_clause,[],[f7825]) ).

fof(f18665,plain,
    ( ~ spl0_652
    | ~ spl0_653
    | ~ spl0_17
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f8063,f7821,f878,f18662,f18658]) ).

fof(f18662,plain,
    ( spl0_653
  <=> c_Wellfounded_Owf(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f7821,plain,
    ( spl0_472
  <=> ! [X0,X5,X2,X1] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X5,X1,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f8063,plain,
    ( ~ c_Wellfounded_Owf(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_17
    | ~ spl0_472 ),
    inference(resolution,[],[f7822,f880]) ).

fof(f7822,plain,
    ( ! [X2,X0,X1,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X1,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0))) )
    | ~ spl0_472 ),
    inference(avatar_component_clause,[],[f7821]) ).

fof(f18579,plain,
    spl0_651,
    inference(avatar_split_clause,[],[f107,f18577]) ).

fof(f18577,plain,
    ( spl0_651
  <=> ! [X5,X4,X9,X0,X6,X7] : c_Product__Type_OSigma(hAPP(c_Set_Oinsert(X5,X0),X4),c_COMBK(hAPP(c_Set_Oinsert(X9,X6),X7),tc_fun(X6,tc_bool),X0),X0,X6) = hAPP(c_Set_Oinsert(c_Pair(X5,X9,X0,X6),tc_prod(X0,X6)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X4,c_COMBK(hAPP(c_Set_Oinsert(X9,X6),X7),tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(hAPP(c_Set_Oinsert(X5,X0),X4),c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f107,axiom,
    ! [X0,X6,X9,X7,X4,X5] : c_Product__Type_OSigma(hAPP(c_Set_Oinsert(X5,X0),X4),c_COMBK(hAPP(c_Set_Oinsert(X9,X6),X7),tc_fun(X6,tc_bool),X0),X0,X6) = hAPP(c_Set_Oinsert(c_Pair(X5,X9,X0,X6),tc_prod(X0,X6)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X4,c_COMBK(hAPP(c_Set_Oinsert(X9,X6),X7),tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(hAPP(c_Set_Oinsert(X5,X0),X4),c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).

fof(f18199,plain,
    ( spl0_650
    | ~ spl0_243
    | ~ spl0_254
    | ~ spl0_573
    | ~ spl0_581
    | ~ spl0_649 ),
    inference(avatar_split_clause,[],[f18195,f18191,f13612,f13374,f2763,f2719,f18197]) ).

fof(f18197,plain,
    ( spl0_650
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11))) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f2719,plain,
    ( spl0_243
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2763,plain,
    ( spl0_254
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f13374,plain,
    ( spl0_573
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f13612,plain,
    ( spl0_581
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f18191,plain,
    ( spl0_649
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f18195,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11))) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4))
    | ~ spl0_243
    | ~ spl0_254
    | ~ spl0_573
    | ~ spl0_581
    | ~ spl0_649 ),
    inference(forward_demodulation,[],[f18194,f13676]) ).

fof(f13676,plain,
    ( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_fun(X1,tc_bool)),X0),tc_fun(X1,tc_bool)),X2) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X1,tc_bool)),X2),tc_fun(X1,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(X1,tc_bool)),X0))
    | ~ spl0_243
    | ~ spl0_573 ),
    inference(superposition,[],[f13375,f2720]) ).

fof(f2720,plain,
    ( ! [X0,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4)
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f2719]) ).

fof(f13375,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4))
    | ~ spl0_573 ),
    inference(avatar_component_clause,[],[f13374]) ).

fof(f18194,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11)))
    | ~ spl0_254
    | ~ spl0_581
    | ~ spl0_649 ),
    inference(forward_demodulation,[],[f18192,f14259]) ).

fof(f14259,plain,
    ( ! [X2,X3,X0,X1] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_fun(X1,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(X1,tc_bool)),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(X1,tc_bool)),X0),tc_fun(X1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,tc_fun(X1,tc_bool)),X3))
    | ~ spl0_254
    | ~ spl0_581 ),
    inference(superposition,[],[f13613,f2764]) ).

fof(f2764,plain,
    ( ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4)
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f2763]) ).

fof(f13613,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11))
    | ~ spl0_581 ),
    inference(avatar_component_clause,[],[f13612]) ).

fof(f18192,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)))
    | ~ spl0_649 ),
    inference(avatar_component_clause,[],[f18191]) ).

fof(f18193,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f785,f18191]) ).

fof(f785,plain,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11))),
    inference(forward_demodulation,[],[f188,f78]) ).

fof(f78,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

fof(f188,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

fof(f18149,plain,
    ( ~ spl0_648
    | ~ spl0_108
    | ~ spl0_625 ),
    inference(avatar_split_clause,[],[f17779,f17077,f1305,f18146]) ).

fof(f18146,plain,
    ( spl0_648
  <=> c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f1305,plain,
    ( spl0_108
  <=> ! [X5,X4,X0] : hAPP(c_Set_Oinsert(X5,X0),X4) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f17077,plain,
    ( spl0_625
  <=> c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f17779,plain,
    ( c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) != c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | ~ spl0_108
    | ~ spl0_625 ),
    inference(superposition,[],[f1306,f17079]) ).

fof(f17079,plain,
    ( c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_625 ),
    inference(avatar_component_clause,[],[f17077]) ).

fof(f1306,plain,
    ( ! [X0,X4,X5] : hAPP(c_Set_Oinsert(X5,X0),X4) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1305]) ).

fof(f18121,plain,
    spl0_647,
    inference(avatar_split_clause,[],[f482,f18119]) ).

fof(f18119,plain,
    ( spl0_647
  <=> ! [X18,X0,X10,X2,X1] :
        ( ~ c_Relation_Osingle__valued(X2,X0,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X10,X18,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X18,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f482,axiom,
    ! [X2,X10,X0,X1,X18] :
      ( ~ c_Relation_Osingle__valued(X2,X0,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X10,X18,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X18,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

fof(f18117,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f90,f18115]) ).

fof(f18115,plain,
    ( spl0_646
  <=> ! [X3,X4,X11,X0,X14,X6,X2,X7] :
        ( ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool))
        | ~ c_lessequals(X3,c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X14,tc_bool),X6),X6,X14),tc_fun(tc_prod(X6,X14),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X2,X3,X0,X6,X14),c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X14,tc_bool),X0),X0,X14),tc_fun(tc_prod(X0,X14),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f90,axiom,
    ! [X2,X3,X0,X11,X6,X7,X14,X4] :
      ( ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool))
      | ~ c_lessequals(X3,c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X14,tc_bool),X6),X6,X14),tc_fun(tc_prod(X6,X14),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X2,X3,X0,X6,X14),c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X14,tc_bool),X0),X0,X14),tc_fun(tc_prod(X0,X14),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).

fof(f18048,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f773,f18046]) ).

fof(f18046,plain,
    ( spl0_645
  <=> ! [X28,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f773,plain,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f618,f574,f574,f574]) ).

fof(f574,axiom,
    ! [X2,X0] : c_Transitive__Closure_Otrancl(X2,X0) = c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

fof(f618,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

fof(f17888,plain,
    spl0_644,
    inference(avatar_split_clause,[],[f772,f17886]) ).

fof(f17886,plain,
    ( spl0_644
  <=> ! [X18,X0,X2,X1] :
        ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f772,plain,
    ! [X2,X0,X1,X18] :
      ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f385,f574,f574]) ).

fof(f385,axiom,
    ! [X2,X0,X1,X18] :
      ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X18,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

fof(f17884,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f771,f17882]) ).

fof(f17882,plain,
    ( spl0_643
  <=> ! [X9,X0,X5,X2] :
        ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f771,plain,
    ! [X2,X0,X9,X5] :
      ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f390,f574,f574]) ).

fof(f390,axiom,
    ! [X2,X0,X9,X5] :
      ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).

fof(f17713,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f768,f17711]) ).

fof(f17711,plain,
    ( spl0_642
  <=> ! [X2,X43,X42] :
        ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
        | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
        | hBOOL(c_in(c_Pair(X42,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f768,plain,
    ! [X2,X42,X43] :
      ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(X42,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ),
    inference(definition_unfolding,[],[f387,f574,f574]) ).

fof(f387,axiom,
    ! [X2,X42,X43] :
      ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(X42,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).

fof(f17709,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f395,f17707]) ).

fof(f17707,plain,
    ( spl0_641
  <=> ! [X5,X4,X0,X9,X2,X1] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f395,axiom,
    ! [X2,X0,X1,X9,X4,X5] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

fof(f17705,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f394,f17703]) ).

fof(f17703,plain,
    ( spl0_640
  <=> ! [X5,X4,X0,X9,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | ~ hBOOL(c_in(X9,X4,X0))
        | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ c_lessequals(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f394,axiom,
    ! [X2,X0,X9,X4,X5] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | ~ hBOOL(c_in(X9,X4,X0))
      | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ c_lessequals(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

fof(f17596,plain,
    spl0_639,
    inference(avatar_split_clause,[],[f775,f17594]) ).

fof(f17594,plain,
    ( spl0_639
  <=> ! [X28,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f775,plain,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f484,f574,f574]) ).

fof(f484,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

fof(f17592,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f774,f17590]) ).

fof(f17590,plain,
    ( spl0_638
  <=> ! [X18,X0,X10,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f774,plain,
    ! [X2,X10,X0,X18,X1] :
      ( ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f485,f574,f574]) ).

fof(f485,axiom,
    ! [X2,X10,X0,X18,X1] :
      ( ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

fof(f17534,plain,
    ( spl0_637
    | ~ spl0_365
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f16380,f16058,f4909,f17532]) ).

fof(f17532,plain,
    ( spl0_637
  <=> ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_b,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f4909,plain,
    ( spl0_365
  <=> ! [X4,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X9,X2,X6,X0),X4,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f16058,plain,
    ( spl0_603
  <=> ! [X0] :
        ( hBOOL(c_in(v_b,hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f16380,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,v_b,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_365
    | ~ spl0_603 ),
    inference(resolution,[],[f16059,f4910]) ).

fof(f4910,plain,
    ( ! [X2,X0,X6,X9,X4] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X9,X2,X6,X0),X4,X6)) )
    | ~ spl0_365 ),
    inference(avatar_component_clause,[],[f4909]) ).

fof(f16059,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_b,hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_603 ),
    inference(avatar_component_clause,[],[f16058]) ).

fof(f17465,plain,
    spl0_636,
    inference(avatar_split_clause,[],[f764,f17463]) ).

fof(f17463,plain,
    ( spl0_636
  <=> ! [X28,X0,X9,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f764,plain,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f595,f574,f574]) ).

fof(f595,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

fof(f17461,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f763,f17459]) ).

fof(f17459,plain,
    ( spl0_635
  <=> ! [X28,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f763,plain,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f596,f574,f574]) ).

fof(f596,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

fof(f17457,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f449,f17455]) ).

fof(f17455,plain,
    ( spl0_634
  <=> ! [X5,X4,X0,X9,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | ~ hBOOL(c_in(X9,X4,X0))
        | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f449,axiom,
    ! [X2,X0,X9,X4,X5] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | ~ hBOOL(c_in(X9,X4,X0))
      | hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

fof(f17393,plain,
    spl0_633,
    inference(avatar_split_clause,[],[f448,f17391]) ).

fof(f17391,plain,
    ( spl0_633
  <=> ! [X4,X0,X14,X6,X2,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) = X4
        | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X2,X6,X0),X0,X6)
        | hAPP(c_Relation_OImage(X2,X6,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X14,tc_fun(X6,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(c_Relation_OImage(X2,X6,X0),X7,tc_fun(X6,tc_bool),tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f448,axiom,
    ! [X2,X0,X6,X7,X14,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)) = X4
      | ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X2,X6,X0),X0,X6)
      | hAPP(c_Relation_OImage(X2,X6,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X14,tc_fun(X6,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(c_Relation_OImage(X2,X6,X0),X7,tc_fun(X6,tc_bool),tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__INT__eq_0) ).

fof(f17389,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f276,f17387]) ).

fof(f276,axiom,
    ! [X2,X0,X9,X4,X5] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | c_lessequals(hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

fof(f17338,plain,
    ( spl0_631
    | ~ spl0_366
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f16379,f16058,f4913,f17336]) ).

fof(f17336,plain,
    ( spl0_631
  <=> ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_b,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f4913,plain,
    ( spl0_366
  <=> ! [X4,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X9,X2,X6,X0),X4,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f16379,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,v_b,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_366
    | ~ spl0_603 ),
    inference(resolution,[],[f16059,f4914]) ).

fof(f4914,plain,
    ( ! [X2,X0,X6,X9,X4] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X9,X2,X6,X0),X4,X6)) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f4913]) ).

fof(f17287,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f770,f17285]) ).

fof(f17285,plain,
    ( spl0_630
  <=> ! [X9,X0,X5,X2] :
        ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X9,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f770,plain,
    ! [X2,X0,X9,X5] :
      ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X9,X0,X0),X2,tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f389,f574]) ).

fof(f389,axiom,
    ! [X2,X0,X9,X5] :
      ( hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X5,X9,X2,X0),X9,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).

fof(f17283,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f769,f17281]) ).

fof(f17281,plain,
    ( spl0_629
  <=> ! [X18,X0,X2,X1] :
        ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f769,plain,
    ! [X2,X0,X1,X18] :
      ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f392,f574]) ).

fof(f392,axiom,
    ! [X2,X0,X1,X18] :
      ( hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X2,X1,X18,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

fof(f17234,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f767,f17232]) ).

fof(f17232,plain,
    ( spl0_628
  <=> ! [X2,X43,X42] :
        ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
        | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
        | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),X43,t_a,t_a),X2,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f767,plain,
    ! [X2,X42,X43] :
      ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),X43,t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    inference(definition_unfolding,[],[f393,f574]) ).

fof(f393,axiom,
    ! [X2,X42,X43] :
      ( hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),X2,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X42,X43,t_a,t_a),c_Transitive__Closure_Otrancl(X2,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X43,X2),X43,t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).

fof(f17133,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f765,f17131]) ).

fof(f17131,plain,
    ( spl0_627
  <=> ! [X28,X0,X9,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f765,plain,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f455,f574]) ).

fof(f455,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

fof(f17129,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f444,f17127]) ).

fof(f444,axiom,
    ! [X2,X10,X0,X1,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
      | hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X10,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

fof(f17080,plain,
    ( spl0_625
    | ~ spl0_154
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f4922,f4861,f1579,f17077]) ).

fof(f1579,plain,
    ( spl0_154
  <=> ! [X5,X4,X0] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | hAPP(c_Set_Oinsert(X5,X0),X4) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f4922,plain,
    ( c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_154
    | ~ spl0_358 ),
    inference(resolution,[],[f4863,f1580]) ).

fof(f1580,plain,
    ( ! [X0,X4,X5] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | hAPP(c_Set_Oinsert(X5,X0),X4) = X4 )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1579]) ).

fof(f17075,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f756,f17073]) ).

fof(f17073,plain,
    ( spl0_624
  <=> ! [X4,X0,X2] :
        ( ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f756,plain,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    inference(definition_unfolding,[],[f138,f574]) ).

fof(f138,axiom,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
      | c_lessequals(c_Transitive__Closure_Otrancl(X2,X0),c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).

fof(f17044,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f20,f17042]) ).

fof(f17042,plain,
    ( spl0_623
  <=> ! [X4,X11,X0,X6,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X11
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X7,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f20,axiom,
    ! [X0,X11,X6,X7,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X11
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X7,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_1) ).

fof(f16939,plain,
    spl0_622,
    inference(avatar_split_clause,[],[f676,f16937]) ).

fof(f16937,plain,
    ( spl0_622
  <=> ! [X4,X0,X23,X2,X1] :
        ( X1 = X23
        | ~ c_Relation_Ototal__on(X4,X2,X0)
        | ~ hBOOL(c_in(X1,X4,X0))
        | ~ hBOOL(c_in(X23,X4,X0))
        | hBOOL(c_in(c_Pair(X1,X23,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X23,X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f676,axiom,
    ! [X2,X0,X1,X4,X23] :
      ( X1 = X23
      | ~ c_Relation_Ototal__on(X4,X2,X0)
      | ~ hBOOL(c_in(X1,X4,X0))
      | ~ hBOOL(c_in(X23,X4,X0))
      | hBOOL(c_in(c_Pair(X1,X23,X0,X0),X2,tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X23,X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

fof(f16935,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f600,f16933]) ).

fof(f16933,plain,
    ( spl0_621
  <=> ! [X28,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f600,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

fof(f16772,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f776,f16770]) ).

fof(f16770,plain,
    ( spl0_620
  <=> ! [X2,X0,X3] :
        ( ~ c_Wellfounded_Owf(X3,X0)
        | ~ c_Wellfounded_Owf(X2,X0)
        | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X3,X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f776,plain,
    ! [X2,X3,X0] :
      ( ~ c_Wellfounded_Owf(X3,X0)
      | ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X3,X0,X0)) ),
    inference(definition_unfolding,[],[f365,f554]) ).

fof(f554,axiom,
    ! [X2,X0,X6] : c_Relation_ODomain(X2,X0,X6) = c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).

fof(f365,axiom,
    ! [X2,X3,X0] :
      ( ~ c_Wellfounded_Owf(X3,X0)
      | ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X2,X0,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X3,X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).

fof(f16768,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f733,f16766]) ).

fof(f16766,plain,
    ( spl0_619
  <=> ! [X4,X0,X6,X7] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X4,X0,X6),X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X6),X6,X0)),c_Relation_ORange(c_Relation_Oconverse(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6),X6,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f733,plain,
    ! [X0,X6,X7,X4] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X4,X0,X6),X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X6),X6,X0)),c_Relation_ORange(c_Relation_Oconverse(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6),X6,X0),tc_fun(X0,tc_bool)),
    inference(definition_unfolding,[],[f33,f554,f554,f554]) ).

fof(f33,axiom,
    ! [X0,X6,X7,X4] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X4,X0,X6),tc_fun(X0,tc_bool)),c_Relation_ODomain(X7,X0,X6)),c_Relation_ODomain(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

fof(f16764,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f616,f16762]) ).

fof(f616,axiom,
    ! [X2,X28,X3,X0,X6,X9,X14,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X6,X14),X3,tc_prod(X6,X14)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X14),c_Relation_Orel__comp(X2,X3,X0,X6,X14),tc_prod(X0,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

fof(f16760,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f275,f16758]) ).

fof(f16758,plain,
    ( spl0_617
  <=> ! [X5,X4,X0,X9,X2] :
        ( X5 = X9
        | hBOOL(c_in(X5,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f275,axiom,
    ! [X2,X0,X9,X4,X5] :
      ( X5 = X9
      | hBOOL(c_in(X5,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).

fof(f16597,plain,
    ( spl0_616
    | ~ spl0_98
    | ~ spl0_603 ),
    inference(avatar_split_clause,[],[f16382,f16058,f1216,f16595]) ).

fof(f16595,plain,
    ( spl0_616
  <=> ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_b)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f16382,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),v_b)) )
    | ~ spl0_98
    | ~ spl0_603 ),
    inference(resolution,[],[f16059,f1217]) ).

fof(f16593,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f598,f16591]) ).

fof(f16591,plain,
    ( spl0_615
  <=> ! [X28,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f598,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

fof(f16589,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f597,f16587]) ).

fof(f16587,plain,
    ( spl0_614
  <=> ! [X28,X0,X9,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f597,axiom,
    ! [X2,X28,X0,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X9,X28,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X28,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

fof(f16585,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f416,f16583]) ).

fof(f16583,plain,
    ( spl0_613
  <=> ! [X4,X0,X12,X6,X7] :
        ( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X12,X6,X0),X0,X6)
        | hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f416,axiom,
    ! [X0,X6,X7,X4,X12] :
      ( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X12,X6,X0),X0,X6)
      | hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

fof(f16581,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f27,f16579]) ).

fof(f16579,plain,
    ( spl0_612
  <=> ! [X4,X11,X0,X6,X1,X7] :
        ( ~ hBOOL(c_in(X1,X11,X0))
        | c_lessequals(X4,X7,tc_fun(X6,tc_bool))
        | ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),tc_fun(tc_prod(X6,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f27,axiom,
    ! [X0,X11,X1,X6,X7,X4] :
      ( ~ hBOOL(c_in(X1,X11,X0))
      | c_lessequals(X4,X7,tc_fun(X6,tc_bool))
      | ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),tc_fun(tc_prod(X6,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).

fof(f16577,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f26,f16575]) ).

fof(f16575,plain,
    ( spl0_611
  <=> ! [X4,X11,X0,X6,X1,X7] :
        ( ~ hBOOL(c_in(X1,X11,X0))
        | ~ c_lessequals(X4,X7,tc_fun(X6,tc_bool))
        | c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),tc_fun(tc_prod(X6,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f26,axiom,
    ! [X0,X11,X1,X6,X7,X4] :
      ( ~ hBOOL(c_in(X1,X11,X0))
      | ~ c_lessequals(X4,X7,tc_fun(X6,tc_bool))
      | c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0),tc_fun(tc_prod(X6,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).

fof(f16471,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f761,f16469]) ).

fof(f16469,plain,
    ( spl0_610
  <=> ! [X3,X0,X36,X2] :
        ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
        | ~ hBOOL(c_in(X36,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(X36,c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f761,plain,
    ! [X2,X3,X0,X36] :
      ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
      | ~ hBOOL(c_in(X36,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(X36,c_Relation_Orel__comp(X3,c_Transitive__Closure_Ortrancl(X3,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f346,f574,f574]) ).

fof(f346,axiom,
    ! [X2,X3,X0,X36] :
      ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
      | ~ hBOOL(c_in(X36,c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(X36,c_Transitive__Closure_Otrancl(X3,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

fof(f16467,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f670,f16465]) ).

fof(f670,axiom,
    ! [X2,X10,X0,X1,X18] :
      ( ~ c_Relation_Otrans(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X10,X18,X0,X0),X2,tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,X18,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

fof(f16080,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f793,f16078]) ).

fof(f16078,plain,
    ( spl0_608
  <=> ! [X13,X0,X12] :
        ( ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X12,X0,X0,X0)),X0)
        | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f793,plain,
    ! [X0,X12,X13] :
      ( ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X12,X0,X0,X0)),X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    inference(forward_demodulation,[],[f792,f204]) ).

fof(f204,axiom,
    ! [X0,X6,X14,X12,X32,X13] : c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X14),tc_bool)),X32),X12,X0,X14,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X12,X0,X14,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Orel__comp(X32,X12,X0,X14,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

fof(f792,plain,
    ! [X0,X12,X13] :
      ( ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X13,X12,X0,X0,X0))),X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    inference(forward_demodulation,[],[f364,f216]) ).

fof(f216,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

fof(f364,axiom,
    ! [X0,X12,X13] :
      ( c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0)
      | ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X13,X12,X0,X0,X0)),tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

fof(f16076,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f791,f16074]) ).

fof(f16074,plain,
    ( spl0_607
  <=> ! [X13,X0,X12] :
        ( c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X12,X0,X0,X0)),X0)
        | ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f791,plain,
    ! [X0,X12,X13] :
      ( c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X12,X0,X0,X0)),X0)
      | ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    inference(forward_demodulation,[],[f790,f204]) ).

fof(f790,plain,
    ! [X0,X12,X13] :
      ( c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X0),tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X13,X12,X0,X0,X0))),X0)
      | ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    inference(forward_demodulation,[],[f363,f216]) ).

fof(f363,axiom,
    ! [X0,X12,X13] :
      ( ~ c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X13,X12,X0,X0,X0)),tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

fof(f16072,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f753,f16070]) ).

fof(f16070,plain,
    ( spl0_606
  <=> ! [X10,X0,X12,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f753,plain,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f439,f574]) ).

fof(f439,axiom,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Otrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

fof(f16068,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f752,f16066]) ).

fof(f16066,plain,
    ( spl0_605
  <=> ! [X10,X0,X12,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f752,plain,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f438,f574]) ).

fof(f438,axiom,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Otrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

fof(f16064,plain,
    spl0_604,
    inference(avatar_split_clause,[],[f732,f16062]) ).

fof(f16062,plain,
    ( spl0_604
  <=> ! [X4,X0,X6,X7] : c_Relation_ORange(c_Relation_Oconverse(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X4,X0,X6),X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X6),X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f732,plain,
    ! [X0,X6,X7,X4] : c_Relation_ORange(c_Relation_Oconverse(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X4,X0,X6),X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X6),X6,X0)),
    inference(definition_unfolding,[],[f219,f554,f554,f554]) ).

fof(f219,axiom,
    ! [X0,X6,X7,X4] : c_Relation_ODomain(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(tc_prod(X0,X6),tc_bool)),X7),X0,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X4,X0,X6),tc_fun(X0,tc_bool)),c_Relation_ODomain(X7,X0,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).

fof(f16060,plain,
    ( spl0_603
    | ~ spl0_17
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f9077,f8243,f878,f16058]) ).

fof(f8243,plain,
    ( spl0_489
  <=> ! [X6,X4,X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X0,X6),X4),X6))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f9077,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_b,hAPP(c_Relation_OImage(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_17
    | ~ spl0_489 ),
    inference(resolution,[],[f8244,f880]) ).

fof(f8244,plain,
    ( ! [X2,X0,X6,X9,X4,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
        | hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X0,X6),X4),X6))
        | ~ hBOOL(c_in(X5,X4,X0)) )
    | ~ spl0_489 ),
    inference(avatar_component_clause,[],[f8243]) ).

fof(f16056,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f19,f16054]) ).

fof(f16054,plain,
    ( spl0_602
  <=> ! [X4,X0,X14,X6,X2,X7] : c_lessequals(hAPP(c_Relation_OImage(X2,X6,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X14,tc_fun(X6,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(c_Relation_OImage(X2,X6,X0),X7,tc_fun(X6,tc_bool),tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f19,axiom,
    ! [X2,X0,X6,X7,X14,X4] : c_lessequals(hAPP(c_Relation_OImage(X2,X6,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X14,tc_fun(X6,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(c_Relation_OImage(X2,X6,X0),X7,tc_fun(X6,tc_bool),tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__INT__subset_0) ).

fof(f15599,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f759,f15597]) ).

fof(f15597,plain,
    ( spl0_601
  <=> ! [X5,X0,X12,X9] :
        ( X5 = X9
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f759,plain,
    ! [X0,X9,X5,X12] :
      ( X5 = X9
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f479,f574]) ).

fof(f479,axiom,
    ! [X0,X9,X5,X12] :
      ( X5 = X9
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Otrancl(X12,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).

fof(f15514,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f399,f15512]) ).

