TSTP Solution File: SCT002-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT002-1 : 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 : n028.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 02:49:58 EDT 2024

% Result   : Unsatisfiable 7.12s 1.45s
% Output   : Refutation 7.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      : 1260
% Syntax   : Number of formulae    : 2360 ( 789 unt;   0 def)
%            Number of atoms       : 5354 ( 797 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 5149 (2155   ~;2300   |;   0   &)
%                                         ( 694 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :  721 ( 719 usr; 695 prp; 0-3 aty)
%            Number of functors    :   85 (  85 usr;   8 con; 0-7 aty)
%            Number of variables   : 4955 (4955   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f20053,plain,
    $false,
    inference(avatar_sat_refutation,[],[f843,f848,f853,f858,f863,f868,f873,f878,f883,f888,f893,f898,f902,f907,f912,f916,f920,f924,f928,f932,f936,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f992,f996,f1000,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1085,f1089,f1093,f1097,f1104,f1110,f1115,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1219,f1223,f1231,f1269,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1322,f1327,f1350,f1354,f1358,f1365,f1369,f1373,f1377,f1381,f1386,f1390,f1394,f1398,f1402,f1406,f1410,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1487,f1520,f1543,f1553,f1557,f1561,f1565,f1569,f1573,f1578,f1582,f1586,f1590,f1594,f1598,f1730,f1734,f1738,f1742,f1746,f1750,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1845,f1849,f1853,f1857,f2030,f2146,f2173,f2177,f2181,f2185,f2189,f2193,f2197,f2201,f2205,f2209,f2213,f2217,f2221,f2225,f2229,f2233,f2238,f2242,f2246,f2250,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2314,f2320,f2329,f2333,f2337,f2341,f2346,f2707,f2747,f2752,f2780,f2784,f2788,f2792,f2796,f2800,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2841,f2897,f3021,f3025,f3042,f3046,f3050,f3054,f3058,f3063,f3067,f3071,f3075,f3079,f3083,f3087,f3091,f3095,f3099,f3103,f3107,f3112,f3116,f3225,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3441,f3445,f3449,f3453,f3457,f3461,f3465,f3469,f3473,f3477,f3481,f3485,f3490,f3494,f3716,f3807,f3833,f3856,f3860,f3864,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3947,f3951,f3955,f3959,f3963,f3967,f3971,f4158,f4344,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4516,f4520,f4524,f4722,f4802,f4806,f4810,f4815,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4860,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4909,f4913,f4917,f5044,f5357,f5361,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f6017,f6238,f6364,f6368,f6372,f6376,f6381,f6449,f6453,f6457,f6461,f6465,f6469,f6473,f6477,f6481,f6485,f6489,f6493,f6497,f6501,f6735,f6872,f6876,f6880,f6884,f6888,f6892,f6896,f6900,f6904,f6908,f6912,f6916,f6920,f7082,f7771,f7775,f7779,f7783,f7787,f7791,f7795,f8148,f8152,f8156,f8160,f8164,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8232,f8236,f8240,f8244,f8248,f8252,f8256,f8415,f9135,f9139,f9143,f9147,f9151,f9156,f9160,f9165,f9169,f9173,f9177,f9181,f9729,f9733,f9737,f9741,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9785,f9789,f9793,f9797,f9801,f10500,f10504,f10508,f10512,f10517,f10521,f10525,f10529,f10534,f10645,f10649,f10653,f10657,f10661,f10665,f10669,f10673,f10677,f10681,f10685,f10689,f10693,f10697,f10701,f10705,f10709,f12527,f12531,f12535,f12539,f12543,f12547,f12551,f12555,f12559,f12563,f12567,f12571,f12575,f13022,f13147,f13151,f13155,f13159,f13163,f13167,f13394,f13398,f13402,f13406,f13410,f13414,f13418,f13686,f13690,f13694,f13698,f13702,f13706,f13710,f13714,f13940,f14079,f14083,f14087,f14091,f14095,f14099,f14442,f14446,f14450,f14454,f14646,f14650,f14762,f14766,f14770,f14774,f14778,f15057,f15061,f15065,f15069,f15229,f15233,f15237,f15241,f15245,f15250,f15254,f15506,f15510,f15559,f15626,f15630,f15634,f15640,f15690,f15862,f15866,f15975,f15979,f16241,f16245,f16250,f16316,f16320,f16432,f16498,f16502,f16506,f16565,f16569,f16573,f16744,f16748,f16867,f16871,f17007,f17011,f17016,f17178,f17183,f17263,f17269,f17628,f17701,f17705,f17783,f17848,f17856,f18003,f18007,f18046,f18065,f18074,f18094,f18099,f18103,f18160,f18165,f18173,f18178,f18182,f18203,f18207,f18211,f18233,f18288,f18292,f18296,f18300,f18304,f18308,f18695,f18699,f18703,f18707,f18830,f18834,f18838,f18852,f18856,f18887,f18971,f18975,f18979,f18983,f18987,f18991,f19367,f19402,f19406,f19492,f19496,f19580,f19633,f19639,f19644,f19649,f19654,f19658,f19662,f19666,f19670,f19674,f19733,f19738,f19742,f19942,f19946,f19950,f20048]) ).

fof(f20048,plain,
    ( ~ spl0_13
    | ~ spl0_683 ),
    inference(avatar_contradiction_clause,[],[f20014]) ).

fof(f20014,plain,
    ( $false
    | ~ spl0_13
    | ~ spl0_683 ),
    inference(resolution,[],[f19653,f901]) ).

fof(f901,plain,
    ( ! [X5] : ~ hBOOL(c_in(c_Pair(X5,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f900]) ).

fof(f900,plain,
    ( spl0_13
  <=> ! [X5] : ~ hBOOL(c_in(c_Pair(X5,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f19653,plain,
    ( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_683 ),
    inference(avatar_component_clause,[],[f19651]) ).

fof(f19651,plain,
    ( spl0_683
  <=> hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f19950,plain,
    ( spl0_694
    | ~ spl0_37
    | ~ spl0_536 ),
    inference(avatar_split_clause,[],[f12953,f12565,f998,f19948]) ).

fof(f19948,plain,
    ( spl0_694
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(X0,X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f998,plain,
    ( spl0_37
  <=> ! [X5,X12] :
        ( X5 = X12
        | hBOOL(c_in(c_Pair(X5,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X12,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f12565,plain,
    ( spl0_536
  <=> ! [X6,X19,X12,X25,X2] :
        ( hBOOL(hAPP(X19,X12))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f12953,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(X0,X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) = X2 )
    | ~ spl0_37
    | ~ spl0_536 ),
    inference(resolution,[],[f12566,f999]) ).

fof(f999,plain,
    ( ! [X5,X12] :
        ( hBOOL(c_in(c_Pair(X12,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X5,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X5 = X12 )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f998]) ).

fof(f12566,plain,
    ( ! [X2,X19,X6,X12,X25] :
        ( ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(hAPP(X19,X12)) )
    | ~ spl0_536 ),
    inference(avatar_component_clause,[],[f12565]) ).

fof(f19946,plain,
    ( spl0_693
    | ~ spl0_37
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f12918,f12561,f998,f19944]) ).

fof(f19944,plain,
    ( spl0_693
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(X0,X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f12561,plain,
    ( spl0_535
  <=> ! [X6,X19,X12,X25,X2] :
        ( hBOOL(hAPP(X19,X12))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f12918,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(X0,X1))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(X0,X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) = X2 )
    | ~ spl0_37
    | ~ spl0_535 ),
    inference(resolution,[],[f12562,f999]) ).

fof(f12562,plain,
    ( ! [X2,X19,X6,X12,X25] :
        ( ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(hAPP(X19,X12)) )
    | ~ spl0_535 ),
    inference(avatar_component_clause,[],[f12561]) ).

fof(f19942,plain,
    ( spl0_692
    | ~ spl0_13
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f7986,f7785,f900,f19940]) ).

fof(f19940,plain,
    ( spl0_692
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(X1,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f7785,plain,
    ( spl0_443
  <=> ! [X4,X0,X5,X2] :
        ( hBOOL(c_in(X5,X4,X2))
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X5,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f7986,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(X1,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_13
    | ~ spl0_443 ),
    inference(resolution,[],[f7786,f901]) ).

fof(f7786,plain,
    ( ! [X2,X0,X4,X5] :
        ( hBOOL(c_in(X5,X4,X2))
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X5,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2) )
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f7785]) ).

fof(f19742,plain,
    ( spl0_691
    | ~ spl0_15
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f5322,f4894,f909,f19740]) ).

fof(f19740,plain,
    ( spl0_691
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_x,v_y,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_691])]) ).

fof(f909,plain,
    ( spl0_15
  <=> hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f4894,plain,
    ( spl0_373
  <=> ! [X0,X6,X25,X2] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | ~ hBOOL(c_in(X25,X0,X2))
        | hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f5322,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_x,v_y,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_15
    | ~ spl0_373 ),
    inference(resolution,[],[f4895,f911]) ).

fof(f911,plain,
    ( hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f909]) ).

fof(f4895,plain,
    ( ! [X2,X0,X6,X25] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | ~ c_Relation_Orefl__on(X0,X6,X2)
        | hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2))) )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f4894]) ).

fof(f19738,plain,
    ( spl0_690
    | ~ spl0_14
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f5321,f4894,f904,f19736]) ).

fof(f19736,plain,
    ( spl0_690
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_y,v_x,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_690])]) ).

fof(f904,plain,
    ( spl0_14
  <=> hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f5321,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Pair(v_y,v_x,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_14
    | ~ spl0_373 ),
    inference(resolution,[],[f4895,f906]) ).

fof(f906,plain,
    ( hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f904]) ).

fof(f19733,plain,
    ( spl0_689
    | ~ spl0_14
    | ~ spl0_666 ),
    inference(avatar_split_clause,[],[f18888,f18885,f904,f19730]) ).

fof(f19730,plain,
    ( spl0_689
  <=> hBOOL(c_in(c_Pair(v_y,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f18885,plain,
    ( spl0_666
  <=> ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f18888,plain,
    ( hBOOL(c_in(c_Pair(v_y,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_14
    | ~ spl0_666 ),
    inference(resolution,[],[f18886,f906]) ).

fof(f18886,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_666 ),
    inference(avatar_component_clause,[],[f18885]) ).

fof(f19674,plain,
    ( spl0_688
    | ~ spl0_110
    | ~ spl0_175
    | ~ spl0_305 ),
    inference(avatar_split_clause,[],[f3851,f3831,f1821,f1375,f19672]) ).

fof(f19672,plain,
    ( spl0_688
  <=> ! [X0] : c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f1375,plain,
    ( spl0_110
  <=> ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1821,plain,
    ( spl0_175
  <=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f3831,plain,
    ( spl0_305
  <=> ! [X6,X2] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f3851,plain,
    ( ! [X0] : c_Relation_Oirrefl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
    | ~ spl0_110
    | ~ spl0_175
    | ~ spl0_305 ),
    inference(forward_demodulation,[],[f3849,f1822]) ).

fof(f1822,plain,
    ( ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f1821]) ).

fof(f3849,plain,
    ( ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_110
    | ~ spl0_305 ),
    inference(superposition,[],[f3832,f1376]) ).

fof(f1376,plain,
    ( ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X2,tc_bool))
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f1375]) ).

fof(f3832,plain,
    ( ! [X2,X6] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_305 ),
    inference(avatar_component_clause,[],[f3831]) ).

fof(f19670,plain,
    ( spl0_687
    | ~ spl0_55
    | ~ spl0_175
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2731,f2303,f1821,f1074,f19668]) ).

fof(f19668,plain,
    ( spl0_687
  <=> ! [X0] : ~ c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f1074,plain,
    ( spl0_55
  <=> ! [X2,X25] : ~ hBOOL(c_in(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f2303,plain,
    ( spl0_217
  <=> ! [X6,X2,X5] :
        ( ~ c_Nitpick_Orefl_H(X6,X2)
        | hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f2731,plain,
    ( ! [X0] : ~ c_Nitpick_Orefl_H(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
    | ~ spl0_55
    | ~ spl0_175
    | ~ spl0_217 ),
    inference(forward_demodulation,[],[f2727,f1822]) ).

fof(f2727,plain,
    ( ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
    | ~ spl0_55
    | ~ spl0_217 ),
    inference(resolution,[],[f2304,f1075]) ).

fof(f1075,plain,
    ( ! [X2,X25] : ~ hBOOL(c_in(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1074]) ).

fof(f2304,plain,
    ( ! [X2,X6,X5] :
        ( hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Nitpick_Orefl_H(X6,X2) )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f2303]) ).

fof(f19666,plain,
    ( spl0_686
    | ~ spl0_19
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f2138,f1833,f926,f19664]) ).

fof(f19664,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(f926,plain,
    ( spl0_19
  <=> ! [X6,X2] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X6,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f1833,plain,
    ( spl0_178
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X6,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X6,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f2138,plain,
    ( ! [X0,X1] : c_Relation_Otrans(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
    | ~ spl0_19
    | ~ spl0_178 ),
    inference(superposition,[],[f927,f1834]) ).

fof(f1834,plain,
    ( ! [X2,X6] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X6,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X6,X2),X2,X2)
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1833]) ).

fof(f927,plain,
    ( ! [X2,X6] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X6,X2),X2)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f19662,plain,
    ( spl0_685
    | ~ spl0_6
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f1330,f1287,f865,f19660]) ).

fof(f19660,plain,
    ( spl0_685
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).

fof(f865,plain,
    ( spl0_6
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1287,plain,
    ( spl0_94
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1330,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
    | ~ spl0_6
    | ~ spl0_94 ),
    inference(resolution,[],[f1288,f867]) ).

fof(f867,plain,
    ( class_Lattices_Obounded__lattice(tc_bool)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f865]) ).

fof(f1288,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X5,X2) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f1287]) ).

fof(f19658,plain,
    ( spl0_684
    | ~ spl0_6
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f1328,f1283,f865,f19656]) ).

fof(f19656,plain,
    ( spl0_684
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f1283,plain,
    ( spl0_93
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f1328,plain,
    ( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
    | ~ spl0_6
    | ~ spl0_93 ),
    inference(resolution,[],[f1284,f867]) ).

fof(f1284,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(X2),X2) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f1283]) ).

fof(f19654,plain,
    ( spl0_683
    | ~ spl0_15
    | ~ spl0_665 ),
    inference(avatar_split_clause,[],[f18857,f18854,f909,f19651]) ).

fof(f18854,plain,
    ( spl0_665
  <=> ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f18857,plain,
    ( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_15
    | ~ spl0_665 ),
    inference(resolution,[],[f18855,f911]) ).

fof(f18855,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_665 ),
    inference(avatar_component_clause,[],[f18854]) ).

fof(f19649,plain,
    ( spl0_682
    | ~ spl0_21
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f1111,f1108,f934,f19647]) ).

fof(f19647,plain,
    ( spl0_682
  <=> ! [X0] : c_Wellfounded_Oacyclic(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f934,plain,
    ( spl0_21
  <=> ! [X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Oacyclic(X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f1108,plain,
    ( spl0_62
  <=> ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1111,plain,
    ( ! [X0] : c_Wellfounded_Oacyclic(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)
    | ~ spl0_21
    | ~ spl0_62 ),
    inference(resolution,[],[f1109,f935]) ).

fof(f935,plain,
    ( ! [X2,X6] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Oacyclic(X6,X2) )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f934]) ).

fof(f1109,plain,
    ( ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1108]) ).

fof(f19644,plain,
    ( ~ spl0_22
    | spl0_681 ),
    inference(avatar_contradiction_clause,[],[f19641]) ).

fof(f19641,plain,
    ( $false
    | ~ spl0_22
    | spl0_681 ),
    inference(resolution,[],[f19638,f939]) ).

fof(f939,plain,
    ( ! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f938]) ).

fof(f938,plain,
    ( spl0_22
  <=> ! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f19638,plain,
    ( ~ c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | spl0_681 ),
    inference(avatar_component_clause,[],[f19636]) ).

fof(f19636,plain,
    ( spl0_681
  <=> c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f19639,plain,
    ( ~ spl0_681
    | ~ spl0_111
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673
    | spl0_680 ),
    inference(avatar_split_clause,[],[f19634,f19630,f19361,f8146,f4477,f1379,f19636]) ).

fof(f1379,plain,
    ( spl0_111
  <=> ! [X4,X2] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f4477,plain,
    ( spl0_338
  <=> ! [X4,X25,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f8146,plain,
    ( spl0_446
  <=> ! [X17,X4,X0,X3,X2] : c_Relation_OImage(X17,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f19361,plain,
    ( spl0_673
  <=> c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f19630,plain,
    ( spl0_680
  <=> c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f19634,plain,
    ( ~ c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | ~ spl0_111
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673
    | spl0_680 ),
    inference(forward_demodulation,[],[f19631,f19395]) ).

fof(f19395,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_111
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(forward_demodulation,[],[f19394,f1380]) ).

fof(f1380,plain,
    ( ! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) = X4
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1379]) ).

fof(f19394,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_111
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(forward_demodulation,[],[f19393,f4478]) ).

fof(f4478,plain,
    ( ! [X2,X1,X4,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X2)
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f4477]) ).

fof(f19393,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_111
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(forward_demodulation,[],[f19392,f1380]) ).

fof(f19392,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_338
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(forward_demodulation,[],[f19391,f4478]) ).

fof(f19391,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(forward_demodulation,[],[f19383,f8147]) ).

fof(f8147,plain,
    ( ! [X2,X3,X0,X4,X17] : c_Relation_OImage(X17,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool))
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f8146]) ).

fof(f19383,plain,
    ( ! [X0] : c_Relation_OImage(v_L,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),X0,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | ~ spl0_446
    | ~ spl0_673 ),
    inference(superposition,[],[f8147,f19363]) ).

fof(f19363,plain,
    ( c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_673 ),
    inference(avatar_component_clause,[],[f19361]) ).

fof(f19631,plain,
    ( ~ c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))
    | spl0_680 ),
    inference(avatar_component_clause,[],[f19630]) ).

fof(f19633,plain,
    ( spl0_680
    | spl0_674
    | ~ spl0_14
    | ~ spl0_598 ),
    inference(avatar_split_clause,[],[f15897,f15860,f904,f19365,f19630]) ).

fof(f19365,plain,
    ( spl0_674
  <=> ! [X0] : ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f15860,plain,
    ( spl0_598
  <=> ! [X0,X6,X25,X2,X26] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | c_lessequals(c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f15897,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_lessequals(c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)) )
    | ~ spl0_14
    | ~ spl0_598 ),
    inference(resolution,[],[f15861,f906]) ).

fof(f15861,plain,
    ( ! [X2,X0,X6,X26,X25] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | c_lessequals(c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) )
    | ~ spl0_598 ),
    inference(avatar_component_clause,[],[f15860]) ).

fof(f19580,plain,
    ( spl0_679
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f1234,f1133,f865,f19578]) ).

fof(f19578,plain,
    ( spl0_679
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f1133,plain,
    ( spl0_68
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X5,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f1234,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
    | ~ spl0_6
    | ~ spl0_68 ),
    inference(resolution,[],[f1134,f867]) ).

fof(f1134,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X5,X2) = X5 )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1133]) ).

fof(f19496,plain,
    ( spl0_678
    | ~ spl0_37
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f9087,f8250,f998,f19494]) ).

fof(f19494,plain,
    ( spl0_678
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_OImage(v_L,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(X2,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f8250,plain,
    ( spl0_466
  <=> ! [X3,X0,X6,X5,X2,X26] :
        ( ~ hBOOL(c_in(X5,X0,X3))
        | hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X5,X26,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f9087,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_OImage(v_L,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(X2,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 )
    | ~ spl0_37
    | ~ spl0_466 ),
    inference(resolution,[],[f8251,f999]) ).

fof(f8251,plain,
    ( ! [X2,X3,X0,X6,X26,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X26,X3,X2),X6,tc_prod(X3,X2)))
        | hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | ~ hBOOL(c_in(X5,X0,X3)) )
    | ~ spl0_466 ),
    inference(avatar_component_clause,[],[f8250]) ).

fof(f19492,plain,
    ( spl0_677
    | ~ spl0_37
    | ~ spl0_465 ),
    inference(avatar_split_clause,[],[f9048,f8246,f998,f19490]) ).

fof(f19490,plain,
    ( spl0_677
  <=> ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f8246,plain,
    ( spl0_465
  <=> ! [X12,X6,X25,X2] :
        ( ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(c_in(X12,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X12,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f9048,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(X1,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_465 ),
    inference(resolution,[],[f8247,f999]) ).

fof(f8247,plain,
    ( ! [X2,X6,X12,X25] :
        ( ~ hBOOL(c_in(c_Pair(X12,X25,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X12,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2)) )
    | ~ spl0_465 ),
    inference(avatar_component_clause,[],[f8246]) ).

fof(f19406,plain,
    ( spl0_676
    | ~ spl0_15
    | ~ spl0_587 ),
    inference(avatar_split_clause,[],[f15455,f15243,f909,f19404]) ).

fof(f19404,plain,
    ( spl0_676
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_x,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_y,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,v_L,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(f15243,plain,
    ( spl0_587
  <=> ! [X3,X16,X7,X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X3,X16),X7,tc_prod(X3,X16)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X16),c_Relation_Orel__comp(X6,X7,X2,X3,X16),tc_prod(X2,X16))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f15455,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_x,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_y,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,v_L,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_15
    | ~ spl0_587 ),
    inference(resolution,[],[f15244,f911]) ).

fof(f15244,plain,
    ( ! [X2,X3,X6,X26,X16,X27,X7,X25] :
        ( ~ hBOOL(c_in(c_Pair(X26,X27,X3,X16),X7,tc_prod(X3,X16)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X16),c_Relation_Orel__comp(X6,X7,X2,X3,X16),tc_prod(X2,X16))) )
    | ~ spl0_587 ),
    inference(avatar_component_clause,[],[f15243]) ).

fof(f19402,plain,
    ( spl0_675
    | ~ spl0_14
    | ~ spl0_587 ),
    inference(avatar_split_clause,[],[f15454,f15243,f904,f19400]) ).

fof(f19400,plain,
    ( spl0_675
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_y,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_x,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,v_L,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_675])]) ).

fof(f15454,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_y,X1,tc_Arrow__Order__Mirabelle_Oalt),X2,tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,v_x,X1,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_Orel__comp(X2,v_L,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(X1,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_14
    | ~ spl0_587 ),
    inference(resolution,[],[f15244,f906]) ).