fof(f15512,plain,
    ( spl0_600
  <=> ! [X2,X28,X0,X14,X6,X5,X3] :
        ( ~ hBOOL(c_in(c_Pair(X5,X28,X0,X6),c_Relation_Orel__comp(X2,X3,X0,X14,X6),tc_prod(X0,X6)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X5,X28,X2,X3,X0,X6,X14),X0,X14),X2,tc_prod(X0,X14))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f399,axiom,
    ! [X2,X28,X3,X0,X6,X14,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X28,X0,X6),c_Relation_Orel__comp(X2,X3,X0,X14,X6),tc_prod(X0,X6)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X5,X28,X2,X3,X0,X6,X14),X0,X14),X2,tc_prod(X0,X14))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

fof(f15510,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f398,f15508]) ).

fof(f15508,plain,
    ( spl0_599
  <=> ! [X2,X28,X0,X14,X6,X5,X3] :
        ( ~ hBOOL(c_in(c_Pair(X5,X28,X0,X6),c_Relation_Orel__comp(X2,X3,X0,X14,X6),tc_prod(X0,X6)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X5,X28,X2,X3,X0,X6,X14),X28,X14,X6),X3,tc_prod(X14,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f398,axiom,
    ! [X2,X28,X3,X0,X6,X14,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X28,X0,X6),c_Relation_Orel__comp(X2,X3,X0,X14,X6),tc_prod(X0,X6)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X5,X28,X2,X3,X0,X6,X14),X28,X14,X6),X3,tc_prod(X14,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

fof(f15506,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f205,f15504]) ).

fof(f15504,plain,
    ( spl0_598
  <=> ! [X0,X14,X12,X6,X13,X32] : c_Relation_Orel__comp(X12,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X14,X6),tc_bool)),X32),X0,X14,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X13,X0,X14,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Orel__comp(X12,X32,X0,X14,X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f205,axiom,
    ! [X0,X6,X14,X12,X32,X13] : c_Relation_Orel__comp(X12,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X14,X6),tc_bool)),X32),X0,X14,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X13,X0,X14,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Orel__comp(X12,X32,X0,X14,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

fof(f15502,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f204,f15500]) ).

fof(f15500,plain,
    ( spl0_597
  <=> ! [X0,X14,X12,X6,X13,X32] : c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X13,tc_fun(tc_prod(X0,X14),tc_bool)),X32),X12,X0,X14,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X12,X0,X14,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Orel__comp(X32,X12,X0,X14,X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f15498,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f133,f15496]) ).

fof(f15496,plain,
    ( spl0_596
  <=> ! [X4,X0,X6,X26,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f133,axiom,
    ! [X0,X6,X26,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib_0) ).

fof(f15494,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f42,f15492]) ).

fof(f15492,plain,
    ( spl0_595
  <=> ! [X3,X19,X0,X14,X6,X2,X20] :
        ( ~ c_lessequals(X19,X2,tc_fun(tc_prod(X0,X6),tc_bool))
        | ~ c_lessequals(X20,X3,tc_fun(tc_prod(X6,X14),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X19,X20,X0,X6,X14),c_Relation_Orel__comp(X2,X3,X0,X6,X14),tc_fun(tc_prod(X0,X14),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f42,axiom,
    ! [X2,X3,X0,X19,X6,X14,X20] :
      ( ~ c_lessequals(X19,X2,tc_fun(tc_prod(X0,X6),tc_bool))
      | ~ c_lessequals(X20,X3,tc_fun(tc_prod(X6,X14),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X19,X20,X0,X6,X14),c_Relation_Orel__comp(X2,X3,X0,X6,X14),tc_fun(tc_prod(X0,X14),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

fof(f15490,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f29,f15488]) ).

fof(f15488,plain,
    ( spl0_594
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),X7),tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f29,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(c_in(X1,X4,X0))
      | c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),X7),tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

fof(f14044,plain,
    ( spl0_593
    | ~ spl0_242
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f11078,f10578,f2715,f14041]) ).

fof(f14041,plain,
    ( spl0_593
  <=> v_F(v_P) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f2715,plain,
    ( spl0_242
  <=> ! [X4,X0,X7] :
        ( ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f10578,plain,
    ( spl0_514
  <=> c_lessequals(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f11078,plain,
    ( v_F(v_P) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P))
    | ~ spl0_242
    | ~ spl0_514 ),
    inference(resolution,[],[f10580,f2716]) ).

fof(f2716,plain,
    ( ! [X0,X7,X4] :
        ( ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X7 )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f2715]) ).

fof(f10580,plain,
    ( c_lessequals(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_514 ),
    inference(avatar_component_clause,[],[f10578]) ).

fof(f13659,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f784,f13657]) ).

fof(f13657,plain,
    ( spl0_592
  <=> ! [X4,X11,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f784,plain,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X7)),
    inference(forward_demodulation,[],[f113,f300]) ).

fof(f300,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

fof(f113,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

fof(f13655,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f751,f13653]) ).

fof(f13653,plain,
    ( spl0_591
  <=> ! [X10,X0,X12,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X10,X0,X0),X12,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f751,plain,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X10,X0,X0),X12,tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f391,f574]) ).

fof(f391,axiom,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Otrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X1,X10,X0),X10,X0,X0),X12,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

fof(f13651,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f750,f13649]) ).

fof(f13649,plain,
    ( spl0_590
  <=> ! [X10,X0,X12,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X0,X0),X12,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f750,plain,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X0,X0),X12,tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f386,f574]) ).

fof(f386,axiom,
    ! [X10,X0,X1,X12] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Otrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X1,X10,X0),X0,X0),X12,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

fof(f13647,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f748,f13645]) ).

fof(f13645,plain,
    ( spl0_589
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f748,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f384,f574]) ).

fof(f384,axiom,
    ! [X2,X0,X1] :
      ( ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X2,X0),X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

fof(f13643,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f379,f13641]) ).

fof(f13641,plain,
    ( spl0_588
  <=> ! [X5,X0,X9,X2] :
        ( X5 = X9
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X5,X9,X2,X0),X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f379,axiom,
    ! [X2,X0,X9,X5] :
      ( X5 = X9
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X5,X9,X2,X0),X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

fof(f13639,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f304,f13637]) ).

fof(f13637,plain,
    ( spl0_587
  <=> ! [X4,X11,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f304,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

fof(f13635,plain,
    ( spl0_586
    | ~ spl0_240
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f11077,f10578,f2707,f13632]) ).

fof(f13632,plain,
    ( spl0_586
  <=> v_F(v_P) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f2707,plain,
    ( spl0_240
  <=> ! [X4,X0,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f11077,plain,
    ( v_F(v_P) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_240
    | ~ spl0_514 ),
    inference(resolution,[],[f10580,f2708]) ).

fof(f2708,plain,
    ( ! [X0,X7,X4] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X4 )
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f2707]) ).

fof(f13630,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f301,f13628]) ).

fof(f13628,plain,
    ( spl0_585
  <=> ! [X37,X4,X0,X6,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7),X37,X6,tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X37,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X37,X6,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f301,axiom,
    ! [X0,X37,X6,X7,X4] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7),X37,X6,tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X37,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X7,X37,X6,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).

fof(f13626,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f299,f13624]) ).

fof(f13624,plain,
    ( spl0_584
  <=> ! [X4,X11,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f299,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

fof(f13622,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f215,f13620]) ).

fof(f13620,plain,
    ( spl0_583
  <=> ! [X4,X11,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f215,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

fof(f13618,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f164,f13616]) ).

fof(f13616,plain,
    ( spl0_582
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f164,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

fof(f13614,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f163,f13612]) ).

fof(f163,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

fof(f13468,plain,
    ( spl0_580
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f13464,f13461,f13466]) ).

fof(f13466,plain,
    ( spl0_580
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f13461,plain,
    ( spl0_579
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f13464,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X7))
    | ~ spl0_579 ),
    inference(forward_demodulation,[],[f13462,f784]) ).

fof(f13462,plain,
    ( ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11))
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f13461]) ).

fof(f13463,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f109,f13461]) ).

fof(f109,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

fof(f13459,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f108,f13457]) ).

fof(f13457,plain,
    ( spl0_578
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f108,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

fof(f13455,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f86,f13453]) ).

fof(f13453,plain,
    ( spl0_577
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X11,X4,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f86,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X11,X4,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

fof(f13388,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f85,f13386]) ).

fof(f13386,plain,
    ( spl0_576
  <=> ! [X4,X11,X0,X7] :
        ( c_lessequals(X11,X4,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f85,axiom,
    ! [X0,X11,X7,X4] :
      ( c_lessequals(X11,X4,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

fof(f13384,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f84,f13382]) ).

fof(f13382,plain,
    ( spl0_575
  <=> ! [X4,X0,X12,X6,X7] : c_lessequals(hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f84,axiom,
    ! [X0,X6,X7,X4,X12] : c_lessequals(hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

fof(f13380,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f35,f13378]) ).

fof(f13378,plain,
    ( spl0_574
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f35,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

fof(f13376,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f34,f13374]) ).

fof(f34,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

fof(f13144,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f237,f13142]) ).

fof(f13142,plain,
    ( spl0_572
  <=> ! [X17,X16,X0,X6,X2,X1] :
        ( c_Recdef_Ocut(X16,X2,X1,X0,X6) = c_Recdef_Ocut(X17,X2,X1,X0,X6)
        | hAPP(X16,c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6)) != hAPP(X17,c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f237,axiom,
    ! [X2,X0,X1,X6,X16,X17] :
      ( c_Recdef_Ocut(X16,X2,X1,X0,X6) = c_Recdef_Ocut(X17,X2,X1,X0,X6)
      | hAPP(X16,c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6)) != hAPP(X17,c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).

fof(f13140,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f43,f13138]) ).

fof(f13138,plain,
    ( spl0_571
  <=> ! [X4,X0,X13,X12,X6] : hAPP(c_Relation_OImage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X6,X0),tc_bool)),X13),X6,X0),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X13,X6,X0),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f43,axiom,
    ! [X0,X6,X4,X12,X13] : hAPP(c_Relation_OImage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X6,X0),tc_bool)),X13),X6,X0),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X13,X6,X0),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).

fof(f13127,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f11,f13125]) ).

fof(f13125,plain,
    ( spl0_570
  <=> ! [X4,X0,X5,X7] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f11,axiom,
    ! [X0,X7,X4,X5] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

fof(f13123,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f10,f13121]) ).

fof(f13121,plain,
    ( spl0_569
  <=> ! [X4,X0,X5,X7] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f10,axiom,
    ! [X0,X7,X4,X5] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),tc_fun(X0,tc_bool)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

fof(f12954,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f608,f12952]) ).

fof(f12952,plain,
    ( spl0_568
  <=> ! [X17,X10,X0,X6,X16,X2,X1] :
        ( hAPP(X16,X10) = hAPP(X17,X10)
        | ~ hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0)))
        | c_Recdef_Ocut(X16,X2,X1,X0,X6) != c_Recdef_Ocut(X17,X2,X1,X0,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f608,axiom,
    ! [X2,X10,X0,X1,X6,X16,X17] :
      ( hAPP(X16,X10) = hAPP(X17,X10)
      | ~ hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0)))
      | c_Recdef_Ocut(X16,X2,X1,X0,X6) != c_Recdef_Ocut(X17,X2,X1,X0,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).

fof(f12950,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f432,f12948]) ).

fof(f12948,plain,
    ( spl0_567
  <=> ! [X15,X44,X2,X1] :
        ( hBOOL(hAPP(X15,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
        | hBOOL(c_in(X44,c_Wellfounded_Oacc(X2,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X44,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f432,axiom,
    ! [X2,X1,X44,X15] :
      ( hBOOL(hAPP(X15,X1))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
      | hBOOL(c_in(X44,c_Wellfounded_Oacc(X2,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X44,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

fof(f12946,plain,
    ( spl0_566
    | ~ spl0_14
    | ~ spl0_268
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f11085,f10578,f3261,f864,f12944]) ).

fof(f12944,plain,
    ( spl0_566
  <=> ! [X0] : c_lessequals(hAPP(v_F(v_P),X0),hAPP(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),X0),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f864,plain,
    ( spl0_14
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f3261,plain,
    ( spl0_268
  <=> ! [X17,X0,X6,X16,X1] :
        ( ~ class_HOL_Oord(X6)
        | ~ c_lessequals(X16,X17,tc_fun(X0,X6))
        | c_lessequals(hAPP(X16,X1),hAPP(X17,X1),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f11085,plain,
    ( ! [X0] :
        ( ~ class_HOL_Oord(tc_bool)
        | c_lessequals(hAPP(v_F(v_P),X0),hAPP(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),X0),tc_bool) )
    | ~ spl0_268
    | ~ spl0_514 ),
    inference(resolution,[],[f10580,f3262]) ).

fof(f3262,plain,
    ( ! [X0,X1,X6,X16,X17] :
        ( ~ c_lessequals(X16,X17,tc_fun(X0,X6))
        | ~ class_HOL_Oord(X6)
        | c_lessequals(hAPP(X16,X1),hAPP(X17,X1),X6) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f3261]) ).

fof(f12942,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f430,f12940]) ).

fof(f12940,plain,
    ( spl0_565
  <=> ! [X15,X44,X2,X1] :
        ( hBOOL(hAPP(X15,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
        | hBOOL(c_in(X44,c_Wellfounded_Oacc(X2,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X44,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f430,axiom,
    ! [X2,X1,X44,X15] :
      ( hBOOL(hAPP(X15,X1))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
      | hBOOL(c_in(X44,c_Wellfounded_Oacc(X2,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X44,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

fof(f12938,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f278,f12936]) ).

fof(f12936,plain,
    ( spl0_564
  <=> ! [X5,X0,X9,X2] :
        ( X5 = X9
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X5,X9,X2,X0),X9,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f278,axiom,
    ! [X2,X0,X9,X5] :
      ( X5 = X9
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X5,X9,X2,X0),X9,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

fof(f12934,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f137,f12932]) ).

fof(f12932,plain,
    ( spl0_563
  <=> ! [X5,X31,X0,X9,X28] :
        ( X9 = X31
        | X9 = X28
        | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X28,X0),hAPP(c_Set_Oinsert(X31,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f137,axiom,
    ! [X31,X28,X0,X9,X5] :
      ( X9 = X31
      | X9 = X28
      | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X28,X0),hAPP(c_Set_Oinsert(X31,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

fof(f12930,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f134,f12928]) ).

fof(f12928,plain,
    ( spl0_562
  <=> ! [X31,X9,X0,X5,X28] :
        ( X5 = X28
        | X5 = X31
        | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X28,X0),hAPP(c_Set_Oinsert(X31,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f134,axiom,
    ! [X31,X28,X0,X9,X5] :
      ( X5 = X28
      | X5 = X31
      | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) != hAPP(c_Set_Oinsert(X28,X0),hAPP(c_Set_Oinsert(X31,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

fof(f12816,plain,
    ( spl0_561
    | ~ spl0_316
    | ~ spl0_443
    | ~ spl0_560 ),
    inference(avatar_split_clause,[],[f11805,f11802,f6748,f3870,f12814]) ).

fof(f12814,plain,
    ( spl0_561
  <=> ! [X2,X0] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),c_Relation_Orel__comp(X2,X2,X0,X0,X0),X0,X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f3870,plain,
    ( spl0_316
  <=> ! [X2,X0] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),X2,X0,X0,X0) = c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f6748,plain,
    ( spl0_443
  <=> ! [X12,X32,X0,X14,X13,X6,X46] : c_Relation_Orel__comp(c_Relation_Orel__comp(X12,X13,X0,X46,X14),X32,X0,X14,X6) = c_Relation_Orel__comp(X12,c_Relation_Orel__comp(X13,X32,X46,X14,X6),X0,X46,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f11802,plain,
    ( spl0_560
  <=> ! [X2,X0] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X2,X0,X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f11805,plain,
    ( ! [X2,X0] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),c_Relation_Orel__comp(X2,X2,X0,X0,X0),X0,X0,X0))
    | ~ spl0_316
    | ~ spl0_443
    | ~ spl0_560 ),
    inference(forward_demodulation,[],[f11803,f7138]) ).

fof(f7138,plain,
    ( ! [X2,X3,X0,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X0,X1),c_Relation_Orel__comp(X0,X2,X1,X1,X3),X1,X1,X3) = c_Relation_Orel__comp(c_Relation_Orel__comp(X0,c_Transitive__Closure_Ortrancl(X0,X1),X1,X1,X1),X2,X1,X1,X3)
    | ~ spl0_316
    | ~ spl0_443 ),
    inference(superposition,[],[f6749,f3871]) ).

fof(f3871,plain,
    ( ! [X2,X0] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),X2,X0,X0,X0) = c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0)
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3870]) ).

fof(f6749,plain,
    ( ! [X0,X46,X6,X14,X12,X32,X13] : c_Relation_Orel__comp(c_Relation_Orel__comp(X12,X13,X0,X46,X14),X32,X0,X14,X6) = c_Relation_Orel__comp(X12,c_Relation_Orel__comp(X13,X32,X46,X14,X6),X0,X46,X6)
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f6748]) ).

fof(f11803,plain,
    ( ! [X2,X0] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X2,X0,X0,X0))
    | ~ spl0_560 ),
    inference(avatar_component_clause,[],[f11802]) ).

fof(f11804,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f730,f11802]) ).

fof(f730,plain,
    ! [X2,X0] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X2,X0,X0,X0)),
    inference(definition_unfolding,[],[f366,f574,f574]) ).

fof(f366,axiom,
    ! [X2,X0] : c_Transitive__Closure_Otrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X2,X0),X2,X0,X0,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

fof(f11764,plain,
    ( spl0_559
    | ~ spl0_281
    | ~ spl0_558 ),
    inference(avatar_split_clause,[],[f11760,f11757,f3314,f11762]) ).

fof(f11762,plain,
    ( spl0_559
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f3314,plain,
    ( spl0_281
  <=> ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f11757,plain,
    ( spl0_558
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f11760,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0)
    | ~ spl0_281
    | ~ spl0_558 ),
    inference(forward_demodulation,[],[f11758,f3315]) ).

fof(f3315,plain,
    ( ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0)
    | ~ spl0_281 ),
    inference(avatar_component_clause,[],[f3314]) ).

fof(f11758,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),X0,X0,X0)
    | ~ spl0_558 ),
    inference(avatar_component_clause,[],[f11757]) ).

fof(f11759,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f715,f11757]) ).

fof(f715,plain,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Relation_Orel__comp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),X0,X0,X0),
    inference(definition_unfolding,[],[f410,f574]) ).

fof(f410,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Otrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

fof(f11755,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f641,f11753]) ).

fof(f11753,plain,
    ( spl0_557
  <=> ! [X18,X53,X10,X1] :
        ( X10 = X18
        | X1 = X18
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f641,axiom,
    ! [X10,X18,X1,X53] :
      ( X10 = X18
      | X1 = X18
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).

fof(f11751,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f640,f11749]) ).

fof(f11749,plain,
    ( spl0_556
  <=> ! [X18,X53,X10,X1] :
        ( X10 = X18
        | X1 = X10
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f640,axiom,
    ! [X10,X18,X1,X53] :
      ( X10 = X18
      | X1 = X10
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).

fof(f11747,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f633,f11745]) ).

fof(f11745,plain,
    ( spl0_555
  <=> ! [X18,X53,X10,X1] :
        ( X1 = X18
        | X10 = X18
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f633,axiom,
    ! [X10,X1,X18,X53] :
      ( X1 = X18
      | X10 = X18
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).

fof(f11743,plain,
    ( ~ spl0_553
    | spl0_554
    | ~ spl0_276
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f11075,f10578,f3294,f11740,f11736]) ).

fof(f11736,plain,
    ( spl0_553
  <=> c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f11740,plain,
    ( spl0_554
  <=> c_Relation_Osingle__valued(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f3294,plain,
    ( spl0_276
  <=> ! [X3,X0,X6,X2] :
        ( ~ c_Relation_Osingle__valued(X3,X0,X6)
        | c_Relation_Osingle__valued(X2,X0,X6)
        | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f11075,plain,
    ( c_Relation_Osingle__valued(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_276
    | ~ spl0_514 ),
    inference(resolution,[],[f10580,f3295]) ).

fof(f3295,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool))
        | c_Relation_Osingle__valued(X2,X0,X6)
        | ~ c_Relation_Osingle__valued(X3,X0,X6) )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f3294]) ).

fof(f11734,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f632,f11732]) ).

fof(f11732,plain,
    ( spl0_552
  <=> ! [X18,X53,X10,X1] :
        ( X1 = X18
        | X1 = X10
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f632,axiom,
    ! [X10,X1,X18,X53] :
      ( X1 = X18
      | X1 = X10
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).

fof(f11730,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f613,f11728]) ).

fof(f11728,plain,
    ( spl0_551
  <=> ! [X16,X10,X0,X6,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Oinv__image(X2,X16,X6,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(c_Pair(hAPP(X16,X1),hAPP(X16,X10),X6,X6),X2,tc_prod(X6,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f613,axiom,
    ! [X2,X10,X0,X1,X6,X16] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Oinv__image(X2,X16,X6,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(hAPP(X16,X1),hAPP(X16,X10),X6,X6),X2,tc_prod(X6,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

fof(f11726,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f612,f11724]) ).

fof(f11724,plain,
    ( spl0_550
  <=> ! [X16,X10,X0,X6,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(hAPP(X16,X1),hAPP(X16,X10),X6,X6),X2,tc_prod(X6,X6)))
        | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Oinv__image(X2,X16,X6,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f612,axiom,
    ! [X2,X10,X0,X1,X6,X16] :
      ( ~ hBOOL(c_in(c_Pair(hAPP(X16,X1),hAPP(X16,X10),X6,X6),X2,tc_prod(X6,X6)))
      | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_Oinv__image(X2,X16,X6,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

fof(f11722,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f408,f11720]) ).

fof(f11720,plain,
    ( spl0_549
  <=> ! [X17,X16,X0,X6,X2,X1] :
        ( c_Recdef_Ocut(X16,X2,X1,X0,X6) = c_Recdef_Ocut(X17,X2,X1,X0,X6)
        | hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6),X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f408,axiom,
    ! [X2,X0,X1,X6,X16,X17] :
      ( c_Recdef_Ocut(X16,X2,X1,X0,X6) = c_Recdef_Ocut(X17,X2,X1,X0,X6)
      | hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X16,X17,X2,X1,X0,X6),X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).

fof(f11718,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f315,f11716]) ).

fof(f11716,plain,
    ( spl0_548
  <=> ! [X38,X4,X19,X0,X6,X2] :
        ( ~ c_lessequals(X38,X4,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X19,X2,tc_fun(tc_prod(X0,X6),tc_bool))
        | c_lessequals(hAPP(c_Relation_OImage(X19,X0,X6),X38),hAPP(c_Relation_OImage(X2,X0,X6),X4),tc_fun(X6,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f315,axiom,
    ! [X2,X38,X0,X19,X6,X4] :
      ( ~ c_lessequals(X38,X4,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X19,X2,tc_fun(tc_prod(X0,X6),tc_bool))
      | c_lessequals(hAPP(c_Relation_OImage(X19,X0,X6),X38),hAPP(c_Relation_OImage(X2,X0,X6),X4),tc_fun(X6,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).

fof(f11714,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f298,f11712]) ).

fof(f11712,plain,
    ( spl0_547
  <=> ! [X4,X11,X0,X29,X7] :
        ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X29,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f298,axiom,
    ! [X0,X11,X29,X7,X4] :
      ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X29,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

fof(f11710,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f146,f11708]) ).

fof(f11708,plain,
    ( spl0_546
  <=> ! [X4,X11,X0,X29,X7] :
        ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X29,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f146,axiom,
    ! [X0,X11,X29,X7,X4] :
      ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X29,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

fof(f11706,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f111,f11704]) ).

fof(f11704,plain,
    ( spl0_545
  <=> ! [X4,X11,X0,X29,X7] :
        ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X29,X7,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f111,axiom,
    ! [X0,X11,X29,X7,X4] :
      ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X29,X7,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X29),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

fof(f11702,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f91,f11700]) ).

fof(f11700,plain,
    ( spl0_544
  <=> ! [X13,X0,X12] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | ~ c_Wellfounded_Owf(X13,X0)
        | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0)
        | ~ c_lessequals(c_Relation_Orel__comp(X12,X13,X0,X0,X0),X12,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f91,axiom,
    ! [X0,X12,X13] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | ~ c_Wellfounded_Owf(X13,X0)
      | c_Wellfounded_Owf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0)
      | ~ c_lessequals(c_Relation_Orel__comp(X12,X13,X0,X0,X0),X12,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

fof(f11698,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f83,f11696]) ).

fof(f11696,plain,
    ( spl0_543
  <=> ! [X4,X0,X6,X16,X7] : c_lessequals(c_Set_Oimage(X16,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7),X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f83,axiom,
    ! [X0,X6,X16,X7,X4] : c_lessequals(c_Set_Oimage(X16,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X6,tc_bool)),X7),X6,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

fof(f11688,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f55,f11686]) ).

fof(f11686,plain,
    ( spl0_542
  <=> ! [X4,X0,X6,X16,X7] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)),c_Set_Oimage(X16,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X6,tc_bool)),X7),X6,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f55,axiom,
    ! [X0,X6,X16,X7,X4] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)),c_Set_Oimage(X16,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X6,tc_bool)),X7),X6,X0),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

fof(f11684,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f44,f11682]) ).

fof(f11682,plain,
    ( spl0_541
  <=> ! [X4,X0,X12,X6,X7] : hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f44,axiom,
    ! [X0,X6,X7,X4,X12] : hAPP(c_Relation_OImage(X12,X6,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_OImage(X12,X6,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Relation_OImage(X12,X6,X0),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

fof(f11680,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f18,f11678]) ).

fof(f11678,plain,
    ( spl0_540
  <=> ! [X13,X0,X12] : c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X13,X0)),c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f18,axiom,
    ! [X0,X12,X13] : c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X13,X0)),c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_fun(tc_prod(X0,X0),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

fof(f11676,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f15,f11674]) ).

fof(f11674,plain,
    ( spl0_539
  <=> ! [X5,X11,X0,X6,X7] : hAPP(c_Set_Oinsert(X5,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X7,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(c_Set_Oinsert(X5,X0),X7,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f15,axiom,
    ! [X0,X11,X6,X7,X5] : hAPP(c_Set_Oinsert(X5,X0),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,X7,X6,tc_fun(X0,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X11,c_COMBB(c_Set_Oinsert(X5,X0),X7,tc_fun(X0,tc_bool),tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I5_J_0) ).

fof(f11287,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f731,f11285]) ).