fof(f19367,plain,
    ( spl0_673
    | spl0_674
    | ~ spl0_14
    | ~ spl0_586 ),
    inference(avatar_split_clause,[],[f15401,f15239,f904,f19365,f19361]) ).

fof(f15239,plain,
    ( spl0_586
  <=> ! [X5,X0,X12,X6,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | c_Relation_OImage(X6,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X6,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f15401,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Relation_OImage(v_L,c_Set_Oinsert(v_y,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) = c_Relation_OImage(v_L,c_Set_Oinsert(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_14
    | ~ spl0_586 ),
    inference(resolution,[],[f15240,f906]) ).

fof(f15240,plain,
    ( ! [X2,X0,X6,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | c_Relation_OImage(X6,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X6,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) )
    | ~ spl0_586 ),
    inference(avatar_component_clause,[],[f15239]) ).

fof(f18991,plain,
    ( spl0_672
    | ~ spl0_37
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f7744,f6914,f998,f18989]) ).

fof(f18989,plain,
    ( spl0_672
  <=> ! [X0,X3,X2,X1] :
        ( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,v_L,X2,tc_Arrow__Order__Mirabelle_Oalt,X3),X1)
        | hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f6914,plain,
    ( spl0_436
  <=> ! [X5,X3,X10,X6,X25,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2)))
        | hAPP(X10,X5) = hAPP(c_Recdef_Ocut(X10,X6,X25,X2,X3),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f7744,plain,
    ( ! [X2,X3,X0,X1] :
        ( hAPP(X0,X1) = hAPP(c_Recdef_Ocut(X0,v_L,X2,tc_Arrow__Order__Mirabelle_Oalt,X3),X1)
        | hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X1 = X2 )
    | ~ spl0_37
    | ~ spl0_436 ),
    inference(resolution,[],[f6915,f999]) ).

fof(f6915,plain,
    ( ! [X2,X3,X10,X6,X5,X25] :
        ( ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2)))
        | hAPP(X10,X5) = hAPP(c_Recdef_Ocut(X10,X6,X25,X2,X3),X5) )
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f6914]) ).

fof(f18987,plain,
    ( spl0_671
    | ~ spl0_13
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f5907,f5380,f900,f18985]) ).

fof(f18985,plain,
    ( spl0_671
  <=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f5380,plain,
    ( spl0_384
  <=> ! [X4,X25,X2,X1] :
        ( hBOOL(c_in(X25,X1,X2))
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f5907,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_13
    | ~ spl0_384 ),
    inference(resolution,[],[f5381,f901]) ).

fof(f5381,plain,
    ( ! [X2,X1,X4,X25] :
        ( hBOOL(c_in(X25,X1,X2))
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) )
    | ~ spl0_384 ),
    inference(avatar_component_clause,[],[f5380]) ).

fof(f18983,plain,
    ( spl0_670
    | ~ spl0_13
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f5861,f5376,f900,f18981]) ).

fof(f18981,plain,
    ( spl0_670
  <=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_L,c_Set_Oinsert(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_670])]) ).

fof(f5376,plain,
    ( spl0_383
  <=> ! [X4,X0,X25,X2] :
        ( hBOOL(c_in(X25,X0,X2))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f5861,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(v_L,c_Set_Oinsert(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_13
    | ~ spl0_383 ),
    inference(resolution,[],[f5377,f901]) ).

fof(f5377,plain,
    ( ! [X2,X0,X4,X25] :
        ( hBOOL(c_in(X25,X0,X2))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) )
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f5376]) ).

fof(f18979,plain,
    ( spl0_669
    | ~ spl0_15
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f5509,f5359,f909,f18977]) ).

fof(f18977,plain,
    ( spl0_669
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f5359,plain,
    ( spl0_380
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X4,X2))
        | c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f5509,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_15
    | ~ spl0_380 ),
    inference(resolution,[],[f5360,f911]) ).

fof(f5360,plain,
    ( ! [X2,X0,X4,X5] :
        ( ~ hBOOL(c_in(X5,X4,X2))
        | c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f5359]) ).

fof(f18975,plain,
    ( spl0_668
    | ~ spl0_14
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f5508,f5359,f904,f18973]) ).

fof(f18973,plain,
    ( spl0_668
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f5508,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_14
    | ~ spl0_380 ),
    inference(resolution,[],[f5360,f906]) ).

fof(f18971,plain,
    ( spl0_667
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1525,f1432,f998,f18969]) ).

fof(f18969,plain,
    ( spl0_667
  <=> ! [X0,X1] :
        ( v_L = c_Set_Oinsert(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f1432,plain,
    ( spl0_124
  <=> ! [X2,X0,X25] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | c_Set_Oinsert(X25,X0,X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1525,plain,
    ( ! [X0,X1] :
        ( v_L = c_Set_Oinsert(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(resolution,[],[f1433,f999]) ).

fof(f1433,plain,
    ( ! [X2,X0,X25] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | c_Set_Oinsert(X25,X0,X2) = X0 )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1432]) ).

fof(f18887,plain,
    ( ~ spl0_2
    | spl0_666
    | ~ spl0_15
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f14810,f14760,f909,f18885,f845]) ).

fof(f845,plain,
    ( spl0_2
  <=> c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f14760,plain,
    ( spl0_574
  <=> ! [X5,X13,X12,X6,X2] :
        ( ~ c_Relation_Otrans(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f14810,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_15
    | ~ spl0_574 ),
    inference(resolution,[],[f14761,f911]) ).

fof(f14761,plain,
    ( ! [X2,X6,X5,X12,X13] :
        ( ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Relation_Otrans(X6,X2)
        | hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2))) )
    | ~ spl0_574 ),
    inference(avatar_component_clause,[],[f14760]) ).

fof(f18856,plain,
    ( ~ spl0_2
    | spl0_665
    | ~ spl0_14
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f14809,f14760,f904,f18854,f845]) ).

fof(f14809,plain,
    ( ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(X0,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_14
    | ~ spl0_574 ),
    inference(resolution,[],[f14761,f906]) ).

fof(f18852,plain,
    ( spl0_664
    | ~ spl0_37
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f6836,f6487,f998,f18850]) ).

fof(f18850,plain,
    ( spl0_664
  <=> ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_ORange(c_Relation_Oconverse(v_L,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))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f6487,plain,
    ( spl0_420
  <=> ! [X5,X3,X6,X25,X2] :
        ( hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X25,X5,X2,X3),X6,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f6836,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_ORange(c_Relation_Oconverse(v_L,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))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_420 ),
    inference(resolution,[],[f6488,f999]) ).

fof(f6488,plain,
    ( ! [X2,X3,X6,X5,X25] :
        ( ~ hBOOL(c_in(c_Pair(X25,X5,X2,X3),X6,tc_prod(X2,X3)))
        | hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2)) )
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f6487]) ).

fof(f18838,plain,
    ( spl0_663
    | ~ spl0_218
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f4270,f3900,f2307,f18836]) ).

fof(f18836,plain,
    ( spl0_663
  <=> ! [X0,X1] :
        ( c_Relation_Oirrefl(X0,X1)
        | ~ c_Wellfounded_Owf(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f2307,plain,
    ( spl0_218
  <=> ! [X6,X2,X25] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f3900,plain,
    ( spl0_316
  <=> ! [X6,X2] :
        ( c_Relation_Oirrefl(X6,X2)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f4270,plain,
    ( ! [X0,X1] :
        ( c_Relation_Oirrefl(X0,X1)
        | ~ c_Wellfounded_Owf(X0,X1) )
    | ~ spl0_218
    | ~ spl0_316 ),
    inference(resolution,[],[f3901,f2308]) ).

fof(f2308,plain,
    ( ! [X2,X6,X25] :
        ( ~ hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Wellfounded_Owf(X6,X2) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2307]) ).

fof(f3901,plain,
    ( ! [X2,X6] :
        ( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2)))
        | c_Relation_Oirrefl(X6,X2) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3900]) ).

fof(f18834,plain,
    ( spl0_662
    | ~ spl0_217
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2737,f2307,f2303,f18832]) ).

fof(f18832,plain,
    ( spl0_662
  <=> ! [X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f2737,plain,
    ( ! [X0,X1] :
        ( ~ c_Wellfounded_Owf(X0,X1)
        | ~ c_Nitpick_Orefl_H(X0,X1) )
    | ~ spl0_217
    | ~ spl0_218 ),
    inference(resolution,[],[f2308,f2304]) ).

fof(f18830,plain,
    ( spl0_661
    | ~ spl0_216
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2726,f2303,f2299,f18828]) ).

fof(f18828,plain,
    ( spl0_661
  <=> ! [X0,X1] :
        ( ~ c_Nitpick_Orefl_H(X0,X1)
        | ~ c_Relation_Oirrefl(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f2299,plain,
    ( spl0_216
  <=> ! [X6,X2,X5] :
        ( ~ c_Relation_Oirrefl(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2726,plain,
    ( ! [X0,X1] :
        ( ~ c_Nitpick_Orefl_H(X0,X1)
        | ~ c_Relation_Oirrefl(X0,X1) )
    | ~ spl0_216
    | ~ spl0_217 ),
    inference(resolution,[],[f2304,f2300]) ).

fof(f2300,plain,
    ( ! [X2,X6,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Relation_Oirrefl(X6,X2) )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2299]) ).

fof(f18707,plain,
    ( spl0_660
    | ~ spl0_13
    | ~ spl0_175
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f6432,f6379,f1821,f900,f18705]) ).

fof(f18705,plain,
    ( spl0_660
  <=> ! [X0] : v_L = c_HOL_Ominus__class_Ominus(v_L,c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_660])]) ).

fof(f6379,plain,
    ( spl0_409
  <=> ! [X5,X2,X0] :
        ( c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0
        | hBOOL(c_in(X5,X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f6432,plain,
    ( ! [X0] : v_L = c_HOL_Ominus__class_Ominus(v_L,c_Set_Oinsert(c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_13
    | ~ spl0_175
    | ~ spl0_409 ),
    inference(forward_demodulation,[],[f6406,f1822]) ).

fof(f6406,plain,
    ( ! [X0] : v_L = c_HOL_Ominus__class_Ominus(v_L,c_Set_Oinsert(c_Pair(X0,X0,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)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_13
    | ~ spl0_409 ),
    inference(resolution,[],[f6380,f901]) ).

fof(f6380,plain,
    ( ! [X2,X0,X5] :
        ( hBOOL(c_in(X5,X0,X2))
        | c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0 )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f6379]) ).

fof(f18703,plain,
    ( spl0_659
    | ~ spl0_15
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f6053,f5400,f909,f18701]) ).

fof(f18701,plain,
    ( spl0_659
  <=> ! [X0,X1] : c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f5400,plain,
    ( spl0_389
  <=> ! [X3,X10,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | c_Set_Oimage(X10,X0,X2,X3) = c_Set_Oinsert(hAPP(X10,X5),c_Set_Oimage(X10,X0,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f6053,plain,
    ( ! [X0,X1] : c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)
    | ~ spl0_15
    | ~ spl0_389 ),
    inference(resolution,[],[f5401,f911]) ).

fof(f5401,plain,
    ( ! [X2,X3,X10,X0,X5] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | c_Set_Oimage(X10,X0,X2,X3) = c_Set_Oinsert(hAPP(X10,X5),c_Set_Oimage(X10,X0,X2,X3),X3) )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f5400]) ).

fof(f18699,plain,
    ( spl0_658
    | ~ spl0_14
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f6052,f5400,f904,f18697]) ).

fof(f18697,plain,
    ( spl0_658
  <=> ! [X0,X1] : c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f6052,plain,
    ( ! [X0,X1] : c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) = c_Set_Oinsert(hAPP(X0,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Set_Oimage(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)
    | ~ spl0_14
    | ~ spl0_389 ),
    inference(resolution,[],[f5401,f906]) ).

fof(f18695,plain,
    ( ~ spl0_657
    | ~ spl0_89
    | spl0_636 ),
    inference(avatar_split_clause,[],[f18090,f18071,f1217,f18692]) ).

fof(f18692,plain,
    ( spl0_657
  <=> hBOOL(hAPP(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f1217,plain,
    ( spl0_89
  <=> ! [X18,X5,X2] :
        ( ~ hBOOL(hAPP(X18,X5))
        | hBOOL(c_in(X5,X18,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f18071,plain,
    ( spl0_636
  <=> hBOOL(c_in(v_y,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f18090,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_y))
    | ~ spl0_89
    | spl0_636 ),
    inference(resolution,[],[f18072,f1218]) ).

fof(f1218,plain,
    ( ! [X2,X18,X5] :
        ( hBOOL(c_in(X5,X18,X2))
        | ~ hBOOL(hAPP(X18,X5)) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f1217]) ).

fof(f18072,plain,
    ( ~ hBOOL(c_in(v_y,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | spl0_636 ),
    inference(avatar_component_clause,[],[f18071]) ).

fof(f18308,plain,
    ( spl0_656
    | ~ spl0_37
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f5289,f4890,f998,f18306]) ).

fof(f18306,plain,
    ( spl0_656
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f4890,plain,
    ( spl0_372
  <=> ! [X5,X0,X12,X6,X2] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | hBOOL(c_in(X5,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f5289,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 )
    | ~ spl0_37
    | ~ spl0_372 ),
    inference(resolution,[],[f4891,f999]) ).

fof(f4891,plain,
    ( ! [X2,X0,X6,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X5,X0,X2))
        | ~ c_Relation_Orefl__on(X0,X6,X2) )
    | ~ spl0_372 ),
    inference(avatar_component_clause,[],[f4890]) ).

fof(f18304,plain,
    ( spl0_655
    | ~ spl0_37
    | ~ spl0_371 ),
    inference(avatar_split_clause,[],[f5265,f4886,f998,f18302]) ).

fof(f18302,plain,
    ( spl0_655
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f4886,plain,
    ( spl0_371
  <=> ! [X5,X0,X12,X6,X2] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | hBOOL(c_in(X12,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f5265,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 )
    | ~ spl0_37
    | ~ spl0_371 ),
    inference(resolution,[],[f4887,f999]) ).

fof(f4887,plain,
    ( ! [X2,X0,X6,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X12,X0,X2))
        | ~ c_Relation_Orefl__on(X0,X6,X2) )
    | ~ spl0_371 ),
    inference(avatar_component_clause,[],[f4886]) ).

fof(f18300,plain,
    ( spl0_654
    | ~ spl0_37
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f5230,f4878,f998,f18298]) ).

fof(f18298,plain,
    ( spl0_654
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f4878,plain,
    ( spl0_369
  <=> ! [X5,X0,X12,X6,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | hBOOL(c_in(X5,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f5230,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X2,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 )
    | ~ spl0_37
    | ~ spl0_369 ),
    inference(resolution,[],[f4879,f999]) ).

fof(f4879,plain,
    ( ! [X2,X0,X6,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X5,X0,X2))
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) )
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f4878]) ).

fof(f18296,plain,
    ( spl0_653
    | ~ spl0_37
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f5206,f4874,f998,f18294]) ).

fof(f18294,plain,
    ( spl0_653
  <=> ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f4874,plain,
    ( spl0_368
  <=> ! [X5,X0,X12,X6,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | hBOOL(c_in(X12,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f5206,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_in(X0,X1,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X1,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X2 )
    | ~ spl0_37
    | ~ spl0_368 ),
    inference(resolution,[],[f4875,f999]) ).

fof(f4875,plain,
    ( ! [X2,X0,X6,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X12,X0,X2))
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) )
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f4874]) ).

fof(f18292,plain,
    ( spl0_652
    | ~ spl0_37
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f5155,f4866,f998,f18290]) ).

fof(f18290,plain,
    ( spl0_652
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f4866,plain,
    ( spl0_366
  <=> ! [X3,X17,X12,X5,X2] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f5155,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_366 ),
    inference(resolution,[],[f4867,f999]) ).

fof(f4867,plain,
    ( ! [X2,X3,X17,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3)))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12)) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f4866]) ).

fof(f18288,plain,
    ( ~ spl0_651
    | ~ spl0_89
    | spl0_635 ),
    inference(avatar_split_clause,[],[f18082,f18067,f1217,f18285]) ).

fof(f18285,plain,
    ( spl0_651
  <=> hBOOL(hAPP(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f18067,plain,
    ( spl0_635
  <=> hBOOL(c_in(v_x,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f18082,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_x))
    | ~ spl0_89
    | spl0_635 ),
    inference(resolution,[],[f18069,f1218]) ).

fof(f18069,plain,
    ( ~ hBOOL(c_in(v_x,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | spl0_635 ),
    inference(avatar_component_clause,[],[f18067]) ).

fof(f18233,plain,
    ( spl0_650
    | ~ spl0_37
    | ~ spl0_347 ),
    inference(avatar_split_clause,[],[f4772,f4518,f998,f18231]) ).

fof(f18231,plain,
    ( spl0_650
  <=> ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f4518,plain,
    ( spl0_347
  <=> ! [X5,X3,X6,X25,X2] :
        ( hBOOL(c_in(X25,c_Relation_ORange(X6,X3,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X5,X25,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f4772,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_in(X0,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_347 ),
    inference(resolution,[],[f4519,f999]) ).

fof(f4519,plain,
    ( ! [X2,X3,X6,X5,X25] :
        ( ~ hBOOL(c_in(c_Pair(X5,X25,X3,X2),X6,tc_prod(X3,X2)))
        | hBOOL(c_in(X25,c_Relation_ORange(X6,X3,X2),X2)) )
    | ~ spl0_347 ),
    inference(avatar_component_clause,[],[f4518]) ).

fof(f18211,plain,
    ( spl0_649
    | ~ spl0_179
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f4289,f3904,f1843,f18209]) ).

fof(f18209,plain,
    ( spl0_649
  <=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f1843,plain,
    ( spl0_179
  <=> ! [X6,X2,X25] : hBOOL(c_in(c_Pair(X25,X25,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f3904,plain,
    ( spl0_317
  <=> ! [X6,X2] :
        ( c_Nitpick_Orefl_H(X6,X2)
        | ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f4289,plain,
    ( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_179
    | ~ spl0_317 ),
    inference(resolution,[],[f3905,f1844]) ).

fof(f1844,plain,
    ( ! [X2,X6,X25] : hBOOL(c_in(c_Pair(X25,X25,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f1843]) ).

fof(f3905,plain,
    ( ! [X2,X6] :
        ( ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2)))
        | c_Nitpick_Orefl_H(X6,X2) )
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f3904]) ).

fof(f18207,plain,
    ( spl0_648
    | ~ spl0_179
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2736,f2307,f1843,f18205]) ).

fof(f18205,plain,
    ( spl0_648
  <=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f2736,plain,
    ( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_179
    | ~ spl0_218 ),
    inference(resolution,[],[f2308,f1844]) ).

fof(f18203,plain,
    ( spl0_647
    | ~ spl0_179
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2720,f2299,f1843,f18201]) ).

fof(f18201,plain,
    ( spl0_647
  <=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f2720,plain,
    ( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1)
    | ~ spl0_179
    | ~ spl0_216 ),
    inference(resolution,[],[f2300,f1844]) ).

fof(f18182,plain,
    ( spl0_646
    | ~ spl0_14
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f6004,f5392,f904,f18180]) ).

fof(f18180,plain,
    ( spl0_646
  <=> ! [X0,X1] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f5392,plain,
    ( spl0_387
  <=> ! [X3,X0,X5,X27,X2] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | c_Set_Oimage(c_COMBK(X27,X3,X2),X0,X2,X3) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f6004,plain,
    ( ! [X0,X1] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Set_Oimage(c_COMBK(X0,X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1)
    | ~ spl0_14
    | ~ spl0_387 ),
    inference(resolution,[],[f5393,f906]) ).

fof(f5393,plain,
    ( ! [X2,X3,X0,X27,X5] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | c_Set_Oimage(c_COMBK(X27,X3,X2),X0,X2,X3) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f5392]) ).

fof(f18178,plain,
    ( ~ spl0_645
    | ~ spl0_421
    | spl0_635 ),
    inference(avatar_split_clause,[],[f18076,f18067,f6491,f18175]) ).

fof(f18175,plain,
    ( spl0_645
  <=> c_Equiv__Relations_Oequiv(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f6491,plain,
    ( spl0_421
  <=> ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f18076,plain,
    ( ~ c_Equiv__Relations_Oequiv(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_421
    | spl0_635 ),
    inference(resolution,[],[f18069,f6492]) ).

fof(f6492,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_421 ),
    inference(avatar_component_clause,[],[f6491]) ).

fof(f18173,plain,
    ( spl0_643
    | ~ spl0_644
    | ~ spl0_14
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f12995,f12569,f904,f18170,f18167]) ).

fof(f18167,plain,
    ( spl0_643
  <=> ! [X0] :
        ( ~ hBOOL(c_in(c_Pair(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | v_x = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f18170,plain,
    ( spl0_644
  <=> c_Relation_Osingle__valued(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f12569,plain,
    ( spl0_537
  <=> ! [X5,X3,X13,X6,X12,X2] :
        ( X12 = X13
        | ~ c_Relation_Osingle__valued(X6,X2,X3)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X6,tc_prod(X2,X3)))
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X3),X6,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f12995,plain,
    ( ! [X0] :
        ( ~ c_Relation_Osingle__valued(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
        | ~ hBOOL(c_in(c_Pair(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | v_x = X0 )
    | ~ spl0_14
    | ~ spl0_537 ),
    inference(resolution,[],[f12570,f906]) ).

fof(f12570,plain,
    ( ! [X2,X3,X6,X5,X12,X13] :
        ( ~ hBOOL(c_in(c_Pair(X5,X13,X2,X3),X6,tc_prod(X2,X3)))
        | ~ c_Relation_Osingle__valued(X6,X2,X3)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X6,tc_prod(X2,X3)))
        | X12 = X13 )
    | ~ spl0_537 ),
    inference(avatar_component_clause,[],[f12569]) ).

fof(f18165,plain,
    ( ~ spl0_642
    | ~ spl0_15
    | spl0_1
    | ~ spl0_14
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f12405,f10699,f904,f840,f909,f18162]) ).

fof(f18162,plain,
    ( spl0_642
  <=> c_Relation_Oantisym(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f840,plain,
    ( spl0_1
  <=> v_x = v_y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f10699,plain,
    ( spl0_523
  <=> ! [X6,X25,X2,X26] :
        ( ~ c_Relation_Oantisym(X6,X2)
        | X25 = X26
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f12405,plain,
    ( v_x = v_y
    | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ c_Relation_Oantisym(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_14
    | ~ spl0_523 ),
    inference(resolution,[],[f10700,f906]) ).