fof(f11285,plain,
    ( spl0_538
  <=> ! [X5,X9,X0,X6,X2] : c_Relation_ORange(c_Relation_Oconverse(hAPP(c_Set_Oinsert(c_Pair(X5,X9,X0,X6),tc_prod(X0,X6)),X2),X0,X6),X6,X0) = hAPP(c_Set_Oinsert(X5,X0),c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f731,plain,
    ! [X2,X0,X6,X9,X5] : c_Relation_ORange(c_Relation_Oconverse(hAPP(c_Set_Oinsert(c_Pair(X5,X9,X0,X6),tc_prod(X0,X6)),X2),X0,X6),X6,X0) = hAPP(c_Set_Oinsert(X5,X0),c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0)),
    inference(definition_unfolding,[],[f5,f554,f554]) ).

fof(f5,axiom,
    ! [X2,X0,X6,X9,X5] : c_Relation_ODomain(hAPP(c_Set_Oinsert(c_Pair(X5,X9,X0,X6),tc_prod(X0,X6)),X2),X0,X6) = hAPP(c_Set_Oinsert(X5,X0),c_Relation_ODomain(X2,X0,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).

fof(f11283,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f587,f11281]) ).

fof(f587,axiom,
    ! [X2,X10,X0,X18,X1,X6] :
      ( X10 = X18
      | ~ c_Relation_Osingle__valued(X2,X0,X6)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X2,tc_prod(X0,X6)))
      | ~ hBOOL(c_in(c_Pair(X1,X18,X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

fof(f11279,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f435,f11277]) ).

fof(f11277,plain,
    ( spl0_536
  <=> ! [X0,X10,X2,X1] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | c_Wellfounded_Owf(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f435,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | c_Wellfounded_Owf(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).

fof(f11275,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f433,f11273]) ).

fof(f11273,plain,
    ( spl0_535
  <=> ! [X2,X10,X0,X5,X15] :
        ( hBOOL(hAPP(X15,X10))
        | hBOOL(hAPP(X15,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f433,axiom,
    ! [X2,X10,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X10))
      | hBOOL(hAPP(X15,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).

fof(f11271,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f427,f11269]) ).

fof(f11269,plain,
    ( spl0_534
  <=> ! [X2,X10,X0,X5,X15] :
        ( hBOOL(hAPP(X15,X10))
        | hBOOL(hAPP(X15,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f427,axiom,
    ! [X2,X10,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X10))
      | hBOOL(hAPP(X15,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

fof(f11267,plain,
    ( ~ spl0_533
    | spl0_508
    | ~ spl0_219
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f11072,f10578,f2136,f9342,f11264]) ).

fof(f11264,plain,
    ( spl0_533
  <=> c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f9342,plain,
    ( spl0_508
  <=> c_Wellfounded_Oacyclic(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f2136,plain,
    ( spl0_219
  <=> ! [X2,X0,X3] :
        ( ~ c_Wellfounded_Oacyclic(X3,X0)
        | c_Wellfounded_Oacyclic(X2,X0)
        | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f11072,plain,
    ( c_Wellfounded_Oacyclic(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_219
    | ~ spl0_514 ),
    inference(resolution,[],[f10580,f2137]) ).

fof(f2137,plain,
    ( ! [X2,X3,X0] :
        ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
        | c_Wellfounded_Oacyclic(X2,X0)
        | ~ c_Wellfounded_Oacyclic(X3,X0) )
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2136]) ).

fof(f11262,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f338,f11260]) ).

fof(f11260,plain,
    ( spl0_532
  <=> ! [X4,X11,X0,X6,X1,X7] :
        ( X4 = X7
        | ~ hBOOL(c_in(X1,X11,X0))
        | c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0) != c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f338,axiom,
    ! [X0,X11,X1,X6,X7,X4] :
      ( X4 = X7
      | ~ hBOOL(c_in(X1,X11,X0))
      | c_Product__Type_OSigma(X4,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0) != c_Product__Type_OSigma(X7,c_COMBK(X11,tc_fun(X0,tc_bool),X6),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).

fof(f11258,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f319,f11256]) ).

fof(f11256,plain,
    ( spl0_531
  <=> ! [X0,X10,X2,X1] :
        ( ~ c_Wellfounded_Oacyclic(X2,X0)
        | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | c_Wellfounded_Oacyclic(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f319,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ c_Wellfounded_Oacyclic(X2,X0)
      | hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | c_Wellfounded_Oacyclic(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).

fof(f11254,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f303,f11252]) ).

fof(f11252,plain,
    ( spl0_530
  <=> ! [X4,X0,X1] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
        | hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4
        | ~ c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f303,axiom,
    ! [X0,X1,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
      | hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4
      | ~ c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

fof(f11250,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f190,f11248]) ).

fof(f11248,plain,
    ( spl0_529
  <=> ! [X11,X0,X6,X27,X26] : c_Product__Type_OSigma(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X26,tc_fun(X0,tc_bool)),X27),X11,X0,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X26,X11,X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(X27,X11,X0,X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f190,axiom,
    ! [X0,X11,X6,X26,X27] : c_Product__Type_OSigma(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X26,tc_fun(X0,tc_bool)),X27),X11,X0,X6) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X26,X11,X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(X27,X11,X0,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

fof(f11246,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f87,f11244]) ).

fof(f11244,plain,
    ( spl0_528
  <=> ! [X11,X0,X6,X27,X26] : c_Product__Type_OSigma(hAPP(c_HOL_Ominus__class_Ominus(X26,tc_fun(X0,tc_bool)),X27),X11,X0,X6) = hAPP(c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X26,X11,X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(X27,X11,X0,X6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f87,axiom,
    ! [X0,X11,X6,X26,X27] : c_Product__Type_OSigma(hAPP(c_HOL_Ominus__class_Ominus(X26,tc_fun(X0,tc_bool)),X27),X11,X0,X6) = hAPP(c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X26,X11,X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)),c_Product__Type_OSigma(X27,X11,X0,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

fof(f11242,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f22,f11240]) ).

fof(f11240,plain,
    ( spl0_527
  <=> ! [X4,X0,X6,X7] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X4,X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X7,X6,X0)),c_Relation_ORange(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(tc_prod(X6,X0),tc_bool)),X7),X6,X0),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f22,axiom,
    ! [X0,X6,X7,X4] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X4,X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X7,X6,X0)),c_Relation_ORange(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(tc_prod(X6,X0),tc_bool)),X7),X6,X0),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

fof(f10700,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f604,f10698]) ).

fof(f10698,plain,
    ( spl0_526
  <=> ! [X0,X10,X2,X1] :
        ( ~ c_Relation_Oantisym(X2,X0)
        | X1 = X10
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | ~ hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f604,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ c_Relation_Oantisym(X2,X0)
      | X1 = X10
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).

fof(f10696,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f443,f10694]) ).

fof(f10694,plain,
    ( spl0_525
  <=> ! [X5,X9,X0,X6,X2] :
        ( hBOOL(c_in(c_Pair(X5,X9,X6,X0),X2,tc_prod(X6,X0)))
        | ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),hAPP(c_Set_Oinsert(X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f443,axiom,
    ! [X2,X0,X6,X9,X5] :
      ( hBOOL(c_in(c_Pair(X5,X9,X6,X0),X2,tc_prod(X6,X0)))
      | ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),hAPP(c_Set_Oinsert(X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)))),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

fof(f10692,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f442,f10690]) ).

fof(f10690,plain,
    ( spl0_524
  <=> ! [X5,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X6,X0),X2,tc_prod(X6,X0)))
        | hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),hAPP(c_Set_Oinsert(X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f442,axiom,
    ! [X2,X0,X6,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X6,X0),X2,tc_prod(X6,X0)))
      | hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),hAPP(c_Set_Oinsert(X5,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)))),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

fof(f10688,plain,
    ( spl0_523
    | ~ spl0_195
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f8184,f6510,f2036,f10686]) ).

fof(f10686,plain,
    ( spl0_523
  <=> ! [X0] :
        ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),X0))
        | ~ hBOOL(hAPP(v_F(v_P),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f2036,plain,
    ( spl0_195
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(hAPP(X4,X1))
        | hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f6510,plain,
    ( spl0_434
  <=> c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f8184,plain,
    ( ! [X0] :
        ( hBOOL(hAPP(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),X0))
        | ~ hBOOL(hAPP(v_F(v_P),X0)) )
    | ~ spl0_195
    | ~ spl0_434 ),
    inference(superposition,[],[f2037,f6512]) ).

fof(f6512,plain,
    ( c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_434 ),
    inference(avatar_component_clause,[],[f6510]) ).

fof(f2037,plain,
    ( ! [X0,X1,X7,X4] :
        ( hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1))
        | ~ hBOOL(hAPP(X4,X1)) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f2036]) ).

fof(f10684,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f431,f10682]) ).

fof(f10682,plain,
    ( spl0_522
  <=> ! [X2,X10,X15,X1] :
        ( hBOOL(hAPP(X15,X10))
        | hBOOL(hAPP(X15,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X10,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f431,axiom,
    ! [X2,X10,X1,X15] :
      ( hBOOL(hAPP(X15,X10))
      | hBOOL(hAPP(X15,X1))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X10,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

fof(f10680,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f428,f10678]) ).

fof(f10678,plain,
    ( spl0_521
  <=> ! [X2,X10,X15,X1] :
        ( hBOOL(hAPP(X15,X10))
        | hBOOL(hAPP(X15,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X10,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f428,axiom,
    ! [X2,X10,X1,X15] :
      ( hBOOL(hAPP(X15,X10))
      | hBOOL(hAPP(X15,X1))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X10,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2),t_a,t_a),X2,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

fof(f10676,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f336,f10674]) ).

fof(f336,axiom,
    ! [X40,X0,X6,X26,X4] :
      ( ~ hBOOL(c_in(X40,X26,X0))
      | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X4,X40),tc_fun(X6,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X0,tc_fun(X6,tc_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).

fof(f10672,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f229,f10670]) ).

fof(f10670,plain,
    ( spl0_519
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(c_in(X1,X7,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),X7) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f229,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(c_in(X1,X7,X0))
      | hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),X7) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

fof(f10668,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f147,f10666]) ).

fof(f10666,plain,
    ( spl0_518
  <=> ! [X3,X0,X6,X2] : c_Relation_Oconverse(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X6,X0),tc_bool)),X3),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X2,X6,X0),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Oconverse(X3,X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f147,axiom,
    ! [X2,X3,X0,X6] : c_Relation_Oconverse(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X6,X0),tc_bool)),X3),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X2,X6,X0),tc_fun(tc_prod(X0,X6),tc_bool)),c_Relation_Oconverse(X3,X6,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).

fof(f10664,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f144,f10662]) ).

fof(f10662,plain,
    ( spl0_517
  <=> ! [X4,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f144,axiom,
    ! [X0,X7,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

fof(f10660,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f143,f10658]) ).

fof(f10658,plain,
    ( spl0_516
  <=> ! [X11,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X11,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f143,axiom,
    ! [X0,X11,X7,X5] :
      ( ~ hBOOL(c_in(X5,X11,X0))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

fof(f10656,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f52,f10654]) ).

fof(f10654,plain,
    ( spl0_515
  <=> ! [X4,X11,X0,X6,X2,X7] :
        ( c_lessequals(hAPP(c_Relation_OImage(X2,X0,X6),X11),X7,tc_fun(X6,tc_bool))
        | ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f52,axiom,
    ! [X2,X0,X11,X6,X7,X4] :
      ( c_lessequals(hAPP(c_Relation_OImage(X2,X0,X6),X11),X7,tc_fun(X6,tc_bool))
      | ~ c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X7,tc_fun(X6,tc_bool),X0),X0,X6),tc_fun(tc_prod(X0,X6),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).

fof(f10581,plain,
    ( spl0_514
    | ~ spl0_144
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f8182,f6510,f1539,f10578]) ).

fof(f1539,plain,
    ( spl0_144
  <=> ! [X4,X0,X7] : c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f8182,plain,
    ( c_lessequals(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_144
    | ~ spl0_434 ),
    inference(superposition,[],[f1540,f6512]) ).

fof(f1540,plain,
    ( ! [X0,X7,X4] : c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool))
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1539]) ).

fof(f9365,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f757,f9363]) ).

fof(f9363,plain,
    ( spl0_513
  <=> ! [X10,X0,X12,X1] :
        ( X1 = X10
        | hBOOL(c_in(X1,c_Relation_ORange(c_Relation_Oconverse(X12,X0,X0),X0,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f757,plain,
    ! [X10,X0,X1,X12] :
      ( X1 = X10
      | hBOOL(c_in(X1,c_Relation_ORange(c_Relation_Oconverse(X12,X0,X0),X0,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f477,f554]) ).

fof(f477,axiom,
    ! [X10,X0,X1,X12] :
      ( X1 = X10
      | hBOOL(c_in(X1,c_Relation_ODomain(X12,X0,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

fof(f9361,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f647,f9359]) ).

fof(f9359,plain,
    ( spl0_512
  <=> ! [X6,X4,X9,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | ~ hBOOL(c_in(X9,hAPP(X7,X5),X6))
        | hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f647,axiom,
    ! [X0,X6,X9,X7,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | ~ hBOOL(c_in(X9,hAPP(X7,X5),X6))
      | hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

fof(f9357,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f643,f9355]) ).

fof(f9355,plain,
    ( spl0_511
  <=> ! [X18,X53,X10,X1] :
        ( X1 = X18
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f643,axiom,
    ! [X10,X1,X18,X53] :
      ( X1 = X18
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).

fof(f9353,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f636,f9351]) ).

fof(f9351,plain,
    ( spl0_510
  <=> ! [X18,X53,X10,X1] :
        ( X10 = X18
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f636,axiom,
    ! [X10,X18,X1,X53] :
      ( X10 = X18
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).

fof(f9349,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f475,f9347]) ).

fof(f9347,plain,
    ( spl0_509
  <=> ! [X9,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | hBOOL(c_in(X9,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X9,X5,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f475,axiom,
    ! [X2,X0,X9,X5] :
      ( ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | hBOOL(c_in(X9,c_Wellfounded_Oacc(X2,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X9,X5,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

fof(f9345,plain,
    ( ~ spl0_508
    | ~ spl0_62
    | spl0_494 ),
    inference(avatar_split_clause,[],[f9300,f8263,f1063,f9342]) ).

fof(f8263,plain,
    ( spl0_494
  <=> c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f9300,plain,
    ( ~ c_Wellfounded_Oacyclic(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_62
    | spl0_494 ),
    inference(resolution,[],[f8264,f1064]) ).

fof(f8264,plain,
    ( ~ c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_494 ),
    inference(avatar_component_clause,[],[f8263]) ).

fof(f9340,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f420,f9338]) ).

fof(f9338,plain,
    ( spl0_507
  <=> ! [X2,X10,X0,X23,X22] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(X23,X22,X0))
        | ~ hBOOL(c_in(X10,X22,X0))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X22,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f420,axiom,
    ! [X2,X10,X0,X22,X23] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(X23,X22,X0))
      | ~ hBOOL(c_in(X10,X22,X0))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X22,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

fof(f9336,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f419,f9334]) ).

fof(f9334,plain,
    ( spl0_506
  <=> ! [X10,X0,X12,X22,X1] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | ~ hBOOL(c_in(X1,X22,X0))
        | ~ hBOOL(c_in(X10,X22,X0))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X22,X12,X0),X0,X0),X12,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f419,axiom,
    ! [X10,X0,X1,X22,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | ~ hBOOL(c_in(X1,X22,X0))
      | ~ hBOOL(c_in(X10,X22,X0))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X22,X12,X0),X0,X0),X12,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

fof(f9332,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f314,f9330]) ).

fof(f9330,plain,
    ( spl0_505
  <=> ! [X5,X4,X0,X6,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Set_Oinsert(X5,X6),X4),X7,X6,tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X7,X5),tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f314,axiom,
    ! [X0,X6,X7,X4,X5] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(c_Set_Oinsert(X5,X6),X4),X7,X6,tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X7,X5),tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).

fof(f9328,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f313,f9326]) ).

fof(f9326,plain,
    ( spl0_504
  <=> ! [X4,X0,X6,X16,X7] : c_Set_Oimage(X16,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f313,axiom,
    ! [X0,X6,X16,X7,X4] : c_Set_Oimage(X16,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X6,tc_bool)),X7),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X16,X4,X6,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X16,X7,X6,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

fof(f9324,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f306,f9322]) ).

fof(f9322,plain,
    ( spl0_503
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
        | hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X4)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f306,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
      | hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X11,tc_fun(X0,tc_bool)),X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

fof(f9320,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f300,f9318]) ).

fof(f9318,plain,
    ( spl0_502
  <=> ! [X4,X11,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f9316,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f228,f9314]) ).

fof(f9314,plain,
    ( spl0_501
  <=> ! [X13,X0,X12] : c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) = c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X13,X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f228,axiom,
    ! [X0,X12,X13] : c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0) = c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X13,X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

fof(f9312,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f101,f9310]) ).

fof(f9310,plain,
    ( spl0_500
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f101,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

fof(f9308,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f100,f9306]) ).

fof(f9306,plain,
    ( spl0_499
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f100,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

fof(f9304,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f57,f9302]) ).

fof(f9302,plain,
    ( spl0_498
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f57,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

fof(f9299,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f56,f9297]) ).

fof(f9297,plain,
    ( spl0_497
  <=> ! [X4,X11,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f56,axiom,
    ! [X0,X11,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

fof(f9295,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f8,f9293]) ).

fof(f9293,plain,
    ( spl0_496
  <=> ! [X4,X0,X5,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f8,axiom,
    ! [X0,X7,X4,X5] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

fof(f8270,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f780,f8268]) ).

fof(f8268,plain,
    ( spl0_495
  <=> ! [X2,X0] : c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X0),X0,X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f780,plain,
    ! [X2,X0] : c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X0),X0,X0),X0,X0,X0),
    inference(forward_demodulation,[],[f727,f566]) ).

fof(f566,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X2,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

fof(f727,plain,
    ! [X2,X0] : c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X2,X0,X0),X0),X0,X0,X0),
    inference(definition_unfolding,[],[f549,f574,f574]) ).

fof(f549,axiom,
    ! [X2,X0] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X2,X0),X0,X0) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X2,X0,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

fof(f8266,plain,
    ( ~ spl0_493
    | spl0_494
    | ~ spl0_260
    | ~ spl0_434 ),
    inference(avatar_split_clause,[],[f8178,f6510,f2787,f8263,f8259]) ).

fof(f8259,plain,
    ( spl0_493
  <=> c_Relation_Oantisym(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f2787,plain,
    ( spl0_260
  <=> ! [X2,X0] :
        ( ~ c_Relation_Oantisym(X2,X0)
        | c_Relation_Oantisym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f8178,plain,
    ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oantisym(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_260
    | ~ spl0_434 ),
    inference(superposition,[],[f2788,f6512]) ).

fof(f2788,plain,
    ( ! [X2,X0] :
        ( c_Relation_Oantisym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0)
        | ~ c_Relation_Oantisym(X2,X0) )
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f2787]) ).

fof(f8257,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f743,f8255]) ).

fof(f8255,plain,
    ( spl0_492
  <=> ! [X3,X0,X6,X2] :
        ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool))
        | c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),c_Relation_ORange(c_Relation_Oconverse(X3,X0,X6),X6,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f743,plain,
    ! [X2,X3,X0,X6] :
      ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool))
      | c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),c_Relation_ORange(c_Relation_Oconverse(X3,X0,X6),X6,X0),tc_fun(X0,tc_bool)) ),
    inference(definition_unfolding,[],[f302,f554,f554]) ).

fof(f302,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool))
      | c_lessequals(c_Relation_ODomain(X2,X0,X6),c_Relation_ODomain(X3,X0,X6),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

fof(f8253,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f742,f8251]) ).

fof(f8251,plain,
    ( spl0_491
  <=> ! [X5,X0,X6,X2] :
        ( ~ hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f742,plain,
    ! [X2,X0,X6,X5] :
      ( ~ hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ),
    inference(definition_unfolding,[],[f424,f554]) ).

fof(f424,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ hBOOL(c_in(X5,c_Relation_ODomain(X2,X0,X6),X0))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

fof(f8249,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f741,f8247]) ).

fof(f8247,plain,
    ( spl0_490
  <=> ! [X5,X0,X6,X2] :
        ( ~ hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f741,plain,
    ! [X2,X0,X6,X5] :
      ( ~ hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ),
    inference(definition_unfolding,[],[f425,f554]) ).

fof(f425,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ hBOOL(c_in(X5,c_Relation_ODomain(X2,X0,X6),X0))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X5,X2,X0,X6),X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

fof(f8245,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f650,f8243]) ).

fof(f650,axiom,
    ! [X2,X0,X6,X9,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X0,X6),X4),X6))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).

fof(f8241,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f440,f8239]) ).

fof(f8239,plain,
    ( spl0_488
  <=> ! [X4,X0,X5,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | ~ hBOOL(c_in(X5,X4,X0))
        | hBOOL(c_in(X5,hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f440,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | ~ hBOOL(c_in(X5,X4,X0))
      | hBOOL(c_in(X5,hAPP(c_Relation_OImage(X2,X0,X0),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

fof(f8237,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f434,f8235]) ).

fof(f8235,plain,
    ( spl0_487
  <=> ! [X0,X10,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | ~ c_Wellfounded_Owf(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f434,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | ~ c_Wellfounded_Owf(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

fof(f8233,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f423,f8231]) ).

fof(f8231,plain,
    ( spl0_486
  <=> ! [X4,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X9,X2,X6,X0),X9,X6,X0),X2,tc_prod(X6,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f423,axiom,
    ! [X2,X0,X6,X9,X4] :
      ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X9,X2,X6,X0),X9,X6,X0),X2,tc_prod(X6,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

fof(f8229,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f422,f8227]) ).

fof(f8227,plain,
    ( spl0_485
  <=> ! [X4,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X9,X2,X6,X0),X9,X6,X0),X2,tc_prod(X6,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f422,axiom,
    ! [X2,X0,X6,X9,X4] :
      ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X9,X2,X6,X0),X9,X6,X0),X2,tc_prod(X6,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

fof(f8225,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f351,f8223]) ).

fof(f8223,plain,
    ( spl0_484
  <=> ! [X4,X0,X14,X6,X16,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Set_Oimage(X16,X4,X14,X6),X7,X6,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(X7,X16,X6,tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f351,axiom,
    ! [X0,X6,X16,X14,X4,X7] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Set_Oimage(X16,X4,X14,X6),X7,X6,tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBB(X7,X16,X6,tc_fun(X0,tc_bool),X14),X14,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).

fof(f8221,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f344,f8219]) ).

fof(f8219,plain,
    ( spl0_483
  <=> ! [X13,X0,X12,X1] :
        ( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X13,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f344,axiom,
    ! [X0,X1,X12,X13] :
      ( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X13,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

fof(f8175,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f343,f8173]) ).

fof(f8173,plain,
    ( spl0_482
  <=> ! [X13,X0,X12,X1] :
        ( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
        | hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f343,axiom,
    ! [X0,X1,X12,X13] :
      ( ~ hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0)))
      | hBOOL(c_in(X1,c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),X13),X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

fof(f8171,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f320,f8169]) ).

fof(f8169,plain,
    ( spl0_481
  <=> ! [X0,X10,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
        | ~ c_Wellfounded_Oacyclic(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f320,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0)))
      | ~ c_Wellfounded_Oacyclic(hAPP(c_Set_Oinsert(c_Pair(X10,X1,X0,X0),tc_prod(X0,X0)),X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).

fof(f8167,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f183,f8165]) ).

fof(f8165,plain,
    ( spl0_480
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f183,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

fof(f8163,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f172,f8161]) ).

fof(f8161,plain,
    ( spl0_479
  <=> ! [X4,X0,X6,X7] : c_Relation_ORange(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(tc_prod(X6,X0),tc_bool)),X7),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X4,X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X7,X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f172,axiom,
    ! [X0,X6,X7,X4] : c_Relation_ORange(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(tc_prod(X6,X0),tc_bool)),X7),X6,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X4,X6,X0),tc_fun(X0,tc_bool)),c_Relation_ORange(X7,X6,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

fof(f8159,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f112,f8157]) ).

fof(f8157,plain,
    ( spl0_478
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f112,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

fof(f8155,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f95,f8153]) ).

fof(f8153,plain,
    ( spl0_477
  <=> ! [X4,X0,X3,X2,X7] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | ~ c_Relation_Orefl__on(X7,X3,X0)
        | c_Relation_Orefl__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f95,axiom,
    ! [X2,X3,X0,X7,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | ~ c_Relation_Orefl__on(X7,X3,X0)
      | c_Relation_Orefl__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

fof(f7844,plain,
    ( spl0_476
    | ~ spl0_199
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f6349,f5499,f2052,f7841]) ).

fof(f7841,plain,
    ( spl0_476
  <=> c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f2052,plain,
    ( spl0_199
  <=> v_F(v_P) = c_Relation_Orel__comp(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f5499,plain,
    ( spl0_420
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f6349,plain,
    ( c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(v_P))
    | ~ spl0_199
    | ~ spl0_420 ),
    inference(superposition,[],[f5500,f2054]) ).

fof(f2054,plain,
    ( v_F(v_P) = c_Relation_Orel__comp(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f2052]) ).

fof(f5500,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0))
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f5499]) ).

fof(f7835,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f649,f7833]) ).

fof(f649,axiom,
    ! [X2,X10,X0,X5] :
      ( ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | hBOOL(c_in(X10,c_Wellfounded_Oacc(X2,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X10,X5,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

fof(f7831,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f629,f7829]) ).

fof(f7829,plain,
    ( spl0_474
  <=> ! [X4,X0,X6,X1,X7] :
        ( ~ hBOOL(c_in(X1,X4,X6))
        | hAPP(X7,X1) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f629,axiom,
    ! [X0,X1,X6,X7,X4] :
      ( ~ hBOOL(c_in(X1,X4,X6))
      | hAPP(X7,X1) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).

fof(f7827,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f614,f7825]) ).

fof(f614,axiom,
    ! [X2,X10,X0,X1] :
      ( ~ c_Relation_Osym(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
      | hBOOL(c_in(c_Pair(X10,X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).

fof(f7823,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f603,f7821]) ).

fof(f603,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X5,X1,X0,X0),X2,tc_prod(X0,X0)))
      | ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

fof(f7819,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f594,f7817]) ).

fof(f7817,plain,
    ( spl0_471
  <=> ! [X5,X9,X0,X6,X2] :
        ( hBOOL(c_in(c_Pair(X9,X5,X6,X0),X2,tc_prod(X6,X0)))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Relation_Oconverse(X2,X6,X0),tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f594,axiom,
    ! [X2,X0,X6,X9,X5] :
      ( hBOOL(c_in(c_Pair(X9,X5,X6,X0),X2,tc_prod(X6,X0)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Relation_Oconverse(X2,X6,X0),tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

fof(f7815,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f593,f7813]) ).