fof(f10700,plain,
    ( ! [X2,X6,X26,X25] :
        ( ~ hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2)))
        | X25 = X26
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Relation_Oantisym(X6,X2) )
    | ~ spl0_523 ),
    inference(avatar_component_clause,[],[f10699]) ).

fof(f18160,plain,
    ( spl0_640
    | ~ spl0_641
    | ~ spl0_37
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f9026,f8242,f998,f18157,f18154]) ).

fof(f18154,plain,
    ( spl0_640
  <=> ! [X0,X1] :
        ( hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f18157,plain,
    ( spl0_641
  <=> c_Relation_Osym(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f8242,plain,
    ( spl0_464
  <=> ! [X6,X25,X2,X26] :
        ( ~ c_Relation_Osym(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f9026,plain,
    ( ! [X0,X1] :
        ( ~ c_Relation_Osym(v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_464 ),
    inference(duplicate_literal_removal,[],[f9007]) ).

fof(f9007,plain,
    ( ! [X0,X1] :
        ( ~ c_Relation_Osym(v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_464 ),
    inference(resolution,[],[f8243,f999]) ).

fof(f8243,plain,
    ( ! [X2,X6,X26,X25] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Relation_Osym(X6,X2)
        | hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2))) )
    | ~ spl0_464 ),
    inference(avatar_component_clause,[],[f8242]) ).

fof(f18103,plain,
    ( spl0_639
    | ~ spl0_15
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f9085,f8250,f909,f18101]) ).

fof(f18101,plain,
    ( spl0_639
  <=> ! [X0] :
        ( hBOOL(c_in(v_y,c_Relation_OImage(v_L,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f9085,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_y,c_Relation_OImage(v_L,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_15
    | ~ spl0_466 ),
    inference(resolution,[],[f8251,f911]) ).

fof(f18099,plain,
    ( ~ spl0_638
    | ~ spl0_428
    | spl0_635 ),
    inference(avatar_split_clause,[],[f18075,f18067,f6882,f18096]) ).

fof(f18096,plain,
    ( spl0_638
  <=> c_Relation_Orefl__on(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f6882,plain,
    ( spl0_428
  <=> ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f18075,plain,
    ( ~ c_Relation_Orefl__on(c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_428
    | spl0_635 ),
    inference(resolution,[],[f18069,f6883]) ).

fof(f6883,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_428 ),
    inference(avatar_component_clause,[],[f6882]) ).

fof(f18094,plain,
    ( spl0_637
    | ~ spl0_14
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f9084,f8250,f904,f18092]) ).

fof(f18092,plain,
    ( spl0_637
  <=> ! [X0] :
        ( hBOOL(c_in(v_x,c_Relation_OImage(v_L,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f9084,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_x,c_Relation_OImage(v_L,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
        | ~ hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt)) )
    | ~ spl0_14
    | ~ spl0_466 ),
    inference(resolution,[],[f8251,f906]) ).

fof(f18074,plain,
    ( ~ spl0_635
    | spl0_636
    | ~ spl0_14
    | ~ spl0_465 ),
    inference(avatar_split_clause,[],[f9045,f8246,f904,f18071,f18067]) ).

fof(f9045,plain,
    ( hBOOL(c_in(v_y,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ hBOOL(c_in(v_x,c_Wellfounded_Oacc(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_14
    | ~ spl0_465 ),
    inference(resolution,[],[f8247,f906]) ).

fof(f18065,plain,
    ( ~ spl0_15
    | ~ spl0_634
    | ~ spl0_14
    | ~ spl0_463 ),
    inference(avatar_split_clause,[],[f8965,f8238,f904,f18062,f909]) ).

fof(f18062,plain,
    ( spl0_634
  <=> c_Wellfounded_Owf(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f8238,plain,
    ( spl0_463
  <=> ! [X5,X6,X25,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X25,X5,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f8965,plain,
    ( ~ c_Wellfounded_Owf(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_14
    | ~ spl0_463 ),
    inference(resolution,[],[f8239,f906]) ).

fof(f8239,plain,
    ( ! [X2,X6,X5,X25] :
        ( ~ hBOOL(c_in(c_Pair(X25,X5,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2))) )
    | ~ spl0_463 ),
    inference(avatar_component_clause,[],[f8238]) ).

fof(f18046,plain,
    ( spl0_633
    | ~ spl0_15
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f7742,f6914,f909,f18044]) ).

fof(f18044,plain,
    ( spl0_633
  <=> ! [X0,X1] : hAPP(X0,v_x) = hAPP(c_Recdef_Ocut(X0,v_L,v_y,tc_Arrow__Order__Mirabelle_Oalt,X1),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f7742,plain,
    ( ! [X0,X1] : hAPP(X0,v_x) = hAPP(c_Recdef_Ocut(X0,v_L,v_y,tc_Arrow__Order__Mirabelle_Oalt,X1),v_x)
    | ~ spl0_15
    | ~ spl0_436 ),
    inference(resolution,[],[f6915,f911]) ).

fof(f18007,plain,
    ( spl0_632
    | ~ spl0_14
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f7741,f6914,f904,f18005]) ).

fof(f18005,plain,
    ( spl0_632
  <=> ! [X0,X1] : hAPP(X0,v_y) = hAPP(c_Recdef_Ocut(X0,v_L,v_x,tc_Arrow__Order__Mirabelle_Oalt,X1),v_y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f7741,plain,
    ( ! [X0,X1] : hAPP(X0,v_y) = hAPP(c_Recdef_Ocut(X0,v_L,v_x,tc_Arrow__Order__Mirabelle_Oalt,X1),v_y)
    | ~ spl0_14
    | ~ spl0_436 ),
    inference(resolution,[],[f6915,f906]) ).

fof(f18003,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f838,f18001]) ).

fof(f18001,plain,
    ( spl0_631
  <=> ! [X6,X25,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
        | ~ hBOOL(c_in(X25,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
        | ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
        | ~ c_Relation_Oantisym(X6,X2)
        | X25 = X26
        | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f838,plain,
    ! [X2,X6,X26,X25] :
      ( ~ hBOOL(c_in(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
      | ~ hBOOL(c_in(X25,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
      | ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f837,f263]) ).

fof(f263,axiom,
    ! [X2,X3,X0,X4] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).

fof(f837,plain,
    ! [X2,X6,X26,X25] :
      ( ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),X2))
      | ~ hBOOL(c_in(X25,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
      | ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f836,f197]) ).

fof(f197,axiom,
    ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

fof(f836,plain,
    ! [X2,X6,X26,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2))
      | ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f835,f263]) ).

fof(f835,plain,
    ! [X2,X6,X26,X25] :
      ( ~ hBOOL(c_in(X25,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),X2))
      | ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f834,f197]) ).

fof(f834,plain,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Orefl__on(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ hBOOL(c_in(X25,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f833,f263]) ).

fof(f833,plain,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),X6,X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ hBOOL(c_in(X25,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(forward_demodulation,[],[f777,f197]) ).

fof(f777,plain,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X6,X2)
      | ~ hBOOL(c_in(X25,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | ~ hBOOL(c_in(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    inference(definition_unfolding,[],[f354,f678,f678,f678]) ).

fof(f678,plain,
    ! [X2,X6] : c_Relation_OField(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f269,f514]) ).

fof(f514,axiom,
    ! [X2,X3,X6] : c_Relation_ODomain(X6,X2,X3) = c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).

fof(f269,axiom,
    ! [X2,X6] : c_Relation_OField(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X6,X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def_0) ).

fof(f354,axiom,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ c_Relation_Orefl__on(c_Relation_OField(X6,X2),X6,X2)
      | ~ hBOOL(c_in(X25,c_Relation_OField(X6,X2),X2))
      | ~ hBOOL(c_in(X26,c_Relation_OField(X6,X2),X2))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).

fof(f17856,plain,
    ( spl0_630
    | ~ spl0_426
    | ~ spl0_444
    | ~ spl0_629 ),
    inference(avatar_split_clause,[],[f17852,f17846,f7789,f6874,f17854]) ).

fof(f17854,plain,
    ( spl0_630
  <=> ! [X6,X2,X7] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f6874,plain,
    ( spl0_426
  <=> ! [X4,X0,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f7789,plain,
    ( spl0_444
  <=> ! [X4,X0,X3,X2] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f17846,plain,
    ( spl0_629
  <=> ! [X6,X2,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f17852,plain,
    ( ! [X2,X6,X7] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
    | ~ spl0_426
    | ~ spl0_444
    | ~ spl0_629 ),
    inference(forward_demodulation,[],[f17851,f7790]) ).

fof(f7790,plain,
    ( ! [X2,X3,X0,X4] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool))
    | ~ spl0_444 ),
    inference(avatar_component_clause,[],[f7789]) ).

fof(f17851,plain,
    ( ! [X2,X6,X7] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
    | ~ spl0_426
    | ~ spl0_444
    | ~ spl0_629 ),
    inference(forward_demodulation,[],[f17850,f7790]) ).

fof(f17850,plain,
    ( ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2)
    | ~ spl0_426
    | ~ spl0_444
    | ~ spl0_629 ),
    inference(forward_demodulation,[],[f17849,f6875]) ).

fof(f6875,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
    | ~ spl0_426 ),
    inference(avatar_component_clause,[],[f6874]) ).

fof(f17849,plain,
    ( ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2)
    | ~ spl0_444
    | ~ spl0_629 ),
    inference(forward_demodulation,[],[f17847,f7790]) ).

fof(f17847,plain,
    ( ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),tc_fun(X2,tc_bool))
    | ~ spl0_629 ),
    inference(avatar_component_clause,[],[f17846]) ).

fof(f17848,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f788,f17846]) ).

fof(f788,plain,
    ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f787,f197]) ).

fof(f787,plain,
    ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f786,f197]) ).

fof(f786,plain,
    ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f714,f197]) ).

fof(f714,plain,
    ! [X2,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),c_Relation_ORange(X7,X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f185,f678,f678,f678]) ).

fof(f185,axiom,
    ! [X2,X6,X7] : c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X6,X2),c_Relation_OField(X7,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__Un_0) ).

fof(f17783,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f101,f17781]) ).

fof(f17781,plain,
    ( spl0_628
  <=> ! [X4,X0,X3,X25,X2,X26] : c_Product__Type_OSigma(c_Set_Oinsert(X25,X0,X2),c_COMBK(c_Set_Oinsert(X26,X4,X3),tc_fun(X3,tc_bool),X2),X2,X3) = c_Set_Oinsert(c_Pair(X25,X26,X2,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X0,c_COMBK(c_Set_Oinsert(X26,X4,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X25,X0,X2),c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f101,axiom,
    ! [X2,X3,X0,X26,X4,X25] : c_Product__Type_OSigma(c_Set_Oinsert(X25,X0,X2),c_COMBK(c_Set_Oinsert(X26,X4,X3),tc_fun(X3,tc_bool),X2),X2,X3) = c_Set_Oinsert(c_Pair(X25,X26,X2,X3),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X0,c_COMBK(c_Set_Oinsert(X26,X4,X3),tc_fun(X3,tc_bool),X2),X2,X3),c_Product__Type_OSigma(c_Set_Oinsert(X25,X0,X2),c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),tc_prod(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).

fof(f17705,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f435,f17703]) ).

fof(f17703,plain,
    ( spl0_627
  <=> ! [X5,X13,X12,X6,X2] :
        ( ~ c_Relation_Osingle__valued(X6,X2,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X12,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X13,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f435,axiom,
    ! [X2,X6,X5,X12,X13] :
      ( ~ c_Relation_Osingle__valued(X6,X2,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X12,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X13,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).

fof(f17701,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f83,f17699]) ).

fof(f17699,plain,
    ( spl0_626
  <=> ! [X6,X4,X16,X0,X7,X3,X2,X1] :
        ( ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
        | ~ c_lessequals(X7,c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X16,tc_bool),X3),X3,X16),tc_fun(tc_prod(X3,X16),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X6,X7,X2,X3,X16),c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X16,tc_bool),X2),X2,X16),tc_fun(tc_prod(X2,X16),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f83,axiom,
    ! [X2,X3,X0,X1,X6,X7,X16,X4] :
      ( ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool))
      | ~ c_lessequals(X7,c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X16,tc_bool),X3),X3,X16),tc_fun(tc_prod(X3,X16),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X6,X7,X2,X3,X16),c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X16,tc_bool),X2),X2,X16),tc_fun(tc_prod(X2,X16),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).

fof(f17628,plain,
    spl0_625,
    inference(avatar_split_clause,[],[f773,f17626]) ).

fof(f17626,plain,
    ( spl0_625
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f773,plain,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f616,f538,f538,f538]) ).

fof(f538,axiom,
    ! [X2,X6] : c_Transitive__Closure_Otrancl(X6,X2) = c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

fof(f616,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).

fof(f17269,plain,
    ( spl0_624
    | ~ spl0_155
    | ~ spl0_163
    | ~ spl0_500
    | ~ spl0_513
    | ~ spl0_623 ),
    inference(avatar_split_clause,[],[f17265,f17261,f10659,f10498,f1773,f1740,f17267]) ).

fof(f17267,plain,
    ( spl0_624
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f1740,plain,
    ( spl0_155
  <=> ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1773,plain,
    ( spl0_163
  <=> ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f10498,plain,
    ( spl0_500
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f10659,plain,
    ( spl0_513
  <=> ! [X4,X0,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f17261,plain,
    ( spl0_623
  <=> ! [X4,X0,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f17265,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_155
    | ~ spl0_163
    | ~ spl0_500
    | ~ spl0_513
    | ~ spl0_623 ),
    inference(forward_demodulation,[],[f17264,f10726]) ).

fof(f10726,plain,
    ( ! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_155
    | ~ spl0_500 ),
    inference(superposition,[],[f10499,f1741]) ).

fof(f1741,plain,
    ( ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool))
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1740]) ).

fof(f10499,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_500 ),
    inference(avatar_component_clause,[],[f10498]) ).

fof(f17264,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_163
    | ~ spl0_513
    | ~ spl0_623 ),
    inference(forward_demodulation,[],[f17262,f11521]) ).

fof(f11521,plain,
    ( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_163
    | ~ spl0_513 ),
    inference(superposition,[],[f10660,f1774]) ).

fof(f1774,plain,
    ( ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool))
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1773]) ).

fof(f10660,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_513 ),
    inference(avatar_component_clause,[],[f10659]) ).

fof(f17262,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_623 ),
    inference(avatar_component_clause,[],[f17261]) ).

fof(f17263,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f797,f17261]) ).

fof(f797,plain,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f163,f153]) ).

fof(f153,axiom,
    ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

fof(f163,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

fof(f17183,plain,
    ( spl0_622
    | ~ spl0_444
    | ~ spl0_621 ),
    inference(avatar_split_clause,[],[f17179,f17176,f7789,f17181]) ).

fof(f17181,plain,
    ( spl0_622
  <=> ! [X6,X2] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_COMBK(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f17176,plain,
    ( spl0_621
  <=> ! [X6,X2] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_COMBK(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f17179,plain,
    ( ! [X2,X6] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_COMBK(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ spl0_444
    | ~ spl0_621 ),
    inference(forward_demodulation,[],[f17177,f7790]) ).

fof(f17177,plain,
    ( ! [X2,X6] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_COMBK(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ spl0_621 ),
    inference(avatar_component_clause,[],[f17176]) ).

fof(f17178,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f789,f17176]) ).

fof(f789,plain,
    ! [X2,X6] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_COMBK(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(forward_demodulation,[],[f716,f197]) ).

fof(f716,plain,
    ! [X2,X6] : c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_COMBK(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(definition_unfolding,[],[f295,f538,f678,f678]) ).

fof(f295,axiom,
    ! [X2,X6] : c_lessequals(c_Transitive__Closure_Otrancl(X6,X2),c_Product__Type_OSigma(c_Relation_OField(X6,X2),c_COMBK(c_Relation_OField(X6,X2),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).

fof(f17016,plain,
    ( spl0_620
    | ~ spl0_90
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f16729,f15556,f1221,f17013]) ).

fof(f17013,plain,
    ( spl0_620
  <=> hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f1221,plain,
    ( spl0_90
  <=> ! [X18,X5,X2] :
        ( hBOOL(hAPP(X18,X5))
        | ~ hBOOL(c_in(X5,X18,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f15556,plain,
    ( spl0_592
  <=> hBOOL(c_in(v_x,c_Relation_ORange(c_Relation_Oconverse(v_L,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_592])]) ).

fof(f16729,plain,
    ( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x))
    | ~ spl0_90
    | ~ spl0_592 ),
    inference(resolution,[],[f15558,f1222]) ).

fof(f1222,plain,
    ( ! [X2,X18,X5] :
        ( ~ hBOOL(c_in(X5,X18,X2))
        | hBOOL(hAPP(X18,X5)) )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f1221]) ).

fof(f15558,plain,
    ( hBOOL(c_in(v_x,c_Relation_ORange(c_Relation_Oconverse(v_L,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_592 ),
    inference(avatar_component_clause,[],[f15556]) ).

fof(f17011,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f772,f17009]) ).

fof(f17009,plain,
    ( spl0_619
  <=> ! [X5,X13,X6,X2] :
        ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f772,plain,
    ! [X2,X6,X5,X13] :
      ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f374,f538,f538]) ).

fof(f374,axiom,
    ! [X2,X6,X5,X13] :
      ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X13,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).

fof(f17007,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f771,f17005]) ).

fof(f17005,plain,
    ( spl0_618
  <=> ! [X6,X25,X2,X26] :
        ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f771,plain,
    ! [X2,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f379,f538,f538]) ).

fof(f379,axiom,
    ! [X2,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).

fof(f16871,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f768,f16869]) ).

fof(f16869,plain,
    ( spl0_617
  <=> ! [X6,X38,X39] :
        ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
        | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
        | hBOOL(c_in(c_Pair(X38,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X38,X39,X6),t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f768,plain,
    ! [X38,X39,X6] :
      ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(X38,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X38,X39,X6),t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,t_a),t_a,t_a,t_a),tc_prod(t_a,t_a))) ),
    inference(definition_unfolding,[],[f376,f538,f538]) ).

fof(f376,axiom,
    ! [X38,X39,X6] :
      ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Otrancl(X6,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(X38,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X38,X39,X6),t_a,t_a),c_Transitive__Closure_Otrancl(X6,t_a),tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).

fof(f16867,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f760,f16865]) ).

fof(f16865,plain,
    ( spl0_616
  <=> ! [X6,X2,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f760,plain,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(definition_unfolding,[],[f6,f538,f538]) ).

fof(f6,axiom,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Otrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).

fof(f16748,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f775,f16746]) ).

fof(f16746,plain,
    ( spl0_615
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f775,plain,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f433,f538,f538]) ).

fof(f433,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).

fof(f16744,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f774,f16742]) ).

fof(f16742,plain,
    ( spl0_614
  <=> ! [X5,X13,X12,X6,X2] :
        ( ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f774,plain,
    ! [X2,X6,X5,X12,X13] :
      ( ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f432,f538,f538]) ).

fof(f432,axiom,
    ! [X2,X6,X5,X12,X13] :
      ( ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).

fof(f16573,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f826,f16571]) ).

fof(f16571,plain,
    ( spl0_613
  <=> ! [X6,X2,X7] :
        ( ~ c_lessequals(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f826,plain,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(forward_demodulation,[],[f761,f481]) ).

fof(f481,axiom,
    ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).

fof(f761,plain,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(definition_unfolding,[],[f317,f500]) ).

fof(f500,axiom,
    ! [X2] : c_Relation_OId(X2) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).

fof(f317,axiom,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(c_Relation_OId(X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)),X6,X2,X2,X2),X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).

fof(f16569,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f764,f16567]) ).

fof(f16567,plain,
    ( spl0_612
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f764,plain,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f594,f538,f538]) ).

fof(f594,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).

fof(f16565,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f763,f16563]) ).

fof(f16563,plain,
    ( spl0_611
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f763,plain,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f593,f538,f538]) ).

fof(f593,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).

fof(f16506,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f832,f16504]) ).

fof(f16504,plain,
    ( spl0_610
  <=> ! [X4,X0,X2,X1] :
        ( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
        | c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
        | c_Relation_Orel__comp(X4,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f832,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X4,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(forward_demodulation,[],[f831,f481]) ).

fof(f831,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X4,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2) ),
    inference(forward_demodulation,[],[f830,f481]) ).

fof(f830,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(X4,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X0,X1,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2) ),
    inference(forward_demodulation,[],[f335,f481]) ).

fof(f335,axiom,
    ! [X2,X0,X1,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X4,X1,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X0,X1,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X2),tc_bool)),X1,X2,X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).

fof(f16502,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f829,f16500]) ).

fof(f16500,plain,
    ( spl0_609
  <=> ! [X4,X0,X2,X1] :
        ( c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
        | c_Relation_Orel__comp(X0,X4,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
        | c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f829,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X0,X4,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    inference(forward_demodulation,[],[f828,f481]) ).

fof(f828,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(X0,X4,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
    inference(forward_demodulation,[],[f827,f481]) ).

fof(f827,plain,
    ! [X2,X0,X1,X4] :
      ( c_Relation_Orel__comp(X0,X1,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X0,X4,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
    inference(forward_demodulation,[],[f336,f481]) ).

fof(f336,axiom,
    ! [X2,X0,X1,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X0,X1,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X0,X4,X2,X2,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_Orel__comp(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).

fof(f16498,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f383,f16496]) ).

fof(f16496,plain,
    ( spl0_608
  <=> ! [X0,X6,X25,X2,X26] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | ~ hBOOL(c_in(X26,X0,X2))
        | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ c_lessequals(c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f383,axiom,
    ! [X2,X0,X6,X26,X25] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | ~ hBOOL(c_in(X26,X0,X2))
      | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ c_lessequals(c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).

fof(f16432,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f384,f16430]) ).

fof(f16430,plain,
    ( spl0_607
  <=> ! [X5,X0,X6,X25,X2,X26] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(X5,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f384,axiom,
    ! [X2,X0,X6,X26,X5,X25] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(X5,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).

fof(f16320,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f770,f16318]) ).

fof(f16318,plain,
    ( spl0_606
  <=> ! [X6,X25,X2,X26] :
        ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X26,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f770,plain,
    ! [X2,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X26,X2,X2),X6,tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f378,f538]) ).