fof(f7813,plain,
    ( spl0_470
  <=> ! [X5,X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
        | hBOOL(c_in(c_Pair(X9,X5,X6,X0),c_Relation_Oconverse(X2,X0,X6),tc_prod(X6,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f593,axiom,
    ! [X2,X0,X6,X9,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
      | hBOOL(c_in(c_Pair(X9,X5,X6,X0),c_Relation_Oconverse(X2,X0,X6),tc_prod(X6,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).

fof(f7811,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f383,f7809]) ).

fof(f7809,plain,
    ( spl0_469
  <=> ! [X15,X10,X0,X5,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X5))
        | hBOOL(hAPP(X15,X10))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f383,axiom,
    ! [X2,X10,X0,X15,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X5))
      | hBOOL(hAPP(X15,X10))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).

fof(f7807,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f382,f7805]) ).

fof(f7805,plain,
    ( spl0_468
  <=> ! [X41,X10,X0,X12,X15] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | hBOOL(hAPP(X15,X41))
        | hBOOL(hAPP(X15,X10))
        | ~ hBOOL(c_in(c_Pair(X10,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X15,X12,X0),X0,X0),X12,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f382,axiom,
    ! [X41,X10,X0,X15,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | hBOOL(hAPP(X15,X41))
      | hBOOL(hAPP(X15,X10))
      | ~ hBOOL(c_in(c_Pair(X10,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X15,X12,X0),X0,X0),X12,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).

fof(f7797,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f381,f7795]) ).

fof(f7795,plain,
    ( spl0_467
  <=> ! [X15,X10,X0,X23,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X23))
        | hBOOL(hAPP(X15,X10))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f381,axiom,
    ! [X2,X10,X0,X15,X23] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X23))
      | hBOOL(hAPP(X15,X10))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).

fof(f7793,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f380,f7791]) ).

fof(f7791,plain,
    ( spl0_466
  <=> ! [X15,X10,X0,X5,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X5))
        | hBOOL(hAPP(X15,X10))
        | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f380,axiom,
    ! [X2,X10,X0,X15,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X5))
      | hBOOL(hAPP(X15,X10))
      | ~ hBOOL(c_in(c_Pair(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X15,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).

fof(f7789,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f334,f7787]) ).

fof(f7787,plain,
    ( spl0_465
  <=> ! [X4,X0,X7,X6,X39,X26] :
        ( ~ hBOOL(c_in(X39,X26,X6))
        | c_lessequals(X7,hAPP(X4,X39),tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f334,axiom,
    ! [X39,X0,X6,X26,X7,X4] :
      ( ~ hBOOL(c_in(X39,X26,X6))
      | c_lessequals(X7,hAPP(X4,X39),tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26,X4,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).

fof(f7722,plain,
    ( spl0_464
    | ~ spl0_79
    | ~ spl0_445
    | ~ spl0_463 ),
    inference(avatar_split_clause,[],[f7718,f7715,f7211,f1139,f7720]) ).

fof(f7715,plain,
    ( spl0_463
  <=> ! [X4,X0,X1] :
        ( hBOOL(c_in(X1,X4,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f7718,plain,
    ( ! [X0,X1,X4] :
        ( hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4
        | hBOOL(c_in(X1,X4,X0)) )
    | ~ spl0_79
    | ~ spl0_445
    | ~ spl0_463 ),
    inference(forward_demodulation,[],[f7716,f7260]) ).

fof(f7260,plain,
    ( ! [X2,X3,X0,X1] : hAPP(c_HOL_Ominus__class_Ominus(X0,tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3)) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X2,X1),X0),tc_fun(X1,tc_bool)),hAPP(c_Set_Oinsert(X2,X1),X3))
    | ~ spl0_79
    | ~ spl0_445 ),
    inference(resolution,[],[f7212,f1140]) ).

fof(f7716,plain,
    ( ! [X0,X1,X4] :
        ( hBOOL(c_in(X1,X4,X0))
        | hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4 )
    | ~ spl0_463 ),
    inference(avatar_component_clause,[],[f7715]) ).

fof(f7717,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f234,f7715]) ).

fof(f234,axiom,
    ! [X0,X1,X4] :
      ( hBOOL(c_in(X1,X4,X0))
      | hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

fof(f7713,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f184,f7711]) ).

fof(f7711,plain,
    ( spl0_462
  <=> ! [X13,X0,X12] :
        ( c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(X13,X0)
        | ~ c_lessequals(X12,X13,tc_fun(tc_prod(X0,X0),tc_bool))
        | ~ c_lessequals(X13,c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f184,axiom,
    ! [X0,X12,X13] :
      ( c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(X13,X0)
      | ~ c_lessequals(X12,X13,tc_fun(tc_prod(X0,X0),tc_bool))
      | ~ c_lessequals(X13,c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).

fof(f7709,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f162,f7707]) ).

fof(f7707,plain,
    ( spl0_461
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f162,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

fof(f7705,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f161,f7703]) ).

fof(f7703,plain,
    ( spl0_460
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0),X1) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f161,axiom,
    ! [X10,X0,X18,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0),X1) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1),X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

fof(f7701,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f37,f7699]) ).

fof(f7699,plain,
    ( spl0_459
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18),X0),X1) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f37,axiom,
    ! [X10,X0,X18,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18),X0),X1) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

fof(f7697,plain,
    ( spl0_458
    | ~ spl0_17
    | ~ spl0_444 ),
    inference(avatar_split_clause,[],[f7193,f6752,f878,f7695]) ).

fof(f7695,plain,
    ( spl0_458
  <=> ! [X0,X1] : hAPP(X0,v_a) = hAPP(c_Recdef_Ocut(X0,hAPP(v_P,v_i),v_b,tc_Arrow__Order__Mirabelle_Oalt,X1),v_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f6752,plain,
    ( spl0_444
  <=> ! [X6,X16,X0,X5,X2,X1] :
        ( ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0)))
        | hAPP(X16,X1) = hAPP(c_Recdef_Ocut(X16,X2,X5,X0,X6),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f7193,plain,
    ( ! [X0,X1] : hAPP(X0,v_a) = hAPP(c_Recdef_Ocut(X0,hAPP(v_P,v_i),v_b,tc_Arrow__Order__Mirabelle_Oalt,X1),v_a)
    | ~ spl0_17
    | ~ spl0_444 ),
    inference(resolution,[],[f6753,f880]) ).

fof(f6753,plain,
    ( ! [X2,X0,X1,X6,X16,X5] :
        ( ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0)))
        | hAPP(X16,X1) = hAPP(c_Recdef_Ocut(X16,X2,X5,X0,X6),X1) )
    | ~ spl0_444 ),
    inference(avatar_component_clause,[],[f6752]) ).

fof(f7693,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f36,f7691]) ).

fof(f7691,plain,
    ( spl0_457
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f36,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

fof(f7258,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f354,f7256]) ).

fof(f7256,plain,
    ( spl0_456
  <=> ! [X4,X0,X6,X7] :
        ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X4,X7,X6,X0))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f354,axiom,
    ! [X0,X6,X7,X4] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X4,X7,X6,X0))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_2) ).

fof(f7254,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f353,f7252]) ).

fof(f7252,plain,
    ( spl0_455
  <=> ! [X4,X0,X6,X7] :
        ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1(X4,X7,X6,X0))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f353,axiom,
    ! [X0,X6,X7,X4] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != hAPP(X7,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1(X4,X7,X6,X0))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_2) ).

fof(f7250,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f261,f7248]) ).

fof(f7248,plain,
    ( spl0_454
  <=> ! [X4,X0,X1,X7] :
        ( X4 = X7
        | hBOOL(c_in(X1,X4,X0))
        | hBOOL(c_in(X1,X7,X0))
        | hAPP(c_Set_Oinsert(X1,X0),X4) != hAPP(c_Set_Oinsert(X1,X0),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f261,axiom,
    ! [X0,X1,X7,X4] :
      ( X4 = X7
      | hBOOL(c_in(X1,X4,X0))
      | hBOOL(c_in(X1,X7,X0))
      | hAPP(c_Set_Oinsert(X1,X0),X4) != hAPP(c_Set_Oinsert(X1,X0),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

fof(f7246,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f236,f7244]) ).

fof(f7244,plain,
    ( spl0_453
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool))
        | c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f236,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool))
      | c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

fof(f7242,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f235,f7240]) ).

fof(f7240,plain,
    ( spl0_452
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f235,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11),tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

fof(f7238,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f197,f7236]) ).

fof(f197,axiom,
    ! [X0,X11,X7,X5] :
      ( hBOOL(c_in(X5,X11,X0))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X7,tc_fun(X0,tc_bool)),X11) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

fof(f7234,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f196,f7232]) ).

fof(f196,axiom,
    ! [X0,X7,X4,X5] :
      ( hBOOL(c_in(X5,X4,X0))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

fof(f7230,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f186,f7228]) ).

fof(f7228,plain,
    ( spl0_449
  <=> ! [X5,X4,X0] : hAPP(c_Set_Oinsert(X5,X0),X4) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f186,axiom,
    ! [X0,X4,X5] : hAPP(c_Set_Oinsert(X5,X0),X4) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

fof(f7226,plain,
    ( spl0_448
    | ~ spl0_98
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f6960,f6719,f1216,f7223]) ).

fof(f6960,plain,
    ( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a))
    | ~ spl0_98
    | ~ spl0_436 ),
    inference(resolution,[],[f6721,f1217]) ).

fof(f7221,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f157,f7219]) ).

fof(f7219,plain,
    ( spl0_447
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X11,X4,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X11,X7,tc_fun(X0,tc_bool))
        | c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f157,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X11,X4,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X11,X7,tc_fun(X0,tc_bool))
      | c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

fof(f7217,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f70,f7215]) ).

fof(f7215,plain,
    ( spl0_446
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f70,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X4,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

fof(f7213,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f25,f7211]) ).

fof(f25,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(c_in(X1,X7,X0))
      | hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(X1,X0),X4),tc_fun(X0,tc_bool)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

fof(f6754,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f589,f6752]) ).

fof(f589,axiom,
    ! [X2,X0,X1,X6,X16,X5] :
      ( ~ hBOOL(c_in(c_Pair(X1,X5,X0,X0),X2,tc_prod(X0,X0)))
      | hAPP(X16,X1) = hAPP(c_Recdef_Ocut(X16,X2,X5,X0,X6),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).

fof(f6750,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f547,f6748]) ).

fof(f547,axiom,
    ! [X0,X46,X6,X14,X12,X32,X13] : c_Relation_Orel__comp(c_Relation_Orel__comp(X12,X13,X0,X46,X14),X32,X0,X14,X6) = c_Relation_Orel__comp(X12,c_Relation_Orel__comp(X13,X32,X46,X14,X6),X0,X46,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).

fof(f6746,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f497,f6744]) ).

fof(f6744,plain,
    ( spl0_442
  <=> ! [X5,X4,X9,X0,X6,X7] :
        ( ~ hBOOL(c_in(X5,X4,X6))
        | hBOOL(c_in(X9,hAPP(X7,X5),X0))
        | ~ hBOOL(c_in(X9,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f497,axiom,
    ! [X0,X6,X9,X7,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X6))
      | hBOOL(c_in(X9,hAPP(X7,X5),X0))
      | ~ hBOOL(c_in(X9,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).

fof(f6742,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f437,f6740]) ).

fof(f6740,plain,
    ( spl0_441
  <=> ! [X5,X0,X6,X2] :
        ( ~ hBOOL(c_in(X5,c_Relation_ORange(X2,X6,X0),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X5,X2,X0,X6),X5,X6,X0),X2,tc_prod(X6,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f437,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ hBOOL(c_in(X5,c_Relation_ORange(X2,X6,X0),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X5,X2,X0,X6),X5,X6,X0),X2,tc_prod(X6,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

fof(f6738,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f436,f6736]) ).

fof(f6736,plain,
    ( spl0_440
  <=> ! [X9,X0,X6,X2] :
        ( ~ hBOOL(c_in(X9,c_Relation_ORange(X2,X6,X0),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X9,X2,X0,X6),X9,X6,X0),X2,tc_prod(X6,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f436,axiom,
    ! [X2,X0,X6,X9] :
      ( ~ hBOOL(c_in(X9,c_Relation_ORange(X2,X6,X0),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X9,X2,X0,X6),X9,X6,X0),X2,tc_prod(X6,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

fof(f6734,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f233,f6732]) ).

fof(f6732,plain,
    ( spl0_439
  <=> ! [X5,X9,X0,X6,X2] : c_Relation_ORange(hAPP(c_Set_Oinsert(c_Pair(X5,X9,X6,X0),tc_prod(X6,X0)),X2),X6,X0) = hAPP(c_Set_Oinsert(X9,X0),c_Relation_ORange(X2,X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f233,axiom,
    ! [X2,X0,X6,X9,X5] : c_Relation_ORange(hAPP(c_Set_Oinsert(c_Pair(X5,X9,X6,X0),tc_prod(X6,X0)),X2),X6,X0) = hAPP(c_Set_Oinsert(X9,X0),c_Relation_ORange(X2,X6,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).

fof(f6730,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f110,f6728]) ).

fof(f6728,plain,
    ( spl0_438
  <=> ! [X4,X0,X6,X28] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
        | c_Set_Oimage(c_COMBK(X28,X0,X6),X4,X6,X0) = hAPP(c_Set_Oinsert(X28,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f110,axiom,
    ! [X28,X0,X6,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
      | c_Set_Oimage(c_COMBK(X28,X0,X6),X4,X6,X0) = hAPP(c_Set_Oinsert(X28,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

fof(f6726,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f17,f6724]) ).

fof(f6724,plain,
    ( spl0_437
  <=> ! [X11,X0,X5,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f17,axiom,
    ! [X0,X11,X7,X5] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),X11) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

fof(f6722,plain,
    ( spl0_436
    | ~ spl0_17
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f6689,f6440,f878,f6719]) ).

fof(f6440,plain,
    ( spl0_433
  <=> ! [X5,X0,X6,X2,X1] :
        ( hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
        | ~ hBOOL(c_in(c_Pair(X5,X1,X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f6689,plain,
    ( hBOOL(c_in(v_a,c_Relation_ORange(c_Relation_Oconverse(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_17
    | ~ spl0_433 ),
    inference(resolution,[],[f6441,f880]) ).

fof(f6441,plain,
    ( ! [X2,X0,X1,X6,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X1,X0,X6),X2,tc_prod(X0,X6)))
        | hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0)) )
    | ~ spl0_433 ),
    inference(avatar_component_clause,[],[f6440]) ).

fof(f6717,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f16,f6715]) ).

fof(f6715,plain,
    ( spl0_435
  <=> ! [X4,X0,X5,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f16,axiom,
    ! [X0,X7,X4,X5] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Set_Oinsert(X5,X0),X7)) = hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

fof(f6513,plain,
    ( spl0_434
    | ~ spl0_199
    | ~ spl0_416 ),
    inference(avatar_split_clause,[],[f6223,f5483,f2052,f6510]) ).

fof(f5483,plain,
    ( spl0_416
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f6223,plain,
    ( c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_F(v_P),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_199
    | ~ spl0_416 ),
    inference(superposition,[],[f5484,f2054]) ).

fof(f5484,plain,
    ( ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0))
    | ~ spl0_416 ),
    inference(avatar_component_clause,[],[f5483]) ).

fof(f6442,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f744,f6440]) ).

fof(f744,plain,
    ! [X2,X0,X1,X6,X5] :
      ( hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X2,X0,X6),X6,X0),X0))
      | ~ hBOOL(c_in(c_Pair(X5,X1,X0,X6),X2,tc_prod(X0,X6))) ),
    inference(definition_unfolding,[],[f658,f554]) ).

fof(f658,axiom,
    ! [X2,X0,X1,X6,X5] :
      ( hBOOL(c_in(X5,c_Relation_ODomain(X2,X0,X6),X0))
      | ~ hBOOL(c_in(c_Pair(X5,X1,X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

fof(f6438,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f722,f6436]) ).

fof(f6436,plain,
    ( spl0_432
  <=> ! [X2,X0] : c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f722,plain,
    ! [X2,X0] : c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0),X0,X0),
    inference(definition_unfolding,[],[f512,f554,f554,f574]) ).

fof(f512,axiom,
    ! [X2,X0] : c_Relation_ODomain(X2,X0,X0) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X2,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

fof(f6434,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f660,f6432]) ).

fof(f6432,plain,
    ( spl0_431
  <=> ! [X5,X4,X9,X7,X0,X6] :
        ( hBOOL(c_in(X9,hAPP(X7,X5),X6))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f660,axiom,
    ! [X0,X6,X9,X7,X4,X5] :
      ( hBOOL(c_in(X9,hAPP(X7,X5),X6))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

fof(f6430,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f534,f6428]) ).

fof(f6428,plain,
    ( spl0_430
  <=> ! [X3,X0,X14,X6,X2] : c_Relation_Oconverse(c_Relation_Orel__comp(X2,X3,X6,X14,X0),X6,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X3,X14,X0),c_Relation_Oconverse(X2,X6,X14),X0,X14,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f534,axiom,
    ! [X2,X3,X0,X6,X14] : c_Relation_Oconverse(c_Relation_Orel__comp(X2,X3,X6,X14,X0),X6,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X3,X14,X0),c_Relation_Oconverse(X2,X6,X14),X0,X14,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

fof(f6426,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f441,f6424]) ).

fof(f6424,plain,
    ( spl0_429
  <=> ! [X2,X0] :
        ( ~ c_Relation_Osym(X2,X0)
        | ~ c_Relation_Otrans(X2,X0)
        | c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0),X2,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f441,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | ~ c_Relation_Otrans(X2,X0)
      | c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0),X2,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

fof(f6422,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f407,f6420]) ).

fof(f6420,plain,
    ( spl0_428
  <=> ! [X4,X0,X28] :
        ( ~ hBOOL(c_in(X28,c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
        | c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),X0,X0) = X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f407,axiom,
    ! [X28,X0,X4] :
      ( ~ hBOOL(c_in(X28,c_Relation_OId__on(X4,X0),tc_prod(X0,X0)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),X0,X0) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).

fof(f6418,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f328,f6416]) ).

fof(f6416,plain,
    ( spl0_427
  <=> ! [X16,X4,X0,X6,X1,X7] :
        ( ~ hBOOL(c_in(X1,X4,X6))
        | hBOOL(c_in(hAPP(X16,X1),X7,X0))
        | ~ c_lessequals(c_Set_Oimage(X16,X4,X6,X0),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f328,axiom,
    ! [X0,X1,X6,X16,X7,X4] :
      ( ~ hBOOL(c_in(X1,X4,X6))
      | hBOOL(c_in(hAPP(X16,X1),X7,X0))
      | ~ c_lessequals(c_Set_Oimage(X16,X4,X6,X0),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

fof(f6414,plain,
    ( spl0_426
    | ~ spl0_117
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f5227,f5004,f1341,f6412]) ).

fof(f5227,plain,
    ( ! [X0] : hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0)))
    | ~ spl0_117
    | ~ spl0_376 ),
    inference(resolution,[],[f5006,f1342]) ).

fof(f6410,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f327,f6408]) ).

fof(f327,axiom,
    ! [X0,X1,X6,X16,X4] :
      ( ~ hBOOL(c_in(X1,X4,X0))
      | c_Set_Oimage(X16,X4,X0,X6) = hAPP(c_Set_Oinsert(hAPP(X16,X1),X6),c_Set_Oimage(X16,X4,X0,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

fof(f6406,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f325,f6404]) ).

fof(f6404,plain,
    ( spl0_424
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(c_in(X1,X7,X0))
        | ~ hBOOL(c_in(X1,X4,X0))
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f325,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(c_in(X1,X7,X0))
      | ~ hBOOL(c_in(X1,X4,X0))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

fof(f6402,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f318,f6400]) ).

fof(f318,axiom,
    ! [X28,X0,X1,X6,X4] :
      ( ~ hBOOL(c_in(X1,X4,X0))
      | c_Set_Oimage(c_COMBK(X28,X6,X0),X4,X0,X6) = hAPP(c_Set_Oinsert(X28,X6),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

fof(f6398,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f226,f6396]) ).

fof(f6396,plain,
    ( spl0_422
  <=> ! [X5,X9,X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9) = c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f226,axiom,
    ! [X0,X9,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9) = c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

fof(f6394,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f139,f6392]) ).

fof(f6392,plain,
    ( spl0_421
  <=> ! [X2,X0,X3] :
        ( ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool))
        | c_lessequals(c_Transitive__Closure_Ortrancl(X2,X0),c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f139,axiom,
    ! [X2,X3,X0] :
      ( ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X2,X0),c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

fof(f5501,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f783,f5499]) ).

fof(f783,plain,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0)),
    inference(forward_demodulation,[],[f412,f724]) ).

fof(f724,plain,
    ! [X2,X0] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),X2,X0,X0,X0) = c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),
    inference(definition_unfolding,[],[f573,f574]) ).

fof(f573,axiom,
    ! [X2,X0] : c_Transitive__Closure_Otrancl(X2,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),X2,X0,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

fof(f412,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X0),X2,X0,X0,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

fof(f5497,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f740,f5495]) ).

fof(f740,plain,
    ! [X2,X0] :
      ( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X2,X0,X0),X0,X0),X2,X0)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) != X2 ),
    inference(definition_unfolding,[],[f552,f554]) ).

fof(f552,axiom,
    ! [X2,X0] :
      ( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X2,X0,X0),X2,X0)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).

fof(f5493,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f739,f5491]) ).

fof(f5491,plain,
    ( spl0_418
  <=> ! [X2,X0,X36] :
        ( ~ hBOOL(c_in(X36,X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X36,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f739,plain,
    ! [X2,X0,X36] :
      ( ~ hBOOL(c_in(X36,X2,tc_prod(X0,X0)))
      | hBOOL(c_in(X36,c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f457,f574]) ).

fof(f457,axiom,
    ! [X2,X0,X36] :
      ( ~ hBOOL(c_in(X36,X2,tc_prod(X0,X0)))
      | hBOOL(c_in(X36,c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

fof(f5489,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f734,f5487]) ).

fof(f5487,plain,
    ( spl0_417
  <=> ! [X2,X0,X1] :
        ( ~ c_Wellfounded_Oacyclic(X2,X0)
        | ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f734,plain,
    ! [X2,X0,X1] :
      ( ~ c_Wellfounded_Oacyclic(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_prod(X0,X0))) ),
    inference(definition_unfolding,[],[f388,f574]) ).

fof(f388,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Wellfounded_Oacyclic(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Otrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).

fof(f5485,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f728,f5483]) ).

fof(f728,plain,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),
    inference(definition_unfolding,[],[f409,f574]) ).

fof(f409,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X2,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

fof(f5481,plain,
    ( spl0_415
    | ~ spl0_17
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f5285,f4949,f878,f5479]) ).

fof(f5479,plain,
    ( spl0_415
  <=> ! [X0] :
        ( hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f4949,plain,
    ( spl0_374
  <=> ! [X4,X0,X10,X2,X1] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | hBOOL(c_in(X1,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f5285,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_17
    | ~ spl0_374 ),
    inference(resolution,[],[f4950,f880]) ).

fof(f4950,plain,
    ( ! [X2,X10,X0,X1,X4] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X1,X4,X0))
        | ~ c_Relation_Orefl__on(X4,X2,X0) )
    | ~ spl0_374 ),
    inference(avatar_component_clause,[],[f4949]) ).

fof(f5477,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f584,f5475]) ).

fof(f5475,plain,
    ( spl0_414
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f584,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_4) ).

fof(f5473,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f583,f5471]) ).

fof(f583,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_5) ).

fof(f5469,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f504,f5467]) ).

fof(f5467,plain,
    ( spl0_412
  <=> ! [X6,X4,X9,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | hBOOL(hAPP(hAPP(X7,X5),X9))
        | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X0,tc_fun(X6,tc_bool)),X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f504,axiom,
    ! [X0,X6,X9,X7,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | hBOOL(hAPP(hAPP(X7,X5),X9))
      | ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X0,tc_fun(X6,tc_bool)),X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).

fof(f5465,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f429,f5463]) ).

fof(f5463,plain,
    ( spl0_411
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X0),X1,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f429,axiom,
    ! [X2,X0,X1] :
      ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X0),X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

fof(f5461,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f426,f5459]) ).

fof(f426,axiom,
    ! [X0,X1,X12] :
      ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X12,X0),X0))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X1,X0),X1,X0,X0),X12,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

fof(f5457,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f397,f5455]) ).

fof(f5455,plain,
    ( spl0_409
  <=> ! [X4,X0,X6,X7] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X4,X7,X6,X0),X4,X6))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f397,axiom,
    ! [X0,X6,X7,X4] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X4,X7,X6,X0),X4,X6))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_1) ).

fof(f5453,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f396,f5451]) ).

fof(f5451,plain,
    ( spl0_408
  <=> ! [X4,X0,X6,X7] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1(X4,X7,X6,X0),X4,X6))
        | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f396,axiom,
    ! [X0,X6,X7,X4] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1(X4,X7,X6,X0),X4,X6))
      | c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X6,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_1) ).

fof(f5449,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f362,f5447]) ).

fof(f5447,plain,
    ( spl0_407
  <=> ! [X15,X0,X5,X2] :
        ( hBOOL(hAPP(X15,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f362,axiom,
    ! [X2,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).

fof(f5445,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f357,f5443]) ).

fof(f5443,plain,
    ( spl0_406
  <=> ! [X15,X0,X5,X2] :
        ( hBOOL(hAPP(X15,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f357,axiom,
    ! [X2,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

fof(f5441,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f316,f5439]) ).

fof(f5439,plain,
    ( spl0_405
  <=> ! [X2,X0,X4] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f316,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).

fof(f5437,plain,
    ( spl0_404
    | ~ spl0_17
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f5264,f4945,f878,f5435]) ).

fof(f5435,plain,
    ( spl0_404
  <=> ! [X0] :
        ( hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f4945,plain,
    ( spl0_373
  <=> ! [X4,X0,X10,X2,X1] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | hBOOL(c_in(X10,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f5264,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_17
    | ~ spl0_373 ),
    inference(resolution,[],[f4946,f880]) ).

fof(f4946,plain,
    ( ! [X2,X10,X0,X1,X4] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X10,X4,X0))
        | ~ c_Relation_Orefl__on(X4,X2,X0) )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f4945]) ).

fof(f5433,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f284,f5431]) ).

fof(f5431,plain,
    ( spl0_403
  <=> ! [X6,X16,X17] :
        ( ~ class_Lattices_Olattice(X6)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X16,tc_fun(t_a,X6)),X17),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X16,v_x),X6),hAPP(X17,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f284,axiom,
    ! [X6,X16,X17] :
      ( ~ class_Lattices_Olattice(X6)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X16,tc_fun(t_a,X6)),X17),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X16,v_x),X6),hAPP(X17,v_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

fof(f5429,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f259,f5427]) ).