fof(f378,axiom,
    ! [X2,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X25,X26,X6,X2),X26,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).

fof(f16316,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f769,f16314]) ).

fof(f16314,plain,
    ( spl0_605
  <=> ! [X5,X13,X6,X2] :
        ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f769,plain,
    ! [X2,X6,X5,X13] :
      ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f381,f538]) ).

fof(f381,axiom,
    ! [X2,X6,X5,X13] :
      ( hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X6,X5,X13,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).

fof(f16250,plain,
    ( spl0_604
    | ~ spl0_90
    | ~ spl0_588 ),
    inference(avatar_split_clause,[],[f15847,f15247,f1221,f16247]) ).

fof(f16247,plain,
    ( spl0_604
  <=> hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f15247,plain,
    ( spl0_588
  <=> hBOOL(c_in(v_y,c_Relation_ORange(c_Relation_Oconverse(v_L,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_588])]) ).

fof(f15847,plain,
    ( hBOOL(hAPP(c_Relation_ORange(c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y))
    | ~ spl0_90
    | ~ spl0_588 ),
    inference(resolution,[],[f15249,f1222]) ).

fof(f15249,plain,
    ( hBOOL(c_in(v_y,c_Relation_ORange(c_Relation_Oconverse(v_L,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_588 ),
    inference(avatar_component_clause,[],[f15247]) ).

fof(f16245,plain,
    spl0_603,
    inference(avatar_split_clause,[],[f767,f16243]) ).

fof(f16243,plain,
    ( spl0_603
  <=> ! [X6,X38,X39] :
        ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
        | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,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(X38,X39,X6),X39,t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f767,plain,
    ! [X38,X39,X6] :
      ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,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(X38,X39,X6),X39,t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    inference(definition_unfolding,[],[f382,f538]) ).

fof(f382,axiom,
    ! [X38,X39,X6] :
      ( hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),X6,tc_prod(t_a,t_a)))
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Otrancl(X6,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X38,X39,X6),X39,t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).

fof(f16241,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f416,f16239]) ).

fof(f16239,plain,
    ( spl0_602
  <=> ! [X0,X6,X25,X2,X26] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | ~ hBOOL(c_in(X26,X0,X2))
        | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f416,axiom,
    ! [X2,X0,X6,X26,X25] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | ~ hBOOL(c_in(X26,X0,X2))
      | hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) != c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).

fof(f15979,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f796,f15977]) ).

fof(f15977,plain,
    ( spl0_601
  <=> ! [X6,X25,X2,X26] : c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),X2),c_Set_Oinsert(X26,c_Relation_ORange(X6,X2,X2),X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f796,plain,
    ! [X2,X6,X26,X25] : c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),X2),c_Set_Oinsert(X26,c_Relation_ORange(X6,X2,X2),X2),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f795,f715]) ).

fof(f715,plain,
    ! [X2,X3,X6,X26,X25] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2),
    inference(definition_unfolding,[],[f67,f514,f514]) ).

fof(f67,axiom,
    ! [X2,X3,X6,X26,X25] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)),X2,X3) = c_Set_Oinsert(X25,c_Relation_ODomain(X6,X2,X3),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).

fof(f795,plain,
    ! [X2,X6,X26,X25] : c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Set_Oinsert(X26,c_Relation_ORange(X6,X2,X2),X2),tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f794,f214]) ).

fof(f214,axiom,
    ! [X2,X3,X6,X26,X25] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)),X3,X2) = c_Set_Oinsert(X26,c_Relation_ORange(X6,X3,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).

fof(f794,plain,
    ! [X2,X6,X26,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2),X2),
    inference(forward_demodulation,[],[f793,f263]) ).

fof(f793,plain,
    ! [X2,X6,X26,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),X2),X2),
    inference(forward_demodulation,[],[f792,f197]) ).

fof(f792,plain,
    ! [X2,X6,X26,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),X2),X2),
    inference(forward_demodulation,[],[f791,f201]) ).

fof(f201,axiom,
    ! [X2,X0,X25] : c_Set_Oinsert(X25,X0,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

fof(f791,plain,
    ! [X2,X6,X26,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X2),
    inference(forward_demodulation,[],[f720,f56]) ).

fof(f56,axiom,
    ! [X2,X1,X4,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

fof(f720,plain,
    ! [X2,X6,X26,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),X2,X2),c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2,X2),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f164,f678,f678]) ).

fof(f164,axiom,
    ! [X2,X6,X26,X25] : c_Relation_OField(c_Set_Oinsert(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),c_Relation_OField(X6,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__insert_0) ).

fof(f15975,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f765,f15973]) ).

fof(f15973,plain,
    ( spl0_600
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f765,plain,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f441,f538]) ).

fof(f441,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).

fof(f15866,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f753,f15864]) ).

fof(f15864,plain,
    ( spl0_599
  <=> ! [X6,X2,X0] :
        ( ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f753,plain,
    ! [X2,X0,X6] :
      ( ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(definition_unfolding,[],[f130,f538]) ).

fof(f130,axiom,
    ! [X2,X0,X6] :
      ( ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Otrancl(X6,X2),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).

fof(f15862,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f352,f15860]) ).

fof(f352,axiom,
    ! [X2,X0,X6,X26,X25] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | c_lessequals(c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),c_Relation_OImage(X6,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).

fof(f15690,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f811,f15688]) ).

fof(f15688,plain,
    ( spl0_597
  <=> ! [X6,X2,X7] :
        ( c_lessequals(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
        | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f811,plain,
    ! [X2,X6,X7] :
      ( c_lessequals(c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(forward_demodulation,[],[f810,f263]) ).

fof(f810,plain,
    ! [X2,X6,X7] :
      ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(forward_demodulation,[],[f809,f197]) ).

fof(f809,plain,
    ! [X2,X6,X7] :
      ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X7,c_Relation_Oconverse(X7,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(forward_demodulation,[],[f808,f263]) ).

fof(f808,plain,
    ! [X2,X6,X7] :
      ( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X7,X2,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(forward_demodulation,[],[f737,f197]) ).

fof(f737,plain,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X6,X2,X2),tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X7,X2,X2),X2,X2),c_Relation_ORange(X7,X2,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    inference(definition_unfolding,[],[f262,f678,f678]) ).

fof(f262,axiom,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Relation_OField(X6,X2),c_Relation_OField(X7,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).

fof(f15640,plain,
    ( spl0_596
    | ~ spl0_175
    | ~ spl0_400
    | ~ spl0_595 ),
    inference(avatar_split_clause,[],[f15636,f15632,f5445,f1821,f15638]) ).

fof(f15638,plain,
    ( spl0_596
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f5445,plain,
    ( spl0_400
  <=> ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f15632,plain,
    ( spl0_595
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f15636,plain,
    ( ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2)
    | ~ spl0_175
    | ~ spl0_400
    | ~ spl0_595 ),
    inference(forward_demodulation,[],[f15635,f5446]) ).

fof(f5446,plain,
    ( ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_400 ),
    inference(avatar_component_clause,[],[f5445]) ).

fof(f15635,plain,
    ( ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2)
    | ~ spl0_175
    | ~ spl0_595 ),
    inference(forward_demodulation,[],[f15633,f1822]) ).

fof(f15633,plain,
    ( ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2)
    | ~ spl0_595 ),
    inference(avatar_component_clause,[],[f15632]) ).

fof(f15634,plain,
    spl0_595,
    inference(avatar_split_clause,[],[f680,f15632]) ).

fof(f680,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2,X2),
    inference(definition_unfolding,[],[f396,f538,f500]) ).

fof(f396,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).

fof(f15630,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f316,f15628]) ).

fof(f15628,plain,
    ( spl0_594
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X26))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X19,X25,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f316,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X26))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X19,X25,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).

fof(f15626,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f315,f15624]) ).

fof(f15624,plain,
    ( spl0_593
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X26))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X19,X26,X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f315,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X26))
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X19,X26,X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).

fof(f15559,plain,
    ( spl0_592
    | ~ spl0_15
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f6834,f6487,f909,f15556]) ).

fof(f6834,plain,
    ( hBOOL(c_in(v_x,c_Relation_ORange(c_Relation_Oconverse(v_L,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_15
    | ~ spl0_420 ),
    inference(resolution,[],[f6488,f911]) ).

fof(f15510,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f639,f15508]) ).

fof(f15508,plain,
    ( spl0_591
  <=> ! [X2,X6,X0,X5,X22] :
        ( X5 = X22
        | ~ c_Relation_Ototal__on(X0,X6,X2)
        | ~ hBOOL(c_in(X5,X0,X2))
        | ~ hBOOL(c_in(X22,X0,X2))
        | hBOOL(c_in(c_Pair(X5,X22,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X22,X5,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f639,axiom,
    ! [X2,X0,X6,X5,X22] :
      ( X5 = X22
      | ~ c_Relation_Ototal__on(X0,X6,X2)
      | ~ hBOOL(c_in(X5,X0,X2))
      | ~ hBOOL(c_in(X22,X0,X2))
      | hBOOL(c_in(c_Pair(X5,X22,X2,X2),X6,tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X22,X5,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).

fof(f15506,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f598,f15504]) ).

fof(f15504,plain,
    ( spl0_590
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f598,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).

fof(f15254,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f819,f15252]) ).

fof(f15252,plain,
    ( spl0_589
  <=> ! [X6,X2,X5] :
        ( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
        | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f819,plain,
    ! [X2,X6,X5] :
      ( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(forward_demodulation,[],[f818,f481]) ).

fof(f818,plain,
    ! [X2,X6,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X6,X2),c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(forward_demodulation,[],[f750,f153]) ).

fof(f750,plain,
    ! [X2,X6,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X6,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    inference(definition_unfolding,[],[f420,f538]) ).

fof(f420,axiom,
    ! [X2,X6,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X6,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).

fof(f15250,plain,
    ( spl0_588
    | ~ spl0_14
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f6833,f6487,f904,f15247]) ).

fof(f6833,plain,
    ( hBOOL(c_in(v_y,c_Relation_ORange(c_Relation_Oconverse(v_L,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_14
    | ~ spl0_420 ),
    inference(resolution,[],[f6488,f906]) ).

fof(f15245,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f614,f15243]) ).

fof(f614,axiom,
    ! [X2,X3,X6,X26,X16,X27,X7,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X3,X16),X7,tc_prod(X3,X16)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X16),c_Relation_Orel__comp(X6,X7,X2,X3,X16),tc_prod(X2,X16))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).

fof(f15241,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f414,f15239]) ).

fof(f414,axiom,
    ! [X2,X0,X6,X5,X12] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
      | c_Relation_OImage(X6,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) = c_Relation_OImage(X6,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).

fof(f15237,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f362,f15235]) ).

fof(f15235,plain,
    ( spl0_585
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X26))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2),X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f362,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X26))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2),X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).

fof(f15233,plain,
    spl0_584,
    inference(avatar_split_clause,[],[f361,f15231]) ).

fof(f15231,plain,
    ( spl0_584
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X26))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2),X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f361,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X26))
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2),X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).

fof(f15229,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f351,f15227]) ).

fof(f15227,plain,
    ( spl0_583
  <=> ! [X2,X0,X6,X25,X26] :
        ( X25 = X26
        | hBOOL(c_in(X25,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f351,axiom,
    ! [X2,X0,X6,X26,X25] :
      ( X25 = X26
      | hBOOL(c_in(X25,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).