fof(f5427,plain,
    ( spl0_402
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X4,X0))
        | hBOOL(c_in(X28,X7,X0))
        | hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f259,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X4,X0))
      | hBOOL(c_in(X28,X7,X0))
      | hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

fof(f5425,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f251,f5423]) ).

fof(f5423,plain,
    ( spl0_401
  <=> ! [X4,X0,X28,X7] :
        ( hBOOL(c_in(X28,X7,X0))
        | hBOOL(c_in(X28,X4,X0))
        | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f251,axiom,
    ! [X28,X0,X7,X4] :
      ( hBOOL(c_in(X28,X7,X0))
      | hBOOL(c_in(X28,X4,X0))
      | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

fof(f5421,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f241,f5419]) ).

fof(f5419,plain,
    ( spl0_400
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X4,X0))
        | ~ hBOOL(c_in(X28,X7,X0))
        | hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f241,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X4,X0))
      | ~ hBOOL(c_in(X28,X7,X0))
      | hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

fof(f5417,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f222,f5415]) ).

fof(f5415,plain,
    ( spl0_399
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f222,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

fof(f5413,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f206,f5411]) ).

fof(f5411,plain,
    ( spl0_398
  <=> ! [X6,X4,X7] :
        ( ~ class_HOL_Ominus(X6)
        | hAPP(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(t_a,X6)),X7),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X4,v_x),X6),hAPP(X7,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f206,axiom,
    ! [X6,X7,X4] :
      ( ~ class_HOL_Ominus(X6)
      | hAPP(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(t_a,X6)),X7),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X4,v_x),X6),hAPP(X7,v_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

fof(f5409,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f203,f5407]) ).

fof(f5407,plain,
    ( spl0_397
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f203,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

fof(f5405,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f202,f5403]) ).

fof(f5403,plain,
    ( spl0_396
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f202,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X7,tc_fun(X0,tc_bool)),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4),tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

fof(f5401,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f193,f5399]) ).

fof(f5399,plain,
    ( spl0_395
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(c_in(X1,X4,X0))
        | c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f193,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(c_in(X1,X4,X0))
      | c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X4,hAPP(c_Set_Oinsert(X1,X0),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

fof(f5397,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f171,f5395]) ).

fof(f5395,plain,
    ( spl0_394
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f171,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

fof(f5393,plain,
    ( spl0_393
    | ~ spl0_17
    | ~ spl0_371 ),
    inference(avatar_split_clause,[],[f5235,f4937,f878,f5391]) ).

fof(f5391,plain,
    ( spl0_393
  <=> ! [X0] :
        ( hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f4937,plain,
    ( spl0_371
  <=> ! [X4,X0,X10,X2,X1] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | hBOOL(c_in(X1,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f5235,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_a,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_17
    | ~ spl0_371 ),
    inference(resolution,[],[f4938,f880]) ).

fof(f4938,plain,
    ( ! [X2,X10,X0,X1,X4] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X1,X4,X0))
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) )
    | ~ spl0_371 ),
    inference(avatar_component_clause,[],[f4937]) ).

fof(f5389,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f166,f5387]) ).

fof(f5387,plain,
    ( spl0_392
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(c_in(X1,X7,X0))
        | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f166,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(c_in(X1,X7,X0))
      | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

fof(f5385,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f145,f5383]) ).

fof(f5383,plain,
    ( spl0_391
  <=> ! [X5,X0,X6,X16,X7] : c_Set_Oimage(X16,hAPP(c_Set_Oinsert(X5,X6),X7),X6,X0) = hAPP(c_Set_Oinsert(hAPP(X16,X5),X0),c_Set_Oimage(X16,X7,X6,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f145,axiom,
    ! [X0,X6,X16,X7,X5] : c_Set_Oimage(X16,hAPP(c_Set_Oinsert(X5,X6),X7),X6,X0) = hAPP(c_Set_Oinsert(hAPP(X16,X5),X0),c_Set_Oimage(X16,X7,X6,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

fof(f5381,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f124,f5379]) ).

fof(f5379,plain,
    ( spl0_390
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f124,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7)) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

fof(f5377,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f99,f5375]) ).

fof(f5375,plain,
    ( spl0_389
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f99,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

fof(f5373,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f98,f5371]) ).

fof(f5371,plain,
    ( spl0_388
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f98,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

fof(f5369,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f97,f5367]) ).

fof(f5367,plain,
    ( spl0_387
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f97,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

fof(f5365,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f96,f5363]) ).

fof(f5363,plain,
    ( spl0_386
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f96,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

fof(f5361,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f61,f5359]) ).

fof(f5359,plain,
    ( spl0_385
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f61,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

fof(f5357,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f60,f5355]) ).

fof(f5355,plain,
    ( spl0_384
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f60,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

fof(f5353,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f59,f5351]) ).

fof(f5351,plain,
    ( spl0_383
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f59,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

fof(f5349,plain,
    ( spl0_382
    | ~ spl0_17
    | ~ spl0_370 ),
    inference(avatar_split_clause,[],[f5213,f4933,f878,f5347]) ).

fof(f5347,plain,
    ( spl0_382
  <=> ! [X0] :
        ( hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f4933,plain,
    ( spl0_370
  <=> ! [X4,X0,X10,X2,X1] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | hBOOL(c_in(X10,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f5213,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_b,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_17
    | ~ spl0_370 ),
    inference(resolution,[],[f4934,f880]) ).

fof(f4934,plain,
    ( ! [X2,X10,X0,X1,X4] :
        ( ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X10,X4,X0))
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) )
    | ~ spl0_370 ),
    inference(avatar_component_clause,[],[f4933]) ).

fof(f5345,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f58,f5343]) ).

fof(f5343,plain,
    ( spl0_381
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f58,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0),X18) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

fof(f5341,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f49,f5339]) ).

fof(f5339,plain,
    ( spl0_380
  <=> ! [X4,X0,X7] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f49,axiom,
    ! [X0,X7,X4] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

fof(f5337,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f39,f5335]) ).

fof(f5335,plain,
    ( spl0_379
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f39,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | c_lessequals(X2,c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).

fof(f5333,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f32,f5331]) ).

fof(f5331,plain,
    ( spl0_378
  <=> ! [X6,X16,X17] :
        ( ~ class_Lattices_Olattice(X6)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X16,tc_fun(t_a,X6)),X17),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X16,v_x),X6),hAPP(X17,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f32,axiom,
    ! [X6,X16,X17] :
      ( ~ class_Lattices_Olattice(X6)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X16,tc_fun(t_a,X6)),X17),v_x) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(X16,v_x),X6),hAPP(X17,v_x)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

fof(f5329,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f31,f5327]) ).

fof(f5327,plain,
    ( spl0_377
  <=> ! [X4,X0,X7] :
        ( hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = X4
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f31,axiom,
    ! [X0,X7,X4] :
      ( hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7) = X4
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

fof(f5007,plain,
    ( spl0_376
    | ~ spl0_98
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f4923,f4861,f1216,f5004]) ).

fof(f4923,plain,
    ( hBOOL(hAPP(c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b))
    | ~ spl0_98
    | ~ spl0_358 ),
    inference(resolution,[],[f4863,f1217]) ).

fof(f4955,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f665,f4953]) ).

fof(f665,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | ~ hBOOL(c_in(X5,X4,X0))
      | hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

fof(f4951,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f664,f4949]) ).

fof(f664,axiom,
    ! [X2,X10,X0,X1,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | hBOOL(c_in(X1,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

fof(f4947,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f663,f4945]) ).

fof(f663,axiom,
    ! [X2,X10,X0,X1,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | hBOOL(c_in(X10,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

fof(f4943,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f661,f4941]) ).

fof(f4941,plain,
    ( spl0_372
  <=> ! [X6,X4,X9,X0,X5,X7] :
        ( hBOOL(c_in(X5,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f661,axiom,
    ! [X0,X6,X9,X7,X4,X5] :
      ( hBOOL(c_in(X5,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),c_Product__Type_OSigma(X4,X7,X0,X6),tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

fof(f4939,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f655,f4937]) ).

fof(f655,axiom,
    ! [X2,X10,X0,X1,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | hBOOL(c_in(X1,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

fof(f4935,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f654,f4933]) ).

fof(f654,axiom,
    ! [X2,X10,X0,X1,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | hBOOL(c_in(X10,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

fof(f4931,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f414,f4929]) ).

fof(f4929,plain,
    ( spl0_369
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f414,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

fof(f4927,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f403,f4925]) ).

fof(f4925,plain,
    ( spl0_368
  <=> ! [X4,X0,X12] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
        | ~ c_lessequals(X4,hAPP(c_Relation_OImage(X12,X0,X0),X4),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f403,axiom,
    ! [X0,X4,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
      | ~ c_lessequals(X4,hAPP(c_Relation_OImage(X12,X0,X0),X4),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

fof(f4919,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f348,f4917]) ).

fof(f4917,plain,
    ( spl0_367
  <=> ! [X4,X0,X6,X28] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
        | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBK(X28,tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) = X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f348,axiom,
    ! [X28,X0,X6,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
      | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBK(X28,tc_fun(X0,tc_bool),X6),X6,tc_fun(X0,tc_bool)) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).

fof(f4915,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f341,f4913]) ).

fof(f341,axiom,
    ! [X2,X0,X6,X9,X4] :
      ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X4,X9,X2,X6,X0),X4,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

fof(f4911,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f340,f4909]) ).

fof(f340,axiom,
    ! [X2,X0,X6,X9,X4] :
      ( ~ hBOOL(c_in(X9,hAPP(c_Relation_OImage(X2,X6,X0),X4),X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X4,X9,X2,X6,X0),X4,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

fof(f4907,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f311,f4905]) ).

fof(f4905,plain,
    ( spl0_364
  <=> ! [X5,X11,X0,X29] :
        ( ~ c_lessequals(X11,X29,tc_fun(X0,tc_bool))
        | c_lessequals(hAPP(c_Set_Oinsert(X5,X0),X11),hAPP(c_Set_Oinsert(X5,X0),X29),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f311,axiom,
    ! [X29,X11,X0,X5] :
      ( ~ c_lessequals(X11,X29,tc_fun(X0,tc_bool))
      | c_lessequals(hAPP(c_Set_Oinsert(X5,X0),X11),hAPP(c_Set_Oinsert(X5,X0),X29),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

fof(f4903,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f309,f4901]) ).

fof(f4901,plain,
    ( spl0_363
  <=> ! [X4,X0,X6,X16,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | c_lessequals(c_Set_Oimage(X16,X4,X0,X6),c_Set_Oimage(X16,X7,X0,X6),tc_fun(X6,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f309,axiom,
    ! [X0,X6,X7,X16,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | c_lessequals(c_Set_Oimage(X16,X4,X0,X6),c_Set_Oimage(X16,X7,X0,X6),tc_fun(X6,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

fof(f4899,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f220,f4897]) ).

fof(f4897,plain,
    ( spl0_362
  <=> ! [X5,X4,X0] : hAPP(c_Set_Oinsert(X5,X0),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),tc_fun(X0,tc_bool)),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f220,axiom,
    ! [X0,X4,X5] : hAPP(c_Set_Oinsert(X5,X0),X4) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

fof(f4895,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f187,f4893]) ).

fof(f4893,plain,
    ( spl0_361
  <=> ! [X9,X5,X0] :
        ( X5 = X9
        | hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) != hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f187,axiom,
    ! [X0,X9,X5] :
      ( X5 = X9
      | hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) != hAPP(c_Set_Oinsert(X9,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

fof(f4891,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f167,f4889]) ).

fof(f4889,plain,
    ( spl0_360
  <=> ! [X17,X4,X0,X14,X6,X16] : c_Set_Oimage(X16,c_Set_Oimage(X17,X4,X14,X6),X6,X0) = c_Set_Oimage(c_COMBB(X16,X17,X6,X0,X14),X4,X14,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f167,axiom,
    ! [X0,X6,X16,X14,X4,X17] : c_Set_Oimage(X16,c_Set_Oimage(X17,X4,X14,X6),X6,X0) = c_Set_Oimage(c_COMBB(X16,X17,X6,X0,X14),X4,X14,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

fof(f4887,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f2,f4885]) ).

fof(f4885,plain,
    ( spl0_359
  <=> ! [X2,X0,X3] :
        ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
        | c_lessequals(c_Transitive__Closure_Ortrancl(X2,X0),c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f2,axiom,
    ! [X2,X3,X0] :
      ( ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X2,X0),c_Transitive__Closure_Ortrancl(X3,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).

fof(f4864,plain,
    ( spl0_358
    | ~ spl0_17
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f4841,f4701,f878,f4861]) ).

fof(f4701,plain,
    ( spl0_356
  <=> ! [X5,X9,X0,X6,X2] :
        ( hBOOL(c_in(X9,c_Relation_ORange(X2,X0,X6),X6))
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f4841,plain,
    ( hBOOL(c_in(v_b,c_Relation_ORange(hAPP(v_P,v_i),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_17
    | ~ spl0_356 ),
    inference(resolution,[],[f4702,f880]) ).

fof(f4702,plain,
    ( ! [X2,X0,X6,X9,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6)))
        | hBOOL(c_in(X9,c_Relation_ORange(X2,X0,X6),X6)) )
    | ~ spl0_356 ),
    inference(avatar_component_clause,[],[f4701]) ).

fof(f4707,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f738,f4705]) ).

fof(f4705,plain,
    ( spl0_357
  <=> ! [X2,X0] :
        ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X2,X0,X0),X0)
        | c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f738,plain,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X2,X0,X0),X0)
      | c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0),X0) ),
    inference(definition_unfolding,[],[f519,f574]) ).

fof(f519,axiom,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X2,X0,X0),X0)
      | c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X2,X0),X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

fof(f4703,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f657,f4701]) ).

fof(f657,axiom,
    ! [X2,X0,X6,X9,X5] :
      ( hBOOL(c_in(X9,c_Relation_ORange(X2,X0,X6),X6))
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X6),X2,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).

fof(f4699,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f402,f4697]) ).

fof(f4697,plain,
    ( spl0_355
  <=> ! [X36,X0] :
        ( ~ hBOOL(c_in(X36,c_Relation_OId(X0),tc_prod(X0,X0)))
        | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X36,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X36,X0),X0,X0) = X36 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f402,axiom,
    ! [X0,X36] :
      ( ~ hBOOL(c_in(X36,c_Relation_OId(X0),tc_prod(X0,X0)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X36,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X36,X0),X0,X0) = X36 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).

fof(f4695,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f335,f4693]) ).

fof(f4693,plain,
    ( spl0_354
  <=> ! [X6,X4,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X4,X0))
        | c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X0,tc_fun(X6,tc_bool)),hAPP(X7,X5),tc_fun(X6,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f335,axiom,
    ! [X0,X6,X7,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X7,X0,tc_fun(X6,tc_bool)),hAPP(X7,X5),tc_fun(X6,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).

fof(f4691,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f46,f4689]) ).

fof(f4689,plain,
    ( spl0_353
  <=> ! [X4,X0,X10,X1] : hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X10,X0),X4)) = hAPP(c_Set_Oinsert(X10,X0),hAPP(c_Set_Oinsert(X1,X0),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f46,axiom,
    ! [X10,X0,X1,X4] : hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X10,X0),X4)) = hAPP(c_Set_Oinsert(X10,X0),hAPP(c_Set_Oinsert(X1,X0),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

fof(f4687,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f38,f4685]) ).

fof(f4685,plain,
    ( spl0_352
  <=> ! [X4,X0] : c_lessequals(c_Relation_OId__on(X4,X0),c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f38,axiom,
    ! [X0,X4] : c_lessequals(c_Relation_OId__on(X4,X0),c_Product__Type_OSigma(X4,c_COMBK(X4,tc_fun(X0,tc_bool),X0),X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).

fof(f4562,plain,
    ( spl0_351
    | ~ spl0_160
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f4525,f4136,f1603,f4560]) ).

fof(f4560,plain,
    ( spl0_351
  <=> ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f4525,plain,
    ( ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)
    | ~ spl0_160
    | ~ spl0_337 ),
    inference(resolution,[],[f4137,f1604]) ).

fof(f4425,plain,
    ( spl0_350
    | ~ spl0_183
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2631,f2164,f1795,f4423]) ).

fof(f4423,plain,
    ( spl0_350
  <=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f2631,plain,
    ( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_183
    | ~ spl0_226 ),
    inference(resolution,[],[f2165,f1796]) ).

fof(f4187,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f666,f4185]) ).

fof(f666,axiom,
    ! [X2,X0] :
      ( c_Relation_Oirrefl(X2,X0)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

fof(f4183,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f653,f4181]) ).

fof(f4181,plain,
    ( spl0_348
  <=> ! [X4,X0,X1] :
        ( ~ hBOOL(c_in(X1,X4,X0))
        | hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f653,axiom,
    ! [X0,X1,X4] :
      ( ~ hBOOL(c_in(X1,X4,X0))
      | hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

fof(f4179,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f652,f4177]) ).

fof(f4177,plain,
    ( spl0_347
  <=> ! [X4,X0,X10,X1] :
        ( hBOOL(c_in(X1,X4,X0))
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f652,axiom,
    ! [X10,X0,X1,X4] :
      ( hBOOL(c_in(X1,X4,X0))
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

fof(f4175,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f626,f4173]) ).

fof(f4173,plain,
    ( spl0_346
  <=> ! [X0,X1,X15] :
        ( hBOOL(hAPP(X15,X1))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X15,X0)))
        | ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f626,axiom,
    ! [X0,X1,X15] :
      ( hBOOL(hAPP(X15,X1))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2(X15,X0)))
      | ~ hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_2) ).

fof(f4171,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f622,f4169]) ).

fof(f4169,plain,
    ( spl0_345
  <=> ! [X0,X23,X15] :
        ( ~ hBOOL(hAPP(X15,X23))
        | hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X15,X0)))
        | ~ hBOOL(c_in(X23,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f622,axiom,
    ! [X0,X15,X23] :
      ( ~ hBOOL(hAPP(X15,X23))
      | hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X15,X0)))
      | ~ hBOOL(c_in(X23,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).

fof(f4167,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f582,f4165]) ).

fof(f4165,plain,
    ( spl0_344
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f582,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_2) ).

fof(f4163,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f581,f4161]) ).

fof(f4161,plain,
    ( spl0_343
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__2(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f581,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__2(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_0) ).

fof(f4159,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f580,f4157]) ).

fof(f4157,plain,
    ( spl0_342
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f580,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_3) ).

fof(f4155,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f579,f4153]) ).

fof(f4153,plain,
    ( spl0_341
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f579,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_1) ).

fof(f4151,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f447,f4149]) ).

fof(f447,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__2(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_1) ).

fof(f4147,plain,
    ( spl0_339
    | ~ spl0_17
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f4018,f3862,f878,f4144]) ).

fof(f4018,plain,
    ( c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_17
    | ~ spl0_314 ),
    inference(resolution,[],[f3863,f880]) ).

fof(f4142,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f446,f4140]) ).

fof(f446,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X2,X0),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_2) ).

fof(f4138,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f418,f4136]) ).

fof(f418,axiom,
    ! [X2,X0] :
      ( c_Nitpick_Orefl_H(X2,X0)
      | ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X2,X0),X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

fof(f4134,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f417,f4132]) ).

fof(f4132,plain,
    ( spl0_336
  <=> ! [X2,X0] :
        ( ~ c_Relation_Oantisym(X2,X0)
        | ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Otrans(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f417,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Oantisym(X2,X0)
      | ~ c_Relation_Otrans(X2,X0)
      | c_Relation_Otrans(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

fof(f4130,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f359,f4128]) ).

fof(f4128,plain,
    ( spl0_335
  <=> ! [X15,X0,X5,X2] :
        ( hBOOL(hAPP(X15,X5))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0)))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f359,axiom,
    ! [X2,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X5))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X15,X2,X0)))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

fof(f4126,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f355,f4124]) ).

fof(f4124,plain,
    ( spl0_334
  <=> ! [X15,X0,X5,X2] :
        ( hBOOL(hAPP(X15,X5))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0)))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f355,axiom,
    ! [X2,X0,X15,X5] :
      ( hBOOL(hAPP(X15,X5))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X15,X2,X0)))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).

fof(f4122,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f345,f4120]) ).

fof(f4120,plain,
    ( spl0_333
  <=> ! [X37,X4,X0,X6] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
        | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBK(X37,X6,X0),X0,X6) = X37 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f345,axiom,
    ! [X0,X37,X6,X4] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
      | c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,c_COMBK(X37,X6,X0),X0,X6) = X37 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).

fof(f4118,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f305,f4116]) ).

fof(f4116,plain,
    ( spl0_332
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(hAPP(X4,X1))
        | ~ hBOOL(hAPP(X7,X1))
        | hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f305,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(X7,X1))
      | hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

fof(f4114,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f289,f4112]) ).

fof(f4112,plain,
    ( spl0_331
  <=> ! [X4,X11,X0,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
        | c_lessequals(X4,X11,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f289,axiom,
    ! [X0,X11,X7,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X11,tc_fun(X0,tc_bool))
      | c_lessequals(X4,X11,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

fof(f4110,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f283,f4108]) ).

fof(f4108,plain,
    ( spl0_330
  <=> ! [X4,X0,X11,X7] :
        ( c_lessequals(X7,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f283,axiom,
    ! [X0,X11,X7,X4] :
      ( c_lessequals(X7,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

fof(f4106,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f282,f4104]) ).

fof(f4104,plain,
    ( spl0_329
  <=> ! [X4,X11,X0,X7] :
        ( c_lessequals(X4,X11,tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f282,axiom,
    ! [X0,X11,X7,X4] :
      ( c_lessequals(X4,X11,tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X11,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

fof(f4102,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f225,f4100]) ).

fof(f4100,plain,
    ( spl0_328
  <=> ! [X4,X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f225,axiom,
    ! [X0,X7,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(X7,tc_fun(X0,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

fof(f4098,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f221,f4096]) ).

fof(f4096,plain,
    ( spl0_327
  <=> ! [X34,X0,X33] :
        ( ~ c_lessequals(X34,X33,tc_fun(tc_prod(X0,X0),tc_bool))
        | c_lessequals(c_Wellfounded_Oacc(X33,X0),c_Wellfounded_Oacc(X34,X0),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f221,axiom,
    ! [X0,X34,X33] :
      ( ~ c_lessequals(X34,X33,tc_fun(tc_prod(X0,X0),tc_bool))
      | c_lessequals(c_Wellfounded_Oacc(X33,X0),c_Wellfounded_Oacc(X34,X0),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).

fof(f4094,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f208,f4092]) ).

fof(f4092,plain,
    ( spl0_326
  <=> ! [X4,X11,X0,X7] :
        ( c_lessequals(X11,X4,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f208,axiom,
    ! [X0,X11,X7,X4] :
      ( c_lessequals(X11,X4,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

fof(f4090,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f207,f4088]) ).

fof(f4088,plain,
    ( spl0_325
  <=> ! [X4,X11,X0,X7] :
        ( c_lessequals(X11,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f207,axiom,
    ! [X0,X11,X7,X4] :
      ( c_lessequals(X11,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X11,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

fof(f4086,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f199,f4084]) ).

fof(f4084,plain,
    ( spl0_324
  <=> ! [X4,X0,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f199,axiom,
    ! [X0,X7,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

fof(f4082,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f198,f4080]) ).

fof(f4080,plain,
    ( spl0_323
  <=> ! [X4,X0,X7] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f198,axiom,
    ! [X0,X7,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

fof(f4078,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f151,f4076]) ).

fof(f4076,plain,
    ( spl0_322
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X1,X10,X0)
        | ~ c_lessequals(X1,X18,X0)
        | c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f151,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X1,X10,X0)
      | ~ c_lessequals(X1,X18,X0)
      | c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

fof(f4074,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f92,f4072]) ).

fof(f4072,plain,
    ( spl0_321
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(hAPP(X7,X1))
        | hBOOL(hAPP(X4,X1))
        | ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f92,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(hAPP(X7,X1))
      | hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

fof(f4070,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f71,f4068]) ).

fof(f4068,plain,
    ( spl0_320
  <=> ! [X9,X0,X5,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X5,X1,X0)
        | ~ c_lessequals(X9,X1,X0)
        | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f71,axiom,
    ! [X0,X1,X9,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X5,X1,X0)
      | ~ c_lessequals(X9,X1,X0)
      | c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

fof(f4056,plain,
    ( ~ spl0_319
    | spl0_16
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f4034,f3866,f873,f4053]) ).

fof(f4034,plain,
    ( ~ c_FunDef_Oin__rel(v_F(v_P),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_16
    | ~ spl0_315 ),
    inference(resolution,[],[f3867,f875]) ).

fof(f3962,plain,
    ( spl0_318
    | ~ spl0_186
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2626,f2160,f1807,f3960]) ).

fof(f3960,plain,
    ( spl0_318
  <=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f2626,plain,
    ( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_186
    | ~ spl0_225 ),
    inference(resolution,[],[f2161,f1808]) ).

fof(f3876,plain,
    ( spl0_317
    | ~ spl0_185
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2625,f2160,f1803,f3874]) ).

fof(f3874,plain,
    ( spl0_317
  <=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f2625,plain,
    ( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_185
    | ~ spl0_225 ),
    inference(resolution,[],[f2161,f1804]) ).

fof(f3872,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f724,f3870]) ).

fof(f3868,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f591,f3866]) ).

fof(f591,axiom,
    ! [X10,X0,X1,X6,X12] :
      ( ~ c_FunDef_Oin__rel(X12,X1,X10,X0,X6)
      | hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).

fof(f3864,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f590,f3862]) ).

fof(f590,axiom,
    ! [X10,X0,X1,X6,X12] :
      ( c_FunDef_Oin__rel(X12,X1,X10,X0,X6)
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X6),X12,tc_prod(X0,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

fof(f3860,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f556,f3858]) ).

fof(f3858,plain,
    ( spl0_313
  <=> ! [X3,X0,X14,X6,X2] :
        ( ~ c_Relation_Osingle__valued(X2,X0,X6)
        | ~ c_Relation_Osingle__valued(X3,X6,X14)
        | c_Relation_Osingle__valued(c_Relation_Orel__comp(X2,X3,X0,X6,X14),X0,X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f556,axiom,
    ! [X2,X3,X0,X6,X14] :
      ( ~ c_Relation_Osingle__valued(X2,X0,X6)
      | ~ c_Relation_Osingle__valued(X3,X6,X14)
      | c_Relation_Osingle__valued(c_Relation_Orel__comp(X2,X3,X0,X6,X14),X0,X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

fof(f3856,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f548,f3854]) ).

fof(f3854,plain,
    ( spl0_312
  <=> ! [X0,X12,X6,X16] : c_Relation_Oconverse(c_Relation_Oinv__image(X12,X16,X6,X0),X0,X0) = c_Relation_Oinv__image(c_Relation_Oconverse(X12,X6,X6),X16,X6,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f548,axiom,
    ! [X0,X6,X16,X12] : c_Relation_Oconverse(c_Relation_Oinv__image(X12,X16,X6,X0),X0,X0) = c_Relation_Oinv__image(c_Relation_Oconverse(X12,X6,X6),X16,X6,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

fof(f3852,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f488,f3850]) ).

fof(f3850,plain,
    ( spl0_311
  <=> ! [X5,X9,X14,X0,X6,X16] : hAPP(hAPP(X16,X5),X9) = hAPP(c_split(X16,X6,X14,X0),c_Pair(X5,X9,X6,X14)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f488,axiom,
    ! [X0,X6,X9,X16,X14,X5] : hAPP(hAPP(X16,X5),X9) = hAPP(c_split(X16,X6,X14,X0),c_Pair(X5,X9,X6,X14)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

fof(f3848,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f406,f3846]) ).

fof(f3846,plain,
    ( spl0_310
  <=> ! [X4,X0,X28] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),X4,X0))
        | ~ hBOOL(c_in(X28,c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f406,axiom,
    ! [X28,X0,X4] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X4,X28,X0),X4,X0))
      | ~ hBOOL(c_in(X28,c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

fof(f3844,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f378,f3842]) ).

fof(f3842,plain,
    ( spl0_309
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Ototal__on(X4,X2,X0)
        | c_Relation_Ototal__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f378,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Ototal__on(X4,X2,X0)
      | c_Relation_Ototal__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

fof(f3840,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f377,f3838]) ).

fof(f3838,plain,
    ( spl0_308
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | ~ c_Relation_Ototal__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f377,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | ~ c_Relation_Ototal__on(X4,hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

fof(f3836,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f361,f3834]) ).

fof(f3834,plain,
    ( spl0_307
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0))
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X0),c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f361,axiom,
    ! [X2,X0,X1] :
      ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0))
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X2,X1,X0),c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

fof(f3829,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f360,f3827]) ).

fof(f3827,plain,
    ( spl0_306
  <=> ! [X2,X1,X15] :
        ( hBOOL(hAPP(X15,X1))
        | ~ hBOOL(hAPP(X15,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2)))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f360,axiom,
    ! [X2,X1,X15] :
      ( hBOOL(hAPP(X15,X1))
      | ~ hBOOL(hAPP(X15,v_sko__Wellfounded__Xacc__Xinduct__1(X15,X2)))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

fof(f3825,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f358,f3823]) ).

fof(f3823,plain,
    ( spl0_305
  <=> ! [X0,X12,X1] :
        ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X12,X0),X0))
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X1,X0),c_Wellfounded_Oacc(X12,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f358,axiom,
    ! [X0,X1,X12] :
      ( hBOOL(c_in(X1,c_Wellfounded_Oacc(X12,X0),X0))
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X1,X0),c_Wellfounded_Oacc(X12,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

fof(f3821,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f356,f3819]) ).

fof(f3819,plain,
    ( spl0_304
  <=> ! [X2,X1,X15] :
        ( hBOOL(hAPP(X15,X1))
        | ~ hBOOL(hAPP(X15,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2)))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f356,axiom,
    ! [X2,X1,X15] :
      ( hBOOL(hAPP(X15,X1))
      | ~ hBOOL(hAPP(X15,v_sko__Wellfounded__Xacc__Xinducts__1(X15,X2)))
      | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

fof(f3817,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f330,f3815]) ).

fof(f3815,plain,
    ( spl0_303
  <=> ! [X37,X4,X0,X6,X39] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
        | ~ hBOOL(c_in(X39,X4,X0))
        | c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X37,X0,X6),hAPP(X37,X39),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f330,axiom,
    ! [X39,X0,X37,X6,X4] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X6)
      | ~ hBOOL(c_in(X39,X4,X0))
      | c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X37,X0,X6),hAPP(X37,X39),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).

fof(f3813,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f250,f3811]) ).

fof(f3811,plain,
    ( spl0_302
  <=> ! [X5,X4,X0,X9] :
        ( X5 = X9
        | hBOOL(c_in(X5,X4,X0))
        | ~ hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X9,X0),X4),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f250,axiom,
    ! [X0,X9,X4,X5] :
      ( X5 = X9
      | hBOOL(c_in(X5,X4,X0))
      | ~ hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X9,X0),X4),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

fof(f3809,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f224,f3807]) ).

fof(f3807,plain,
    ( spl0_301
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f224,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

fof(f3805,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f223,f3803]) ).

fof(f3803,plain,
    ( spl0_300
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f223,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

fof(f3801,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f170,f3799]) ).

fof(f3799,plain,
    ( spl0_299
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f170,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

fof(f3797,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f169,f3795]) ).

fof(f3795,plain,
    ( spl0_298
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f169,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

fof(f3793,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f12,f3791]) ).

fof(f3791,plain,
    ( spl0_297
  <=> ! [X5,X4,X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),X4),X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),c_Complete__Lattice_OSup__class_OSup(X4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f12,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),X4),X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),c_Complete__Lattice_OSup__class_OSup(X4,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

fof(f3789,plain,
    ( spl0_296
    | ~ spl0_15
    | ~ spl0_231 ),
    inference(avatar_split_clause,[],[f2655,f2192,f869,f3787]) ).

fof(f3787,plain,
    ( spl0_296
  <=> ! [X0] :
        ( ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f2192,plain,
    ( spl0_231
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Oirrefl(X2,X0)
        | ~ c_Relation_Otrans(X2,X0)
        | ~ c_Relation_Ototal__on(X4,X2,X0)
        | c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2655,plain,
    ( ! [X0] :
        ( ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_15
    | ~ spl0_231 ),
    inference(resolution,[],[f2193,f870]) ).

fof(f2193,plain,
    ( ! [X2,X0,X4] :
        ( ~ c_Relation_Ototal__on(X4,X2,X0)
        | ~ c_Relation_Otrans(X2,X0)
        | ~ c_Relation_Oirrefl(X2,X0)
        | c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) )
    | ~ spl0_231 ),
    inference(avatar_component_clause,[],[f2192]) ).

fof(f3785,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f4,f3783]) ).

fof(f3783,plain,
    ( spl0_295
  <=> ! [X2,X0,X3] :
        ( ~ c_Relation_Osym(X2,X0)
        | ~ c_Relation_Osym(X3,X0)
        | c_Relation_Osym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f4,axiom,
    ! [X2,X3,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | ~ c_Relation_Osym(X3,X0)
      | c_Relation_Osym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),X3),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).

fof(f3502,plain,
    ( spl0_294
    | ~ spl0_97
    | ~ spl0_57
    | ~ spl0_231
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2656,f2501,f2192,f1041,f1211,f3499]) ).

fof(f3499,plain,
    ( spl0_294
  <=> c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f1211,plain,
    ( spl0_97
  <=> c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1041,plain,
    ( spl0_57
  <=> c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f2501,plain,
    ( spl0_237
  <=> c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f2656,plain,
    ( ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_231
    | ~ spl0_237 ),
    inference(resolution,[],[f2193,f2503]) ).

fof(f2503,plain,
    ( c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_237 ),
    inference(avatar_component_clause,[],[f2501]) ).

fof(f3365,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f778,f3363]) ).

fof(f3363,plain,
    ( spl0_293
  <=> ! [X53,X1,X23] :
        ( X1 = X23
        | hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f778,plain,
    ! [X1,X53,X23] :
      ( X1 = X23
      | hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(duplicate_literal_removal,[],[f642]) ).

fof(f642,axiom,
    ! [X1,X53,X23] :
      ( X1 = X23
      | X1 = X23
      | hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).

fof(f3361,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f777,f3359]) ).

fof(f3359,plain,
    ( spl0_292
  <=> ! [X53,X1,X10] :
        ( X1 = X10
        | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f777,plain,
    ! [X10,X1,X53] :
      ( X1 = X10
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(duplicate_literal_removal,[],[f637]) ).

fof(f637,axiom,
    ! [X10,X1,X53] :
      ( X1 = X10
      | X1 = X10
      | hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).

fof(f3357,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f723,f3355]) ).

fof(f3355,plain,
    ( spl0_291
  <=> ! [X2,X0] : c_Relation_ORange(X2,X0,X0) = c_Relation_ORange(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f723,plain,
    ! [X2,X0] : c_Relation_ORange(X2,X0,X0) = c_Relation_ORange(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0,X0),
    inference(definition_unfolding,[],[f533,f574]) ).

fof(f533,axiom,
    ! [X2,X0] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X2,X0),X0,X0) = c_Relation_ORange(X2,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).

fof(f3352,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f718,f3350]) ).

fof(f3350,plain,
    ( spl0_290
  <=> ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X12,X0),X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f718,plain,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X12,X0),X0),X0,X0,X0),
    inference(definition_unfolding,[],[f543,f574]) ).

fof(f543,axiom,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X12,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

fof(f3348,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f607,f3346]) ).

fof(f3346,plain,
    ( spl0_289
  <=> ! [X4,X0,X10,X1] :
        ( X1 = X10
        | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f607,axiom,
    ! [X10,X0,X1,X4] :
      ( X1 = X10
      | ~ hBOOL(c_in(c_Pair(X1,X10,X0,X0),c_Relation_OId__on(X4,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

fof(f3344,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f575,f3342]) ).

fof(f3342,plain,
    ( spl0_288
  <=> ! [X4,X0,X6,X16] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
        | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X16,X4,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f575,axiom,
    ! [X0,X6,X16,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)) = X4
      | c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X16,X4,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

fof(f3340,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f494,f3338]) ).

fof(f3338,plain,
    ( spl0_287
  <=> ! [X4,X0,X16,X45,X1] :
        ( ~ hBOOL(c_in(X1,X4,X45))
        | hBOOL(c_in(hAPP(X16,X1),c_Set_Oimage(X16,X4,X45,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f494,axiom,
    ! [X0,X1,X45,X16,X4] :
      ( ~ hBOOL(c_in(X1,X4,X45))
      | hBOOL(c_in(hAPP(X16,X1),c_Set_Oimage(X16,X4,X45,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

fof(f3336,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f458,f3334]) ).

fof(f3334,plain,
    ( spl0_286
  <=> ! [X2,X0,X36] :
        ( ~ hBOOL(c_in(X36,X2,tc_prod(X0,X0)))
        | hBOOL(c_in(X36,c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f458,axiom,
    ! [X2,X0,X36] :
      ( ~ hBOOL(c_in(X36,X2,tc_prod(X0,X0)))
      | hBOOL(c_in(X36,c_Transitive__Closure_Ortrancl(X2,X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

fof(f3332,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f413,f3330]) ).

fof(f3330,plain,
    ( spl0_285
  <=> ! [X2,X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f413,axiom,
    ! [X2,X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).

fof(f3328,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f374,f3326]) ).

fof(f3326,plain,
    ( spl0_284
  <=> ! [X4,X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Relation_OImage(c_Relation_OId__on(X4,X0),X0,X0),X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f374,axiom,
    ! [X0,X7,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = hAPP(c_Relation_OImage(c_Relation_OId__on(X4,X0),X0,X0),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).

fof(f3324,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f371,f3322]) ).

fof(f3322,plain,
    ( spl0_283
  <=> ! [X2,X0] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_lessequals(c_Relation_Orel__comp(X2,X2,X0,X0,X0),X2,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f371,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_lessequals(c_Relation_Orel__comp(X2,X2,X0,X0,X0),X2,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

fof(f3320,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f369,f3318]) ).

fof(f3318,plain,
    ( spl0_282
  <=> ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f369,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

fof(f3316,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f368,f3314]) ).

fof(f368,axiom,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

fof(f3312,plain,
    ( spl0_280
    | ~ spl0_57
    | ~ spl0_97
    | ~ spl0_99
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2639,f2501,f1243,f1211,f1041,f3310]) ).

fof(f3310,plain,
    ( spl0_280
  <=> ! [X0,X1] : c_Relation_Oirrefl(v_F(c_COMBK(v_F(v_P),X0,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1243,plain,
    ( spl0_99
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f2639,plain,
    ( ! [X0,X1] :
        ( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(v_F(v_P),X0,X1)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_99
    | ~ spl0_237 ),
    inference(resolution,[],[f2503,f1244]) ).

fof(f1244,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f1243]) ).

fof(f3308,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f367,f3306]) ).

fof(f3306,plain,
    ( spl0_279
  <=> ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f367,axiom,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

fof(f3304,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f332,f3302]) ).

fof(f332,axiom,
    ! [X0,X1,X22,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | ~ hBOOL(c_in(X1,X22,X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X22,X12,X0),X22,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

fof(f3300,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f331,f3298]) ).

fof(f331,axiom,
    ! [X2,X0,X22,X23] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(X23,X22,X0))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X22,X2,X0),X22,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

fof(f3296,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f297,f3294]) ).

fof(f297,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ c_Relation_Osingle__valued(X3,X0,X6)
      | c_Relation_Osingle__valued(X2,X0,X6)
      | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X6),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

fof(f3292,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f258,f3290]) ).

fof(f3290,plain,
    ( spl0_275
  <=> ! [X4,X0,X28,X7] :
        ( hBOOL(c_in(X28,X4,X0))
        | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f258,axiom,
    ! [X28,X0,X7,X4] :
      ( hBOOL(c_in(X28,X4,X0))
      | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

fof(f3288,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f257,f3286]) ).

fof(f3286,plain,
    ( spl0_274
  <=> ! [X4,X0,X28,X7] :
        ( hBOOL(c_in(X28,X7,X0))
        | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f257,axiom,
    ! [X28,X0,X7,X4] :
      ( hBOOL(c_in(X28,X7,X0))
      | ~ hBOOL(c_in(X28,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

fof(f3284,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f253,f3282]) ).

fof(f3282,plain,
    ( spl0_273
  <=> ! [X4,X0,X28,X7] :
        ( hBOOL(c_in(X28,X4,X0))
        | ~ hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f253,axiom,
    ! [X28,X0,X7,X4] :
      ( hBOOL(c_in(X28,X4,X0))
      | ~ hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

fof(f3280,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f252,f3278]) ).

fof(f3278,plain,
    ( spl0_272
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X7,X0))
        | ~ hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f252,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X7,X0))
      | ~ hBOOL(c_in(X28,hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

fof(f3276,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f249,f3274]) ).

fof(f3274,plain,
    ( spl0_271
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X7,X0))
        | hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f249,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X7,X0))
      | hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

fof(f3272,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f248,f3270]) ).

fof(f3270,plain,
    ( spl0_270
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X4,X0))
        | hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f248,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X4,X0))
      | hBOOL(c_in(X28,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

fof(f3267,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f246,f3265]) ).

fof(f3265,plain,
    ( spl0_269
  <=> ! [X4,X0,X28,X7] :
        ( ~ hBOOL(c_in(X28,X4,X0))
        | hBOOL(c_in(X28,X7,X0))
        | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f246,axiom,
    ! [X28,X0,X7,X4] :
      ( ~ hBOOL(c_in(X28,X4,X0))
      | hBOOL(c_in(X28,X7,X0))
      | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

fof(f3263,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f239,f3261]) ).

fof(f239,axiom,
    ! [X0,X1,X6,X16,X17] :
      ( ~ class_HOL_Oord(X6)
      | ~ c_lessequals(X16,X17,tc_fun(X0,X6))
      | c_lessequals(hAPP(X16,X1),hAPP(X17,X1),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

fof(f3259,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f24,f3257]) ).

fof(f3257,plain,
    ( spl0_267
  <=> ! [X4,X0,X1,X7] :
        ( c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f24,axiom,
    ! [X0,X1,X7,X4] :
      ( c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

fof(f3255,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f23,f3253]) ).

fof(f3253,plain,
    ( spl0_266
  <=> ! [X4,X0,X9,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | c_lessequals(X4,hAPP(c_Set_Oinsert(X9,X0),X7),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f23,axiom,
    ! [X0,X9,X7,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | c_lessequals(X4,hAPP(c_Set_Oinsert(X9,X0),X7),tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

fof(f3233,plain,
    ( spl0_265
    | ~ spl0_57
    | ~ spl0_97
    | ~ spl0_142
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2638,f2501,f1493,f1211,f1041,f3231]) ).

fof(f3231,plain,
    ( spl0_265
  <=> ! [X0,X1] : c_Relation_Otrans(v_F(c_COMBK(v_F(v_P),X0,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f1493,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f2638,plain,
    ( ! [X0,X1] :
        ( ~ c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(v_F(v_P),X0,X1)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_142
    | ~ spl0_237 ),
    inference(resolution,[],[f2503,f1494]) ).

fof(f1494,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1493]) ).

fof(f2805,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f714,f2803]) ).

fof(f2803,plain,
    ( spl0_264
  <=> ! [X6,X2,X0] : c_Relation_ORange(X2,X6,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X2,X6,X0),X0,X6),X6,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f714,plain,
    ! [X2,X0,X6] : c_Relation_ORange(X2,X6,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X2,X6,X0),X0,X6),X6,X0),
    inference(definition_unfolding,[],[f576,f554]) ).

fof(f576,axiom,
    ! [X2,X0,X6] : c_Relation_ORange(X2,X6,X0) = c_Relation_ODomain(c_Relation_Oconverse(X2,X6,X0),X0,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).

fof(f2801,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f609,f2799]) ).

fof(f2799,plain,
    ( spl0_263
  <=> ! [X9,X5,X0] :
        ( X5 = X9
        | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f609,axiom,
    ! [X0,X9,X5] :
      ( X5 = X9
      | ~ hBOOL(c_in(c_Pair(X5,X9,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

fof(f2797,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f569,f2795]) ).

fof(f2795,plain,
    ( spl0_262
  <=> ! [X6,X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X7,X6,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f569,axiom,
    ! [X0,X6,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X7,X6,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).

fof(f2793,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f559,f2791]) ).

fof(f2791,plain,
    ( spl0_261
  <=> ! [X2,X0,X4] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f559,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X2,X0,X0),X2,X0,X0,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).

fof(f2789,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f376,f2787]) ).

fof(f376,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Oantisym(X2,X0)
      | c_Relation_Oantisym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

fof(f2785,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f373,f2783]) ).

fof(f2783,plain,
    ( spl0_259
  <=> ! [X2,X0] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Otrans(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f373,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_Relation_Otrans(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

fof(f2781,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f337,f2779]) ).

fof(f2779,plain,
    ( spl0_258
  <=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f337,axiom,
    ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

fof(f2777,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f324,f2775]) ).

fof(f2775,plain,
    ( spl0_257
  <=> ! [X9,X5,X0] :
        ( X5 = X9
        | ~ hBOOL(c_in(X9,hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f324,axiom,
    ! [X0,X9,X5] :
      ( X5 = X9
      | ~ hBOOL(c_in(X9,hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

fof(f2773,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f274,f2771]) ).

fof(f274,axiom,
    ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

fof(f2769,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f273,f2767]) ).

fof(f2767,plain,
    ( spl0_255
  <=> ! [X4,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f273,axiom,
    ! [X0,X4] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

fof(f2765,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f216,f2763]) ).

fof(f2761,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f189,f2759]) ).

fof(f2759,plain,
    ( spl0_253
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(c_in(X1,X7,X0))
        | ~ c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f189,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(c_in(X1,X7,X0))
      | ~ c_lessequals(hAPP(c_Set_Oinsert(X1,X0),X4),X7,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

fof(f2757,plain,
    ( spl0_252
    | ~ spl0_160
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f2663,f2204,f1603,f2755]) ).

fof(f2755,plain,
    ( spl0_252
  <=> ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2663,plain,
    ( ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0)
    | ~ spl0_160
    | ~ spl0_234 ),
    inference(resolution,[],[f2205,f1604]) ).

fof(f2753,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f140,f2751]) ).

fof(f2751,plain,
    ( spl0_251
  <=> ! [X4,X0] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
        | ~ c_lessequals(X4,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f140,axiom,
    ! [X0,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X4
      | ~ c_lessequals(X4,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(f2749,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f130,f2747]) ).

fof(f2747,plain,
    ( spl0_250
  <=> ! [X4,X0,X7] :
        ( c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) != X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f130,axiom,
    ! [X0,X7,X4] :
      ( c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) != X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

fof(f2745,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f129,f2743]) ).

fof(f2743,plain,
    ( spl0_249
  <=> ! [X4,X0,X7] :
        ( ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f129,axiom,
    ! [X0,X7,X4] :
      ( ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

fof(f2741,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f128,f2739]) ).

fof(f2739,plain,
    ( spl0_248
  <=> ! [X4,X0,X7] :
        ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f128,axiom,
    ! [X0,X7,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

fof(f2737,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f119,f2735]) ).

fof(f2735,plain,
    ( spl0_247
  <=> ! [X4,X0,X7] :
        ( X4 = X7
        | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
        | ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f119,axiom,
    ! [X0,X7,X4] :
      ( X4 = X7
      | ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

fof(f2733,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f106,f2731]) ).

fof(f106,axiom,
    ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

fof(f2729,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f81,f2727]) ).

fof(f2727,plain,
    ( spl0_245
  <=> ! [X4,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f81,axiom,
    ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

fof(f2725,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f80,f2723]) ).

fof(f80,axiom,
    ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

fof(f2721,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f78,f2719]) ).

fof(f2717,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f63,f2715]) ).

fof(f63,axiom,
    ! [X0,X7,X4] :
      ( ~ c_lessequals(X7,X4,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

fof(f2713,plain,
    ( spl0_241
    | ~ spl0_160
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f2632,f2164,f1603,f2711]) ).

fof(f2711,plain,
    ( spl0_241
  <=> ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f2632,plain,
    ( ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0)
    | ~ spl0_160
    | ~ spl0_226 ),
    inference(resolution,[],[f2165,f1604]) ).

fof(f2709,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f62,f2707]) ).

fof(f62,axiom,
    ! [X0,X7,X4] :
      ( ~ c_lessequals(X4,X7,tc_fun(X0,tc_bool))
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

fof(f2705,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f7,f2703]) ).

fof(f2703,plain,
    ( spl0_239
  <=> ! [X4,X0,X1] : hAPP(c_Set_Oinsert(X1,X0),X4) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X1,X0),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f7,axiom,
    ! [X0,X1,X4] : hAPP(c_Set_Oinsert(X1,X0),X4) = hAPP(c_Set_Oinsert(X1,X0),hAPP(c_Set_Oinsert(X1,X0),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f2701,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f6,f2699]) ).

fof(f2699,plain,
    ( spl0_238
  <=> ! [X4,X0,X10,X1] :
        ( X1 = X10
        | hBOOL(hAPP(X4,X1))
        | ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X10,X0),X4),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f6,axiom,
    ! [X10,X0,X1,X4] :
      ( X1 = X10
      | hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(hAPP(c_Set_Oinsert(X10,X0),X4),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

fof(f2504,plain,
    ( ~ spl0_59
    | spl0_237
    | ~ spl0_58
    | ~ spl0_15
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f1106,f1103,f869,f1045,f2501,f1049]) ).

fof(f1049,plain,
    ( spl0_59
  <=> c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1045,plain,
    ( spl0_58
  <=> c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f1106,plain,
    ( ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_15
    | ~ spl0_71 ),
    inference(resolution,[],[f1104,f870]) ).

fof(f2214,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f721,f2212]) ).

fof(f2212,plain,
    ( spl0_236
  <=> ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X12,X0),X0,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f721,plain,
    ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X12,X0),X0,X0),X0,X0),
    inference(definition_unfolding,[],[f511,f554]) ).

fof(f511,axiom,
    ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X12,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).

fof(f2210,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f719,f2208]) ).

fof(f2208,plain,
    ( spl0_235
  <=> ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f719,plain,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X12,c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),X0),
    inference(definition_unfolding,[],[f577,f574]) ).

fof(f577,axiom,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X12,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

fof(f2206,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f672,f2204]) ).

fof(f672,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Relation_Oirrefl(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

fof(f2202,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f669,f2200]) ).

fof(f2200,plain,
    ( spl0_233
  <=> ! [X9,X6,X54,X0,X55,X5] :
        ( X5 = X54
        | c_Pair(X5,X9,X0,X6) != c_Pair(X54,X55,X0,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f669,axiom,
    ! [X0,X54,X6,X9,X55,X5] :
      ( X5 = X54
      | c_Pair(X5,X9,X0,X6) != c_Pair(X54,X55,X0,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

fof(f2198,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f668,f2196]) ).

fof(f2196,plain,
    ( spl0_232
  <=> ! [X5,X55,X9,X0,X54,X6] :
        ( X9 = X55
        | c_Pair(X5,X9,X0,X6) != c_Pair(X54,X55,X0,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f668,axiom,
    ! [X0,X54,X6,X9,X55,X5] :
      ( X9 = X55
      | c_Pair(X5,X9,X0,X6) != c_Pair(X54,X55,X0,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

fof(f2194,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f667,f2192]) ).

fof(f667,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Oirrefl(X2,X0)
      | ~ c_Relation_Otrans(X2,X0)
      | ~ c_Relation_Ototal__on(X4,X2,X0)
      | c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

fof(f2190,plain,
    ( ~ spl0_230
    | ~ spl0_64
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f2182,f2178,f1071,f2187]) ).

fof(f2187,plain,
    ( spl0_230
  <=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f2178,plain,
    ( spl0_229
  <=> 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_229])]) ).

fof(f2182,plain,
    ( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
    | ~ spl0_64
    | ~ spl0_229 ),
    inference(superposition,[],[f1072,f2180]) ).

fof(f2180,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_229 ),
    inference(avatar_component_clause,[],[f2178]) ).

fof(f2181,plain,
    ( spl0_229
    | ~ spl0_12
    | ~ spl0_136
    | ~ spl0_228 ),
    inference(avatar_split_clause,[],[f2176,f2172,f1466,f854,f2178]) ).

fof(f2172,plain,
    ( spl0_228
  <=> 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_228])]) ).

fof(f2176,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_12
    | ~ spl0_136
    | ~ spl0_228 ),
    inference(forward_demodulation,[],[f2174,f1523]) ).

fof(f2174,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_228 ),
    inference(avatar_component_clause,[],[f2172]) ).

fof(f2175,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f630,f2172]) ).

fof(f630,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(f2170,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f627,f2168]) ).

fof(f627,axiom,
    ! [X0,X1,X6,X16] : hBOOL(c_in(hAPP(X16,X1),c_Set_Oimage(X16,c_Orderings_Otop__class_Otop(tc_fun(X6,tc_bool)),X6,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

fof(f2166,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f611,f2164]) ).

fof(f611,axiom,
    ! [X2,X0,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(c_Pair(X5,X5,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

fof(f2162,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f610,f2160]) ).

fof(f610,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Nitpick_Orefl_H(X2,X0)
      | hBOOL(c_in(c_Pair(X1,X1,X0,X0),X2,tc_prod(X0,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

fof(f2158,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f560,f2156]) ).

fof(f2156,plain,
    ( spl0_224
  <=> ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X0),c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f560,axiom,
    ! [X0,X12] : c_Transitive__Closure_Ortrancl(X12,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X0),c_Transitive__Closure_Ortrancl(X12,X0),X0,X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

fof(f2154,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f546,f2152]) ).

fof(f2152,plain,
    ( spl0_223
  <=> ! [X6,X0,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Relation_OImage(X12,X6,X0),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f546,axiom,
    ! [X0,X6,X12] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_Relation_OImage(X12,X6,X0),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

fof(f2150,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f372,f2148]) ).

fof(f372,axiom,
    ! [X2,X0] : c_Relation_Osym(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_Oconverse(X2,X0,X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

fof(f2146,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f342,f2144]) ).

fof(f2144,plain,
    ( spl0_221
  <=> ! [X5,X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f342,axiom,
    ! [X0,X5] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Complete__Lattice_OSup__class_OSup(hAPP(c_Set_Oinsert(X5,X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

fof(f2142,plain,
    ( spl0_220
    | ~ spl0_1
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2007,f1819,f801,f2140]) ).

fof(f2140,plain,
    ( spl0_220
  <=> ! [X0] : hAPP(v_P,X0) = c_Relation_Orel__comp(hAPP(v_P,X0),c_Transitive__Closure_Ortrancl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1819,plain,
    ( spl0_189
  <=> ! [X2,X0] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f2007,plain,
    ( ! [X0] : hAPP(v_P,X0) = c_Relation_Orel__comp(hAPP(v_P,X0),c_Transitive__Closure_Ortrancl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_1
    | ~ spl0_189 ),
    inference(resolution,[],[f1820,f802]) ).

fof(f1820,plain,
    ( ! [X2,X0] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = X2 )
    | ~ spl0_189 ),
    inference(avatar_component_clause,[],[f1819]) ).

fof(f2138,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f296,f2136]) ).

fof(f296,axiom,
    ! [X2,X3,X0] :
      ( ~ c_Wellfounded_Oacyclic(X3,X0)
      | c_Wellfounded_Oacyclic(X2,X0)
      | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

fof(f2134,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f294,f2132]) ).

fof(f2132,plain,
    ( spl0_218
  <=> ! [X2,X0,X3] :
        ( ~ c_Relation_Oantisym(X3,X0)
        | c_Relation_Oantisym(X2,X0)
        | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f294,axiom,
    ! [X2,X3,X0] :
      ( ~ c_Relation_Oantisym(X3,X0)
      | c_Relation_Oantisym(X2,X0)
      | ~ c_lessequals(X2,X3,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

fof(f2130,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f291,f2128]) ).

fof(f2128,plain,
    ( spl0_217
  <=> ! [X2,X0,X36] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | c_Wellfounded_Owf(X36,X0)
        | ~ c_lessequals(X36,X2,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f291,axiom,
    ! [X2,X0,X36] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(X36,X0)
      | ~ c_lessequals(X36,X2,tc_fun(tc_prod(X0,X0),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).

fof(f2126,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f290,f2124]) ).

fof(f2124,plain,
    ( spl0_216
  <=> ! [X15,X0,X22,X1] :
        ( ~ hBOOL(hAPP(X15,X1))
        | hBOOL(hAPP(X22,X1))
        | ~ c_lessequals(X15,X22,tc_fun(X0,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f290,axiom,
    ! [X0,X1,X15,X22] :
      ( ~ hBOOL(hAPP(X15,X1))
      | hBOOL(hAPP(X22,X1))
      | ~ c_lessequals(X15,X22,tc_fun(X0,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

fof(f2122,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f286,f2120]) ).

fof(f2120,plain,
    ( spl0_215
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X10,X0)
        | ~ c_lessequals(X10,X18,X0)
        | c_lessequals(X1,X18,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f286,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X10,X0)
      | ~ c_lessequals(X10,X18,X0)
      | c_lessequals(X1,X18,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f2118,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f285,f2116]) ).

fof(f2116,plain,
    ( spl0_214
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X10,X1,X0)
        | ~ c_lessequals(X18,X10,X0)
        | c_lessequals(X18,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f285,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X10,X1,X0)
      | ~ c_lessequals(X18,X10,X0)
      | c_lessequals(X18,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f2114,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f279,f2112]) ).

fof(f2112,plain,
    ( spl0_213
  <=> ! [X9,X0,X5,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X5,X0)
        | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f279,axiom,
    ! [X0,X1,X9,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X5,X0)
      | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

fof(f2110,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f267,f2108]) ).

fof(f2108,plain,
    ( spl0_212
  <=> ! [X4,X0,X7] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = X7
        | c_Orderings_Otop__class_Otop(X0) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X0),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f267,axiom,
    ! [X0,X7,X4] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = X7
      | c_Orderings_Otop__class_Otop(X0) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X0),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

fof(f2106,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f266,f2104]) ).

fof(f2104,plain,
    ( spl0_211
  <=> ! [X4,X0,X7] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = X4
        | c_Orderings_Otop__class_Otop(X0) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X0),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f266,axiom,
    ! [X0,X7,X4] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = X4
      | c_Orderings_Otop__class_Otop(X0) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,X0),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

fof(f2102,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f243,f2100]) ).

fof(f2100,plain,
    ( spl0_210
  <=> ! [X9,X0,X5,X7] :
        ( ~ hBOOL(c_in(X5,X7,X0))
        | hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X9,X0),X7),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f243,axiom,
    ! [X0,X9,X7,X5] :
      ( ~ hBOOL(c_in(X5,X7,X0))
      | hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X9,X0),X7),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

fof(f2095,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f232,f2093]) ).

fof(f2093,plain,
    ( spl0_209
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(hAPP(X4,X1))
        | ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f232,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(hAPP(X4,X1))
      | ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

fof(f2091,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f231,f2089]) ).

fof(f2089,plain,
    ( spl0_208
  <=> ! [X4,X0,X1,X7] :
        ( hBOOL(hAPP(X7,X1))
        | ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f231,axiom,
    ! [X0,X1,X7,X4] :
      ( hBOOL(hAPP(X7,X1))
      | ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

fof(f2087,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f227,f2085]) ).

fof(f2085,plain,
    ( spl0_207
  <=> ! [X15,X0,X5,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X5))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X15,X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f227,axiom,
    ! [X2,X0,X15,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X5))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X15,X2,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

fof(f2083,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f214,f2081]) ).

fof(f2081,plain,
    ( spl0_206
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X18,X0)
        | ~ c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f214,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X18,X0)
      | ~ c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

fof(f2079,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f213,f2077]) ).

fof(f2077,plain,
    ( spl0_205
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X10,X0)
        | ~ c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f213,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X10,X0)
      | ~ c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X18),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

fof(f2075,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f212,f2073]) ).

fof(f2073,plain,
    ( spl0_204
  <=> ! [X5,X9,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X9,X1,X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X0),X9),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f212,axiom,
    ! [X0,X1,X9,X5] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X9,X1,X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X0),X9),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

fof(f2071,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f211,f2069]) ).

fof(f2069,plain,
    ( spl0_203
  <=> ! [X9,X0,X5,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X5,X1,X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X0),X9),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f211,axiom,
    ! [X0,X1,X9,X5] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X5,X1,X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,X0),X9),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

fof(f2067,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f201,f2065]) ).

fof(f2065,plain,
    ( spl0_202
  <=> ! [X4,X0,X7] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = X7
        | c_Orderings_Obot__class_Obot(X0) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X0),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f201,axiom,
    ! [X0,X7,X4] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = X7
      | c_Orderings_Obot__class_Obot(X0) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X0),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

fof(f2063,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f200,f2061]) ).

fof(f2061,plain,
    ( spl0_201
  <=> ! [X4,X0,X7] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = X4
        | c_Orderings_Obot__class_Obot(X0) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X0),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f200,axiom,
    ! [X0,X7,X4] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = X4
      | c_Orderings_Obot__class_Obot(X0) != hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,X0),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

fof(f2059,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f178,f2057]) ).

fof(f2057,plain,
    ( spl0_200
  <=> ! [X9,X0,X5,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X9,X0)
        | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f178,axiom,
    ! [X0,X1,X9,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X9,X0)
      | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X5,X0),X9),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

fof(f2055,plain,
    ( spl0_199
    | ~ spl0_57
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2014,f1819,f1041,f2052]) ).

fof(f2014,plain,
    ( v_F(v_P) = c_Relation_Orel__comp(v_F(v_P),c_Transitive__Closure_Ortrancl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_57
    | ~ spl0_189 ),
    inference(resolution,[],[f1820,f1043]) ).

fof(f1043,plain,
    ( c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1041]) ).

fof(f2050,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f177,f2048]) ).

fof(f2048,plain,
    ( spl0_198
  <=> ! [X18,X0,X10,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,X18,X0)
        | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X18,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f177,axiom,
    ! [X10,X0,X1,X18] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,X18,X0)
      | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X18,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

fof(f2046,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f176,f2044]) ).

fof(f2044,plain,
    ( spl0_197
  <=> ! [X18,X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X10,X18,X0)
        | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X18,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f176,axiom,
    ! [X10,X0,X18,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X10,X18,X0)
      | ~ c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X18,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

fof(f2042,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f115,f2040]) ).

fof(f2040,plain,
    ( spl0_196
  <=> ! [X15,X0,X30,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X30))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X15,X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f115,axiom,
    ! [X2,X0,X15,X30] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X30))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X15,X2,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).

fof(f2038,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f94,f2036]) ).

fof(f94,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

fof(f2034,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f93,f2032]) ).

fof(f2032,plain,
    ( spl0_194
  <=> ! [X4,X0,X1,X7] :
        ( ~ hBOOL(hAPP(X7,X1))
        | hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f93,axiom,
    ! [X0,X1,X7,X4] :
      ( ~ hBOOL(hAPP(X7,X1))
      | hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

fof(f2030,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f47,f2028]) ).

fof(f2028,plain,
    ( spl0_193
  <=> ! [X15,X6,X14,X0,X12,X22] : hAPP(c_COMBB(X15,X22,X6,X0,X14),X12) = hAPP(X15,hAPP(X22,X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f47,axiom,
    ! [X0,X6,X14,X15,X22,X12] : hAPP(c_COMBB(X15,X22,X6,X0,X14),X12) = hAPP(X15,hAPP(X22,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

fof(f2026,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f45,f2024]) ).

fof(f2024,plain,
    ( spl0_192
  <=> ! [X15,X0,X12,X21] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | hBOOL(hAPP(X15,X21))
        | ~ hBOOL(hAPP(X15,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X15,X12,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f45,axiom,
    ! [X21,X0,X15,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | hBOOL(hAPP(X15,X21))
      | ~ hBOOL(hAPP(X15,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X15,X12,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

fof(f2022,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f21,f2020]) ).

fof(f2020,plain,
    ( spl0_191
  <=> ! [X15,X0,X5,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | hBOOL(hAPP(X15,X5))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X15,X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f21,axiom,
    ! [X2,X0,X15,X5] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(hAPP(X15,X5))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X15,X2,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).

fof(f1967,plain,
    ( spl0_190
    | ~ spl0_15
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1639,f1493,f869,f1965]) ).

fof(f1965,plain,
    ( spl0_190
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(hAPP(v_P,X0),X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1639,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(hAPP(v_P,X0),X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_15
    | ~ spl0_142 ),
    inference(resolution,[],[f1494,f870]) ).

fof(f1821,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f737,f1819]) ).

fof(f737,plain,
    ! [X2,X0] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0) = X2 ),
    inference(definition_unfolding,[],[f469,f574]) ).

fof(f469,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_Transitive__Closure_Otrancl(X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

fof(f1817,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f736,f1815]) ).

fof(f1815,plain,
    ( spl0_188
  <=> ! [X2,X0] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | c_Wellfounded_Owf(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f736,plain,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0) ),
    inference(definition_unfolding,[],[f545,f574]) ).

fof(f545,axiom,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

fof(f1813,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f735,f1811]) ).

fof(f1811,plain,
    ( spl0_187
  <=> ! [X2,X0] :
        ( ~ c_Relation_Osym(X2,X0)
        | c_Relation_Osym(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f735,plain,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Osym(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0) ),
    inference(definition_unfolding,[],[f508,f574]) ).

fof(f508,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Osym(c_Transitive__Closure_Otrancl(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

fof(f1809,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f639,f1807]) ).

fof(f639,axiom,
    ! [X1,X53,X23] : ~ hBOOL(c_in(c_Pair(X23,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).

fof(f1805,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f635,f1803]) ).

fof(f635,axiom,
    ! [X10,X1,X53] : ~ hBOOL(c_in(c_Pair(X1,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).

fof(f1801,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f625,f1799]) ).

fof(f1799,plain,
    ( spl0_184
  <=> ! [X4,X0] :
        ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X4
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X4,X0),X4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f625,axiom,
    ! [X0,X4] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X4
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X4,X0),X4,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).

fof(f1797,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f602,f1795]) ).

fof(f602,axiom,
    ! [X0,X1,X12] : hBOOL(c_in(c_Pair(X1,X1,X0,X0),c_Transitive__Closure_Ortrancl(X12,X0),tc_prod(X0,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).

fof(f1793,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f566,f1791]) ).

fof(f1789,plain,
    ( ~ spl0_181
    | ~ spl0_108
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1740,f1679,f1305,f1786]) ).

fof(f1786,plain,
    ( spl0_181
  <=> hAPP(v_P,v_i) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1679,plain,
    ( spl0_163
  <=> hAPP(v_P,v_i) = hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f1740,plain,
    ( hAPP(v_P,v_i) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_108
    | ~ spl0_163 ),
    inference(superposition,[],[f1306,f1681]) ).

fof(f1681,plain,
    ( hAPP(v_P,v_i) = hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i))
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1679]) ).

fof(f1784,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f529,f1782]) ).

fof(f1782,plain,
    ( spl0_180
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0) != c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f529,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0) != c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_3) ).

fof(f1780,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f513,f1778]) ).

fof(f1778,plain,
    ( spl0_179
  <=> ! [X6,X0,X16] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X16,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f513,axiom,
    ! [X0,X6,X16] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X16,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

fof(f1776,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f329,f1774]) ).

fof(f1774,plain,
    ( spl0_178
  <=> ! [X4,X0,X1] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | ~ hBOOL(c_in(X1,X4,X0))
        | c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f329,axiom,
    ! [X0,X1,X4] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | ~ hBOOL(c_in(X1,X4,X0))
      | c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

fof(f1772,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f218,f1770]) ).

fof(f1770,plain,
    ( spl0_177
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f218,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f1768,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f217,f1766]) ).

fof(f1766,plain,
    ( spl0_176
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f217,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f1764,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f180,f1762]) ).

fof(f1762,plain,
    ( spl0_175
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f180,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f1760,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f179,f1758]) ).

fof(f1758,plain,
    ( spl0_174
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f179,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f1756,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f127,f1754]) ).

fof(f1754,plain,
    ( spl0_173
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X1,X10,X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = X10 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f127,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X1,X10,X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

fof(f1752,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f126,f1750]) ).

fof(f1750,plain,
    ( spl0_172
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,X10,X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) != X10 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f126,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,X10,X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) != X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

fof(f1748,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f125,f1746]) ).

fof(f1746,plain,
    ( spl0_171
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ c_lessequals(X10,X1,X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f125,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | ~ c_lessequals(X10,X1,X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

fof(f1738,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f123,f1736]) ).

fof(f1736,plain,
    ( spl0_170
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f123,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f1734,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f122,f1732]) ).

fof(f1732,plain,
    ( spl0_169
  <=> ! [X0,X1,X10] :
        ( ~ class_Orderings_Oorder(X0)
        | X1 = X10
        | ~ c_lessequals(X10,X1,X0)
        | ~ c_lessequals(X1,X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f122,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | X1 = X10
      | ~ c_lessequals(X10,X1,X0)
      | ~ c_lessequals(X1,X10,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

fof(f1730,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f114,f1728]) ).

fof(f1728,plain,
    ( spl0_168
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f114,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f1726,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f66,f1724]) ).

fof(f1724,plain,
    ( spl0_167
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X10,X1,X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = X10 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f66,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X10,X1,X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = X10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

fof(f1722,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f65,f1720]) ).

fof(f1720,plain,
    ( spl0_166
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(X1,X10,X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f65,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(X1,X10,X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

fof(f1718,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f64,f1716]) ).

fof(f1716,plain,
    ( spl0_165
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | ~ c_lessequals(X1,X10,X0)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f64,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | ~ c_lessequals(X1,X10,X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

fof(f1692,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f687,f1690]) ).

fof(f687,axiom,
    ! [X9,X15,X5] :
      ( X5 = X9
      | ~ c_Relation_Oirrefl(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X15,v_Pa(X15)),tc_Arrow__Order__Mirabelle_Oalt)
      | hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(X5,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X15,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).

fof(f1682,plain,
    ( spl0_163
    | ~ spl0_17
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1646,f1579,f878,f1679]) ).

fof(f1646,plain,
    ( hAPP(v_P,v_i) = hAPP(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_P,v_i))
    | ~ spl0_17
    | ~ spl0_154 ),
    inference(resolution,[],[f1580,f880]) ).

fof(f1613,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f645,f1611]) ).

fof(f1611,plain,
    ( spl0_162
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),X4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f645,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2(X4,X2,X0),X4,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_2) ).

fof(f1609,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f644,f1607]) ).

fof(f1607,plain,
    ( spl0_161
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),X4,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f644,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1(X4,X2,X0),X4,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_1) ).

fof(f1605,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f620,f1603]) ).

fof(f620,axiom,
    ! [X0,X5] : hBOOL(c_in(c_Pair(X5,X5,X0,X0),c_Relation_OId(X0),tc_prod(X0,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).

fof(f1601,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f405,f1599]) ).

fof(f1599,plain,
    ( spl0_159
  <=> ! [X2,X0] :
        ( c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f405,axiom,
    ! [X2,X0] :
      ( c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

fof(f1597,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f404,f1595]) ).

fof(f1595,plain,
    ( spl0_158
  <=> ! [X2,X0] :
        ( c_Wellfounded_Owf(X2,X0)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f404,axiom,
    ! [X2,X0] :
      ( c_Wellfounded_Owf(X2,X0)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X2,X0),c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

fof(f1593,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f277,f1591]) ).

fof(f277,axiom,
    ! [X2,X0] : c_Relation_Oirrefl(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(tc_prod(X0,X0),tc_bool)),c_Relation_OId(X0)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

fof(f1589,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f272,f1587]) ).

fof(f1587,plain,
    ( spl0_156
  <=> ! [X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f272,axiom,
    ! [X0,X7] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) = X7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

fof(f1585,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f271,f1583]) ).

fof(f1583,plain,
    ( spl0_155
  <=> ! [X4,X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f271,axiom,
    ! [X0,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

fof(f1581,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f262,f1579]) ).

fof(f262,axiom,
    ! [X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X0))
      | hAPP(c_Set_Oinsert(X5,X0),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f1577,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f191,f1575]) ).

fof(f1575,plain,
    ( spl0_153
  <=> ! [X4,X0,X1,X10] :
        ( ~ hBOOL(hAPP(X4,X1))
        | hBOOL(hAPP(hAPP(c_Set_Oinsert(X10,X0),X4),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f191,axiom,
    ! [X10,X0,X1,X4] :
      ( ~ hBOOL(hAPP(X4,X1))
      | hBOOL(hAPP(hAPP(c_Set_Oinsert(X10,X0),X4),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f1573,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f185,f1571]) ).

fof(f1571,plain,
    ( spl0_152
  <=> ! [X4,X0,X7] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X4,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f185,axiom,
    ! [X0,X7,X4] : c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X7),X4,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f1569,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f156,f1567]) ).

fof(f1567,plain,
    ( spl0_151
  <=> ! [X4,X0,X7] : c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X7,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f156,axiom,
    ! [X0,X7,X4] : c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X7,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

fof(f1565,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f155,f1563]) ).

fof(f1563,plain,
    ( spl0_150
  <=> ! [X4,X0,X7] : c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X4,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f155,axiom,
    ! [X0,X7,X4] : c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X7),X4,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

fof(f1561,plain,
    ( spl0_149
    | ~ spl0_15
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f1525,f1243,f869,f1559]) ).

fof(f1559,plain,
    ( spl0_149
  <=> ! [X2,X0,X1] :
        ( ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(hAPP(v_P,X0),X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1525,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Oirrefl(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(hAPP(v_P,X0),tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(hAPP(v_P,X0),X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_15
    | ~ spl0_99 ),
    inference(resolution,[],[f1244,f870]) ).

fof(f1557,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f105,f1555]) ).

fof(f1555,plain,
    ( spl0_148
  <=> ! [X4,X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f105,axiom,
    ! [X0,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

fof(f1553,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f104,f1551]) ).

fof(f1551,plain,
    ( spl0_147
  <=> ! [X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f104,axiom,
    ! [X0,X7] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X7) = X7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

fof(f1549,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f89,f1547]) ).

fof(f89,axiom,
    ! [X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f1545,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f88,f1543]) ).

fof(f1543,plain,
    ( spl0_145
  <=> ! [X4,X0] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f88,axiom,
    ! [X0,X4] : hAPP(c_HOL_Ominus__class_Ominus(X4,tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f1541,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f69,f1539]) ).

fof(f69,axiom,
    ! [X0,X7,X4] : c_lessequals(X4,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

fof(f1537,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f68,f1535]) ).

fof(f1535,plain,
    ( spl0_143
  <=> ! [X4,X0,X7] : c_lessequals(X7,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f68,axiom,
    ! [X0,X7,X4] : c_lessequals(X7,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

fof(f1495,plain,
    ( spl0_142
    | ~ spl0_55
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f1099,f1055,f1032,f1493]) ).

fof(f1099,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Otrans(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_55
    | ~ spl0_60 ),
    inference(superposition,[],[f1033,f1056]) ).

fof(f1488,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f717,f1486]) ).

fof(f1486,plain,
    ( spl0_141
  <=> ! [X4,X0] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X4,X0),X0,X0),X0,X0) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f717,plain,
    ! [X0,X4] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X4,X0),X0,X0),X0,X0) = X4,
    inference(definition_unfolding,[],[f530,f554]) ).

fof(f530,axiom,
    ! [X0,X4] : c_Relation_ODomain(c_Relation_OId__on(X4,X0),X0,X0) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

fof(f1484,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f673,f1482]) ).

fof(f673,axiom,
    ! [X6] :
      ( ~ class_Orderings_Otop(X6)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X6)),v_x) = c_Orderings_Otop__class_Otop(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

fof(f1480,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f631,f1478]) ).

fof(f631,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(f1476,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f565,f1474]) ).

fof(f1474,plain,
    ( spl0_138
  <=> ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X12,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f565,axiom,
    ! [X0,X12] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X12,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).

fof(f1472,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f550,f1470]) ).

fof(f550,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(f1468,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f540,f1466]) ).

fof(f540,axiom,
    ! [X6] :
      ( ~ class_Orderings_Obot(X6)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X6)),v_x) = c_Orderings_Obot__class_Obot(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f1464,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f524,f1462]) ).

fof(f1462,plain,
    ( spl0_135
  <=> ! [X0,X12] :
        ( c_Wellfounded_Owf(X12,X0)
        | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X0,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f524,axiom,
    ! [X0,X12] :
      ( c_Wellfounded_Owf(X12,X0)
      | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X0,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

fof(f1460,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f523,f1458]) ).

fof(f1458,plain,
    ( spl0_134
  <=> ! [X0,X12] :
        ( ~ c_Wellfounded_Owf(X12,X0)
        | c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X0,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f523,axiom,
    ! [X0,X12] :
      ( ~ c_Wellfounded_Owf(X12,X0)
      | c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X0,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

fof(f1456,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f521,f1454]) ).

fof(f1454,plain,
    ( spl0_133
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Orefl__on(X4,X2,X0)
        | c_Relation_Orefl__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f521,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Orefl__on(X4,X2,X0)
      | c_Relation_Orefl__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

fof(f1451,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f520,f1449]) ).

fof(f1449,plain,
    ( spl0_132
  <=> ! [X2,X0,X4] :
        ( c_Relation_Orefl__on(X4,X2,X0)
        | ~ c_Relation_Orefl__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f520,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Orefl__on(X4,X2,X0)
      | ~ c_Relation_Orefl__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

fof(f1447,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f471,f1445]) ).

fof(f1445,plain,
    ( spl0_131
  <=> ! [X2,X0,X4] :
        ( c_Relation_Ototal__on(X4,X2,X0)
        | ~ c_Relation_Ototal__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f471,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Ototal__on(X4,X2,X0)
      | ~ c_Relation_Ototal__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

fof(f1443,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f470,f1441]) ).

fof(f1441,plain,
    ( spl0_130
  <=> ! [X2,X0,X4] :
        ( ~ c_Relation_Ototal__on(X4,X2,X0)
        | c_Relation_Ototal__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f470,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Relation_Ototal__on(X4,X2,X0)
      | c_Relation_Ototal__on(X4,c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

fof(f1439,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f269,f1437]) ).

fof(f269,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Otop__class_Otop(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

fof(f1435,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f268,f1433]) ).

fof(f268,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

fof(f1431,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f79,f1429]) ).

fof(f79,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f1427,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f1,f1425]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Obot__class_Obot(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f1404,plain,
    ( spl0_125
    | ~ spl0_117
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1392,f1369,f1341,f1402]) ).

fof(f1392,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(v_P,v_i),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(hAPP(v_P,v_i),X0)))
    | ~ spl0_117
    | ~ spl0_124 ),
    inference(resolution,[],[f1342,f1371]) ).

fof(f1372,plain,
    ( spl0_124
    | ~ spl0_17
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1267,f1216,f878,f1369]) ).

fof(f1267,plain,
    ( hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_17
    | ~ spl0_98 ),
    inference(resolution,[],[f1217,f880]) ).

fof(f1367,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f716,f1365]) ).

fof(f1365,plain,
    ( spl0_123
  <=> ! [X2,X0] : c_Relation_Otrans(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f716,plain,
    ! [X2,X0] : c_Relation_Otrans(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X0),X0,X0,X0),X0),
    inference(definition_unfolding,[],[f467,f574]) ).

fof(f467,axiom,
    ! [X2,X0] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X2,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

fof(f1363,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f571,f1361]) ).

fof(f1361,plain,
    ( spl0_122
  <=> ! [X0,X30,X15] :
        ( hBOOL(hAPP(X15,X30))
        | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(X15,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f571,axiom,
    ! [X0,X15,X30] :
      ( hBOOL(hAPP(X15,X30))
      | ~ hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1(X15,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_1) ).

fof(f1359,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f551,f1357]) ).

fof(f1357,plain,
    ( spl0_121
  <=> ! [X4,X0] : c_Relation_OId__on(X4,X0) = c_Relation_Oconverse(c_Relation_OId__on(X4,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f551,axiom,
    ! [X0,X4] : c_Relation_OId__on(X4,X0) = c_Relation_Oconverse(c_Relation_OId__on(X4,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

fof(f1355,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f541,f1353]) ).

fof(f1353,plain,
    ( spl0_120
  <=> ! [X16,X0,X6,X2] :
        ( ~ c_Relation_Osym(X2,X0)
        | c_Relation_Osym(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f541,axiom,
    ! [X2,X0,X6,X16] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Osym(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

fof(f1351,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f538,f1349]) ).

fof(f538,axiom,
    ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id_0) ).

fof(f1347,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f537,f1345]) ).

fof(f1345,plain,
    ( spl0_118
  <=> ! [X16,X0,X6,X2] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | c_Wellfounded_Owf(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f537,axiom,
    ! [X2,X0,X6,X16] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Owf(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

fof(f1343,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f515,f1341]) ).

fof(f515,axiom,
    ! [X0,X1,X15] :
      ( ~ hBOOL(hAPP(X15,X1))
      | hBOOL(hAPP(X15,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X15,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).

fof(f1339,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f506,f1337]) ).

fof(f506,axiom,
    ! [X2,X0,X1] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | hBOOL(c_in(X1,c_Wellfounded_Oacc(X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

fof(f1335,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f463,f1333]) ).

fof(f1333,plain,
    ( spl0_115
  <=> ! [X16,X0,X6,X2] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Otrans(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f463,axiom,
    ! [X2,X0,X6,X16] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_Relation_Otrans(c_Relation_Oinv__image(X2,X16,X0,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

fof(f1331,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f265,f1329]) ).

fof(f265,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),c_Orderings_Otop__class_Otop(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

fof(f1327,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f264,f1325]) ).

fof(f264,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

fof(f1323,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f154,f1321]) ).

fof(f1321,plain,
    ( spl0_112
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f154,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f1319,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f153,f1317]) ).

fof(f1317,plain,
    ( spl0_111
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f153,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X10,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f1315,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f149,f1313]) ).

fof(f1313,plain,
    ( spl0_110
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f149,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X10,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f1311,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f148,f1309]) ).

fof(f1309,plain,
    ( spl0_109
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f148,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X10),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f1307,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f142,f1305]) ).

fof(f142,axiom,
    ! [X0,X4,X5] : hAPP(c_Set_Oinsert(X5,X0),X4) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

fof(f1303,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f103,f1301]) ).

fof(f103,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1299,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f102,f1297]) ).

fof(f102,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),c_Orderings_Obot__class_Obot(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1295,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f82,f1293]) ).

fof(f1293,plain,
    ( spl0_105
  <=> ! [X5,X0,X7] : c_lessequals(X7,hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f82,axiom,
    ! [X0,X7,X5] : c_lessequals(X7,hAPP(c_Set_Oinsert(X5,X0),X7),tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1291,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f77,f1289]) ).

fof(f1289,plain,
    ( spl0_104
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f77,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1287,plain,
    ( ~ spl0_103
    | spl0_16
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1265,f1207,f873,f1284]) ).

fof(f1265,plain,
    ( ~ hBOOL(hAPP(v_F(v_P),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_16
    | ~ spl0_96 ),
    inference(resolution,[],[f1208,f875]) ).

fof(f1282,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f76,f1280]) ).

fof(f1280,plain,
    ( spl0_102
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X10,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f76,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X10,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1278,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f73,f1276]) ).

fof(f1276,plain,
    ( spl0_101
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X10,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f73,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X10,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1274,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f72,f1272]) ).

fof(f1272,plain,
    ( spl0_100
  <=> ! [X0,X1,X10] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f72,axiom,
    ! [X10,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X10),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1245,plain,
    ( spl0_99
    | ~ spl0_56
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f1098,f1055,f1036,f1243]) ).

fof(f1098,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Oirrefl(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ c_Relation_Otrans(X0,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_Oirrefl(v_F(c_COMBK(X0,X1,X2)),tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_56
    | ~ spl0_60 ),
    inference(superposition,[],[f1037,f1056]) ).

fof(f1218,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f678,f1216]) ).

fof(f678,axiom,
    ! [X0,X1,X13] :
      ( hBOOL(hAPP(X13,X1))
      | ~ hBOOL(c_in(X1,X13,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1214,plain,
    ( spl0_97
    | ~ spl0_58
    | ~ spl0_59
    | ~ spl0_15
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f1053,f1036,f869,f1049,f1045,f1211]) ).

fof(f1053,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_15
    | ~ spl0_56 ),
    inference(resolution,[],[f1037,f870]) ).

fof(f1209,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f677,f1207]) ).

fof(f677,axiom,
    ! [X0,X1,X13] :
      ( ~ hBOOL(hAPP(X13,X1))
      | hBOOL(c_in(X1,X13,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1205,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f578,f1203]) ).

fof(f578,axiom,
    ! [X2,X0] : c_Transitive__Closure_Ortrancl(X2,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

fof(f1201,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f562,f1199]) ).

fof(f1199,plain,
    ( spl0_94
  <=> ! [X2,X0] :
        ( ~ c_Relation_Oantisym(X2,X0)
        | c_Relation_Oantisym(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f562,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Oantisym(X2,X0)
      | c_Relation_Oantisym(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

fof(f1197,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f561,f1195]) ).

fof(f1195,plain,
    ( spl0_93
  <=> ! [X2,X0] :
        ( c_Relation_Oantisym(X2,X0)
        | ~ c_Relation_Oantisym(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f561,axiom,
    ! [X2,X0] :
      ( c_Relation_Oantisym(X2,X0)
      | ~ c_Relation_Oantisym(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

fof(f1193,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f558,f1191]) ).

fof(f1191,plain,
    ( spl0_92
  <=> ! [X2,X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f558,axiom,
    ! [X2,X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Transitive__Closure_Ortrancl(X2,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).

fof(f1189,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f557,f1187]) ).

fof(f1187,plain,
    ( spl0_91
  <=> ! [X6,X2,X0] : c_Relation_Oconverse(c_Relation_Oconverse(X2,X0,X6),X6,X0) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f557,axiom,
    ! [X2,X0,X6] : c_Relation_Oconverse(c_Relation_Oconverse(X2,X0,X6),X6,X0) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

fof(f1185,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f532,f1183]) ).

fof(f1183,plain,
    ( spl0_90
  <=> ! [X2,X0] :
        ( c_Relation_Osym(X2,X0)
        | c_Relation_Oconverse(X2,X0,X0) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f532,axiom,
    ! [X2,X0] :
      ( c_Relation_Osym(X2,X0)
      | c_Relation_Oconverse(X2,X0,X0) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

fof(f1181,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f531,f1179]) ).

fof(f1179,plain,
    ( spl0_89
  <=> ! [X2,X0] :
        ( ~ c_Relation_Osym(X2,X0)
        | c_Relation_Oconverse(X2,X0,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f531,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Oconverse(X2,X0,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

fof(f1177,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f525,f1175]) ).

fof(f525,axiom,
    ! [X0,X4] : hAPP(c_Relation_OImage(c_Relation_OId(X0),X0,X0),X4) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).

fof(f1173,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f517,f1171]) ).

fof(f1171,plain,
    ( spl0_87
  <=> ! [X6,X0,X12] : c_Relation_Orel__comp(X12,c_Relation_OId(X6),X0,X6,X6) = X12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f517,axiom,
    ! [X0,X6,X12] : c_Relation_Orel__comp(X12,c_Relation_OId(X6),X0,X6,X6) = X12,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

fof(f1169,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f516,f1167]) ).

fof(f516,axiom,
    ! [X0,X6,X12] : c_Relation_Orel__comp(c_Relation_OId(X0),X12,X0,X0,X6) = X12,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

fof(f1165,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f510,f1163]) ).

fof(f1163,plain,
    ( spl0_85
  <=> ! [X2,X0] :
        ( ~ c_Relation_Osym(X2,X0)
        | c_Relation_Osym(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f510,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Osym(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

fof(f1161,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f509,f1159]) ).

fof(f1159,plain,
    ( spl0_84
  <=> ! [X2,X0] :
        ( c_Relation_Osym(X2,X0)
        | ~ c_Relation_Osym(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f509,axiom,
    ! [X2,X0] :
      ( c_Relation_Osym(X2,X0)
      | ~ c_Relation_Osym(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

fof(f1157,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f465,f1155]) ).

fof(f1155,plain,
    ( spl0_83
  <=> ! [X2,X0] :
        ( c_Relation_Otrans(X2,X0)
        | ~ c_Relation_Otrans(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f465,axiom,
    ! [X2,X0] :
      ( c_Relation_Otrans(X2,X0)
      | ~ c_Relation_Otrans(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

fof(f1153,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f464,f1151]) ).

fof(f1151,plain,
    ( spl0_82
  <=> ! [X2,X0] :
        ( ~ c_Relation_Otrans(X2,X0)
        | c_Relation_Otrans(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f464,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Otrans(X2,X0)
      | c_Relation_Otrans(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

fof(f1149,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f459,f1147]) ).

fof(f1147,plain,
    ( spl0_81
  <=> ! [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_81])]) ).

fof(f459,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(f1145,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f270,f1143]) ).

fof(f1143,plain,
    ( spl0_80
  <=> ! [X4,X0] : c_lessequals(X4,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f270,axiom,
    ! [X0,X4] : c_lessequals(X4,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(f1141,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f255,f1139]) ).

fof(f255,axiom,
    ! [X0,X7,X5] : hBOOL(c_in(X5,hAPP(c_Set_Oinsert(X5,X0),X7),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

fof(f1137,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f175,f1135]) ).

fof(f1135,plain,
    ( spl0_78
  <=> ! [X4,X0] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X4) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f175,axiom,
    ! [X0,X4] : hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X0,tc_bool)),X4) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1133,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f174,f1131]) ).

fof(f174,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1129,plain,
    ( ~ spl0_2
    | spl0_59 ),
    inference(avatar_contradiction_clause,[],[f1128]) ).

fof(f1128,plain,
    ( $false
    | ~ spl0_2
    | spl0_59 ),
    inference(resolution,[],[f1051,f806]) ).

fof(f1051,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_59 ),
    inference(avatar_component_clause,[],[f1049]) ).

fof(f1127,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f117,f1125]) ).

fof(f1125,plain,
    ( spl0_76
  <=> ! [X2,X0] :
        ( ~ c_Wellfounded_Oacyclic(X2,X0)
        | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f117,axiom,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Oacyclic(X2,X0)
      | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

fof(f1123,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f116,f1121]) ).

fof(f1121,plain,
    ( spl0_75
  <=> ! [X2,X0] :
        ( c_Wellfounded_Oacyclic(X2,X0)
        | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X2,X0,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f116,axiom,
    ! [X2,X0] :
      ( c_Wellfounded_Oacyclic(X2,X0)
      | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X2,X0,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

fof(f1119,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f41,f1117]) ).

fof(f41,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1115,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f40,f1113]) ).

fof(f1113,plain,
    ( spl0_73
  <=> ! [X4,X0] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X4) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f40,axiom,
    ! [X0,X4] : hAPP(c_Lattices_Oupper__semilattice__class_Osup(X4,tc_fun(X0,tc_bool)),X4) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f1111,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f14,f1109]) ).

fof(f1109,plain,
    ( spl0_72
  <=> ! [X4,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f14,axiom,
    ! [X0,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X4,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1105,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f686,f1103]) ).

fof(f686,axiom,
    ! [X23] :
      ( ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).

fof(f1101,plain,
    ( ~ spl0_1
    | spl0_58 ),
    inference(avatar_contradiction_clause,[],[f1100]) ).

fof(f1100,plain,
    ( $false
    | ~ spl0_1
    | spl0_58 ),
    inference(resolution,[],[f1047,f802]) ).

fof(f1047,plain,
    ( ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_58 ),
    inference(avatar_component_clause,[],[f1045]) ).

fof(f1097,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f675,f1095]) ).

fof(f675,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(f1093,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f567,f1091]) ).

fof(f1091,plain,
    ( spl0_69
  <=> ! [X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f567,axiom,
    ! [X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__Id_0) ).

fof(f1089,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f564,f1087]) ).

fof(f1087,plain,
    ( spl0_68
  <=> ! [X2,X0,X4] :
        ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
        | c_Relation_Orefl__on(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f564,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Equiv__Relations_Oequiv(X4,X2,X0)
      | c_Relation_Orefl__on(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

fof(f1085,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f555,f1083]) ).

fof(f1083,plain,
    ( spl0_67
  <=> ! [X4,X0] : c_Relation_ORange(c_Relation_OId__on(X4,X0),X0,X0) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f555,axiom,
    ! [X0,X4] : c_Relation_ORange(c_Relation_OId__on(X4,X0),X0,X0) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

fof(f1081,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f544,f1079]) ).

fof(f544,axiom,
    ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).

fof(f1077,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f522,f1075]) ).

fof(f1075,plain,
    ( spl0_65
  <=> ! [X2,X0] :
        ( ~ c_Relation_Osym(X2,X0)
        | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f522,axiom,
    ! [X2,X0] :
      ( ~ c_Relation_Osym(X2,X0)
      | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

fof(f1073,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f502,f1071]) ).

fof(f502,axiom,
    ! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

fof(f1069,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f473,f1067]) ).

fof(f1067,plain,
    ( spl0_63
  <=> ! [X2,X0,X4] :
        ( ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0)
        | c_Relation_Ototal__on(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f473,axiom,
    ! [X2,X0,X4] :
      ( ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0)
      | c_Relation_Ototal__on(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

fof(f1065,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f370,f1063]) ).

fof(f370,axiom,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Oacyclic(X2,X0)
      | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

fof(f1061,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f165,f1059]) ).

fof(f165,axiom,
    ! [X0,X1,X4] : hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X0),X4),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f1057,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f48,f1055]) ).

fof(f48,axiom,
    ! [X0,X6,X15,X22] : hAPP(c_COMBK(X15,X0,X6),X22) = X15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1052,plain,
    ( spl0_57
    | ~ spl0_58
    | ~ spl0_59
    | ~ spl0_15
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f1039,f1032,f869,f1049,f1045,f1041]) ).

fof(f1039,plain,
    ( ~ c_Relation_Oirrefl(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(hAPP(v_P,hAPP(v_x,v_P)),tc_Arrow__Order__Mirabelle_Oalt)
    | c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_15
    | ~ spl0_55 ),
    inference(resolution,[],[f1033,f870]) ).

fof(f1038,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f685,f1036]) ).

fof(f685,axiom,
    ! [X23] :
      ( c_Relation_Oirrefl(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

fof(f1034,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f684,f1032]) ).

fof(f684,axiom,
    ! [X23] :
      ( c_Relation_Otrans(v_F(X23),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Oirrefl(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Otrans(hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt)
      | ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X23,hAPP(v_x,X23)),tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f1029,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f713,f1027]) ).

fof(f1027,plain,
    ( spl0_54
  <=> ! [X0,X59,X58] :
        ( X58 = X59
        | ~ c_fequal(X58,X59,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f713,axiom,
    ! [X58,X59,X0] :
      ( X58 = X59
      | ~ c_fequal(X58,X59,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1025,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f674,f1023]) ).

fof(f674,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(f1021,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f568,f1019]) ).

fof(f1019,plain,
    ( spl0_52
  <=> ! [X2,X0,X4] :
        ( c_Relation_Osym(X2,X0)
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f568,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Osym(X2,X0)
      | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

fof(f1017,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f563,f1015]) ).

fof(f1015,plain,
    ( spl0_51
  <=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f563,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(f1013,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f478,f1011]) ).

fof(f1011,plain,
    ( spl0_50
  <=> ! [X2,X0,X4] :
        ( c_Relation_Oirrefl(X2,X0)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f478,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Oirrefl(X2,X0)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

fof(f1009,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f472,f1007]) ).

fof(f1007,plain,
    ( spl0_49
  <=> ! [X2,X0] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f472,axiom,
    ! [X2,X0] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X2,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

fof(f1005,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f461,f1003]) ).

fof(f1003,plain,
    ( spl0_48
  <=> ! [X2,X0,X4] :
        ( c_Relation_Otrans(X2,X0)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f461,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Otrans(X2,X0)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

fof(f1001,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f460,f999]) ).

fof(f999,plain,
    ( spl0_47
  <=> ! [X2,X0,X4] :
        ( c_Relation_Otrans(X2,X0)
        | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f460,axiom,
    ! [X2,X0,X4] :
      ( c_Relation_Otrans(X2,X0)
      | ~ c_Equiv__Relations_Oequiv(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

fof(f997,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f263,f995]) ).

fof(f995,plain,
    ( spl0_46
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Otop(X0)
        | c_lessequals(X1,c_Orderings_Otop__class_Otop(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f263,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(f993,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f13,f991]) ).

fof(f991,plain,
    ( spl0_45
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Obot(X0)
        | c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f13,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(f989,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f699,f987]) ).

fof(f987,plain,
    ( spl0_44
  <=> ! [X57,X56] :
        ( ~ class_HOL_Oord(X57)
        | class_HOL_Oord(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f699,axiom,
    ! [X56,X57] :
      ( ~ class_HOL_Oord(X57)
      | class_HOL_Oord(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f985,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f698,f983]) ).

fof(f983,plain,
    ( spl0_43
  <=> ! [X57,X56] :
        ( ~ class_HOL_Ominus(X57)
        | class_HOL_Ominus(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f698,axiom,
    ! [X56,X57] :
      ( ~ class_HOL_Ominus(X57)
      | class_HOL_Ominus(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f981,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f697,f979]) ).

fof(f979,plain,
    ( spl0_42
  <=> ! [X57,X56] :
        ( ~ class_Orderings_Obot(X57)
        | class_Orderings_Obot(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f697,axiom,
    ! [X56,X57] :
      ( ~ class_Orderings_Obot(X57)
      | class_Orderings_Obot(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f977,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f696,f975]) ).

fof(f975,plain,
    ( spl0_41
  <=> ! [X57,X56] :
        ( ~ class_Orderings_Otop(X57)
        | class_Orderings_Otop(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f696,axiom,
    ! [X56,X57] :
      ( ~ class_Orderings_Otop(X57)
      | class_Orderings_Otop(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

fof(f973,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f695,f971]) ).

fof(f971,plain,
    ( spl0_40
  <=> ! [X57,X56] :
        ( ~ class_Orderings_Oorder(X57)
        | class_Orderings_Oorder(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f695,axiom,
    ! [X56,X57] :
      ( ~ class_Orderings_Oorder(X57)
      | class_Orderings_Oorder(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f969,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f694,f967]) ).

fof(f967,plain,
    ( spl0_39
  <=> ! [X57,X56] :
        ( ~ class_Lattices_Olattice(X57)
        | class_Lattices_Olattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f694,axiom,
    ! [X56,X57] :
      ( ~ class_Lattices_Olattice(X57)
      | class_Lattices_Olattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f965,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f693,f963]) ).

fof(f963,plain,
    ( spl0_38
  <=> ! [X57,X56] :
        ( ~ class_Orderings_Opreorder(X57)
        | class_Orderings_Opreorder(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f693,axiom,
    ! [X56,X57] :
      ( ~ class_Orderings_Opreorder(X57)
      | class_Orderings_Opreorder(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f961,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f692,f959]) ).

fof(f959,plain,
    ( spl0_37
  <=> ! [X57,X56] :
        ( ~ class_Lattices_Obounded__lattice(X57)
        | class_Lattices_Obounded__lattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f692,axiom,
    ! [X56,X57] :
      ( ~ class_Lattices_Obounded__lattice(X57)
      | class_Lattices_Obounded__lattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f957,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f691,f955]) ).

fof(f955,plain,
    ( spl0_36
  <=> ! [X57,X56] :
        ( ~ class_Lattices_Odistrib__lattice(X57)
        | class_Lattices_Odistrib__lattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f691,axiom,
    ! [X56,X57] :
      ( ~ class_Lattices_Odistrib__lattice(X57)
      | class_Lattices_Odistrib__lattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f953,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f690,f951]) ).

fof(f951,plain,
    ( spl0_35
  <=> ! [X57,X56] :
        ( ~ class_Lattices_Olattice(X57)
        | class_Lattices_Olower__semilattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f690,axiom,
    ! [X56,X57] :
      ( ~ class_Lattices_Olattice(X57)
      | class_Lattices_Olower__semilattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f949,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f689,f947]) ).

fof(f947,plain,
    ( spl0_34
  <=> ! [X57,X56] :
        ( ~ class_Lattices_Olattice(X57)
        | class_Lattices_Oupper__semilattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f689,axiom,
    ! [X56,X57] :
      ( ~ class_Lattices_Olattice(X57)
      | class_Lattices_Oupper__semilattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f945,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f688,f943]) ).

fof(f943,plain,
    ( spl0_33
  <=> ! [X57,X56] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X57)
        | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X56,X57)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f688,axiom,
    ! [X56,X57] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X57)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X56,X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(f941,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f536,f939]) ).

fof(f536,axiom,
    ! [X0,X4] : c_Relation_Orefl__on(X4,c_Relation_OId__on(X4,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

fof(f937,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f507,f935]) ).

fof(f935,plain,
    ( spl0_31
  <=> ! [X4,X0] : c_Relation_Osingle__valued(c_Relation_OId__on(X4,X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f507,axiom,
    ! [X0,X4] : c_Relation_Osingle__valued(c_Relation_OId__on(X4,X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

fof(f933,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f293,f931]) ).

fof(f931,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f293,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(f929,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f292,f927]) ).

fof(f927,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f292,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(f925,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f288,f923]) ).

fof(f288,axiom,
    ! [X0,X4] : c_lessequals(X4,X4,tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

fof(f921,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f181,f919]) ).

fof(f919,plain,
    ( spl0_27
  <=> ! [X2,X0] :
        ( ~ c_Wellfounded_Owf(X2,X0)
        | c_Wellfounded_Oacyclic(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f181,axiom,
    ! [X2,X0] :
      ( ~ c_Wellfounded_Owf(X2,X0)
      | c_Wellfounded_Oacyclic(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

fof(f917,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f535,f915]) ).

fof(f915,plain,
    ( spl0_26
  <=> ! [X4,X0] : c_Relation_Osym(c_Relation_OId__on(X4,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f535,axiom,
    ! [X0,X4] : c_Relation_Osym(c_Relation_OId__on(X4,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

fof(f913,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f528,f911]) ).

fof(f911,plain,
    ( spl0_25
  <=> ! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f528,axiom,
    ! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

fof(f909,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f518,f907]) ).

fof(f907,plain,
    ( spl0_24
  <=> ! [X4,X0] : c_Relation_Oantisym(c_Relation_OId__on(X4,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f518,axiom,
    ! [X0,X4] : c_Relation_Oantisym(c_Relation_OId__on(X4,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

fof(f905,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f468,f903]) ).

fof(f903,plain,
    ( spl0_23
  <=> ! [X4,X0] : c_Relation_Otrans(c_Relation_OId__on(X4,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f468,axiom,
    ! [X0,X4] : c_Relation_Otrans(c_Relation_OId__on(X4,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

fof(f901,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f466,f899]) ).

fof(f466,axiom,
    ! [X2,X0] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X2,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

fof(f897,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f712,f895]) ).

fof(f895,plain,
    ( spl0_21
  <=> ! [X0,X1] : c_fequal(X1,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f712,axiom,
    ! [X0,X1] : c_fequal(X1,X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f893,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f553,f891]) ).

fof(f891,plain,
    ( spl0_20
  <=> ! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f553,axiom,
    ! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

fof(f889,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f514,f887]) ).

fof(f887,plain,
    ( spl0_19
  <=> ! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f514,axiom,
    ! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

fof(f885,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f462,f883]) ).

fof(f883,plain,
    ( spl0_18
  <=> ! [X0] : c_Relation_Otrans(c_Relation_OId(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f462,axiom,
    ! [X0] : c_Relation_Otrans(c_Relation_OId(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).

fof(f881,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f682,f878]) ).

fof(f682,axiom,
    hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f876,plain,
    ~ spl0_16,
    inference(avatar_split_clause,[],[f683,f873]) ).

fof(f683,axiom,
    ~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f871,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f681,f869]) ).

fof(f681,axiom,
    ! [X1] : c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f867,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f711,f864]) ).

fof(f711,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f862,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f710,f859]) ).

fof(f859,plain,
    ( spl0_13
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f710,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f857,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f709,f854]) ).

fof(f709,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f852,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f708,f849]) ).

fof(f708,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

fof(f847,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f707,f844]) ).

fof(f844,plain,
    ( spl0_10
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f707,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f842,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f706,f839]) ).

fof(f839,plain,
    ( spl0_9
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f706,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f837,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f705,f834]) ).

fof(f834,plain,
    ( spl0_8
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f705,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f832,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f704,f829]) ).

fof(f704,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f827,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f703,f824]) ).

fof(f824,plain,
    ( spl0_6
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f703,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f822,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f702,f819]) ).

fof(f702,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f817,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f701,f814]) ).

fof(f701,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f812,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f700,f809]) ).

fof(f700,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

fof(f807,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f680,f805]) ).

fof(f680,axiom,
    ! [X1] : c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f803,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f679,f801]) ).

fof(f679,axiom,
    ! [X1] : c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SCT024-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 00:24:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (5582)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (5589)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.41  % (5585)WARNING: value z3 for option sas not known
% 0.21/0.41  % (5583)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.41  % (5586)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.41  % (5584)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.41  % (5585)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)
% 0.21/0.41  % (5588)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)
% 0.21/0.41  % (5587)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)
% 1.49/0.59  TRYING [1]
% 1.65/0.61  TRYING [2]
% 4.56/1.05  TRYING [1]
% 5.06/1.13  TRYING [3]
% 5.06/1.14  TRYING [2]
% 8.66/1.62  TRYING [1]
% 8.66/1.64  TRYING [2]
% 12.31/2.13  TRYING [3]
% 14.30/2.41  % (5587)First to succeed.
% 14.30/2.43  % (5587)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5582"
% 14.30/2.44  % (5587)Refutation found. Thanks to Tanya!
% 14.30/2.44  % SZS status Unsatisfiable for theBenchmark
% 14.30/2.44  % SZS output start Proof for theBenchmark
% See solution above
% 14.30/2.45  % (5587)------------------------------
% 14.30/2.45  % (5587)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 14.30/2.45  % (5587)Termination reason: Refutation
% 14.30/2.45  
% 14.30/2.45  % (5587)Memory used [KB]: 18458
% 14.30/2.45  % (5587)Time elapsed: 2.024 s
% 14.30/2.45  % (5587)Instructions burned: 5547 (million)
% 14.30/2.45  % (5582)Success in time 2.069 s
%------------------------------------------------------------------------------