fof(f15069,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f596,f15067]) ).

fof(f15067,plain,
    ( spl0_582
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f596,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).

fof(f15065,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f595,f15063]) ).

fof(f15063,plain,
    ( spl0_581
  <=> ! [X6,X27,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f595,axiom,
    ! [X2,X6,X26,X27,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X27,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,X27,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).

fof(f15061,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f2,f15059]) ).

fof(f15059,plain,
    ( spl0_580
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ hBOOL(c_in(X5,X1,X2))
        | c_lessequals(X0,X4,tc_fun(X3,tc_bool))
        | ~ c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ hBOOL(c_in(X5,X1,X2))
      | c_lessequals(X0,X4,tc_fun(X3,tc_bool))
      | ~ c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).

fof(f15057,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f1,f15055]) ).

fof(f15055,plain,
    ( spl0_579
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ hBOOL(c_in(X5,X1,X2))
        | ~ c_lessequals(X0,X4,tc_fun(X3,tc_bool))
        | c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ hBOOL(c_in(X5,X1,X2))
      | ~ c_lessequals(X0,X4,tc_fun(X3,tc_bool))
      | c_lessequals(c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2),tc_fun(tc_prod(X3,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).

fof(f14778,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f776,f14776]) ).

fof(f14776,plain,
    ( spl0_578
  <=> ! [X6,X2,X7] :
        ( ~ c_Wellfounded_Owf(X7,X2)
        | ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X7,X2,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f776,plain,
    ! [X2,X6,X7] :
      ( ~ c_Wellfounded_Owf(X7,X2)
      | ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),c_Relation_ORange(X7,X2,X2),tc_fun(X2,tc_bool)) ),
    inference(definition_unfolding,[],[f333,f514]) ).

fof(f333,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Wellfounded_Owf(X7,X2)
      | ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X6,X2,X2),c_Relation_ORange(X7,X2,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).

fof(f14774,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f759,f14772]) ).

fof(f14772,plain,
    ( spl0_577
  <=> ! [X35,X7,X6,X2] :
        ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | ~ hBOOL(c_in(X35,c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(X35,c_Relation_Orel__comp(X7,c_Transitive__Closure_Ortrancl(X7,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f759,plain,
    ! [X2,X6,X7,X35] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ hBOOL(c_in(X35,c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(X35,c_Relation_Orel__comp(X7,c_Transitive__Closure_Ortrancl(X7,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f329,f538,f538]) ).

fof(f329,axiom,
    ! [X2,X6,X7,X35] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X7,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).

fof(f14770,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f719,f14768]) ).

fof(f14768,plain,
    ( spl0_576
  <=> ! [X4,X0,X3,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f719,plain,
    ! [X2,X3,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_Relation_Oconverse(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f10,f514,f514,f514]) ).

fof(f10,axiom,
    ! [X2,X3,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ODomain(X0,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),c_Relation_ODomain(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).

fof(f14766,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f718,f14764]) ).

fof(f14764,plain,
    ( spl0_575
  <=> ! [X4,X0,X3,X2] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f718,plain,
    ! [X2,X3,X0,X4] : c_lessequals(c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f70,f514,f514,f514]) ).

fof(f70,axiom,
    ! [X2,X3,X0,X4] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X0,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).

fof(f14762,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f646,f14760]) ).

fof(f646,axiom,
    ! [X2,X6,X5,X12,X13] :
      ( ~ c_Relation_Otrans(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X12,X13,X2,X2),X6,tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,X13,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).

fof(f14650,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f749,f14648]) ).

fof(f14648,plain,
    ( spl0_573
  <=> ! [X17,X12,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f749,plain,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f409,f538]) ).

fof(f409,axiom,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Otrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).

fof(f14646,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f748,f14644]) ).

fof(f14644,plain,
    ( spl0_572
  <=> ! [X17,X12,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f748,plain,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f408,f538]) ).

fof(f408,axiom,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Otrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).

fof(f14454,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f757,f14452]) ).

fof(f14452,plain,
    ( spl0_571
  <=> ! [X17,X12,X5,X2] :
        ( X5 = X12
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f757,plain,
    ! [X2,X17,X5,X12] :
      ( X5 = X12
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f439,f538]) ).

fof(f439,axiom,
    ! [X2,X17,X5,X12] :
      ( X5 = X12
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Otrancl(X17,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).

fof(f14450,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f386,f14448]) ).

fof(f14448,plain,
    ( spl0_570
  <=> ! [X3,X7,X6,X16,X27,X25,X2] :
        ( ~ hBOOL(c_in(c_Pair(X25,X27,X2,X3),c_Relation_Orel__comp(X6,X7,X2,X16,X3),tc_prod(X2,X3)))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X25,X27,X6,X7,X2,X3,X16),X2,X16),X6,tc_prod(X2,X16))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f386,axiom,
    ! [X2,X3,X6,X7,X27,X16,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X27,X2,X3),c_Relation_Orel__comp(X6,X7,X2,X16,X3),tc_prod(X2,X3)))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X25,X27,X6,X7,X2,X3,X16),X2,X16),X6,tc_prod(X2,X16))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).

fof(f14446,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f385,f14444]) ).

fof(f14444,plain,
    ( spl0_569
  <=> ! [X3,X7,X6,X16,X27,X25,X2] :
        ( ~ hBOOL(c_in(c_Pair(X25,X27,X2,X3),c_Relation_Orel__comp(X6,X7,X2,X16,X3),tc_prod(X2,X3)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X25,X27,X6,X7,X2,X3,X16),X27,X16,X3),X7,tc_prod(X16,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f385,axiom,
    ! [X2,X3,X6,X7,X27,X16,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X27,X2,X3),c_Relation_Orel__comp(X6,X7,X2,X16,X3),tc_prod(X2,X3)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X25,X27,X6,X7,X2,X3,X16),X27,X16,X3),X7,tc_prod(X16,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).

fof(f14442,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f19,f14440]) ).

fof(f14440,plain,
    ( spl0_568
  <=> ! [X15,X3,X16,X14,X6,X2,X7] :
        ( ~ c_lessequals(X14,X6,tc_fun(tc_prod(X2,X3),tc_bool))
        | ~ c_lessequals(X15,X7,tc_fun(tc_prod(X3,X16),tc_bool))
        | c_lessequals(c_Relation_Orel__comp(X14,X15,X2,X3,X16),c_Relation_Orel__comp(X6,X7,X2,X3,X16),tc_fun(tc_prod(X2,X16),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f19,axiom,
    ! [X2,X3,X6,X7,X14,X16,X15] :
      ( ~ c_lessequals(X14,X6,tc_fun(tc_prod(X2,X3),tc_bool))
      | ~ c_lessequals(X15,X7,tc_fun(tc_prod(X3,X16),tc_bool))
      | c_lessequals(c_Relation_Orel__comp(X14,X15,X2,X3,X16),c_Relation_Orel__comp(X6,X7,X2,X3,X16),tc_fun(tc_prod(X2,X16),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).

fof(f14099,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f747,f14097]) ).

fof(f14097,plain,
    ( spl0_567
  <=> ! [X17,X12,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X12,X2,X2),X17,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f747,plain,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X12,X2,X2),X17,tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f380,f538]) ).

fof(f380,axiom,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Otrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X17,X5,X12,X2),X12,X2,X2),X17,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).

fof(f14095,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f746,f14093]) ).

fof(f14093,plain,
    ( spl0_566
  <=> ! [X17,X12,X5,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X2,X2),X17,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f746,plain,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X2,X2),X17,tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f375,f538]) ).

fof(f375,axiom,
    ! [X2,X17,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Otrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X17,X5,X12,X2),X2,X2),X17,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).

fof(f14091,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f744,f14089]) ).

fof(f14089,plain,
    ( spl0_565
  <=> ! [X6,X2,X5] :
        ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f744,plain,
    ! [X2,X6,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f373,f538]) ).

fof(f373,axiom,
    ! [X2,X6,X5] :
      ( ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X6,X2),X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).

fof(f14087,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f717,f14085]) ).

fof(f14085,plain,
    ( spl0_564
  <=> ! [X4,X0,X3,X2] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f717,plain,
    ! [X2,X3,X0,X4] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X0,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X4,X2,X3),X3,X2),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f200,f514,f514,f514]) ).

fof(f200,axiom,
    ! [X2,X3,X0,X4] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X0,X2,X3),c_Relation_ODomain(X4,X2,X3),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).

fof(f14083,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f368,f14081]) ).

fof(f14081,plain,
    ( spl0_563
  <=> ! [X2,X6,X25,X26] :
        ( X25 = X26
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X25,X26,X6,X2),X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f368,axiom,
    ! [X2,X6,X26,X25] :
      ( X25 = X26
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X25,X26,X6,X2),X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).

fof(f14079,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f358,f14077]) ).

fof(f14077,plain,
    ( spl0_562
  <=> ! [X6,X13,X5,X2] :
        ( X5 = X13
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X6,X5,X13,X2),X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f358,axiom,
    ! [X2,X6,X5,X13] :
      ( X5 = X13
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X6,X5,X13,X2),X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).

fof(f13940,plain,
    ( spl0_561
    | ~ spl0_124
    | ~ spl0_438 ),
    inference(avatar_split_clause,[],[f12327,f7080,f1432,f13938]) ).

fof(f13938,plain,
    ( spl0_561
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f7080,plain,
    ( spl0_438
  <=> ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f12327,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 )
    | ~ spl0_124
    | ~ spl0_438 ),
    inference(resolution,[],[f7081,f1433]) ).

fof(f7081,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_438 ),
    inference(avatar_component_clause,[],[f7080]) ).

fof(f13714,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f817,f13712]) ).

fof(f13712,plain,
    ( spl0_560
  <=> ! [X2,X17,X18] :
        ( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f817,plain,
    ! [X2,X18,X17] :
      ( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(forward_demodulation,[],[f816,f183]) ).

fof(f183,axiom,
    ! [X31,X2,X3,X18,X16,X17] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X18,X31,tc_fun(tc_prod(X2,X16),tc_bool)),X17,X2,X16,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X18,X17,X2,X16,X3),c_Relation_Orel__comp(X31,X17,X2,X16,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).

fof(f816,plain,
    ! [X2,X18,X17] :
      ( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X17,X2,X2,X2),c_Relation_Orel__comp(X18,X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(forward_demodulation,[],[f332,f197]) ).

fof(f332,axiom,
    ! [X2,X18,X17] :
      ( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X17,X2,X2,X2),c_Relation_Orel__comp(X18,X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).

fof(f13710,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f815,f13708]) ).

fof(f13708,plain,
    ( spl0_559
  <=> ! [X2,X17,X18] :
        ( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f815,plain,
    ! [X2,X18,X17] :
      ( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(forward_demodulation,[],[f814,f183]) ).

fof(f814,plain,
    ! [X2,X18,X17] :
      ( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X17,X2,X2,X2),c_Relation_Orel__comp(X18,X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(forward_demodulation,[],[f331,f197]) ).

fof(f331,axiom,
    ! [X2,X18,X17] :
      ( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X17,X2,X2,X2),c_Relation_Orel__comp(X18,X17,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).

fof(f13706,plain,
    spl0_558,
    inference(avatar_split_clause,[],[f402,f13704]) ).

fof(f13704,plain,
    ( spl0_558
  <=> ! [X17,X4,X0,X3,X2] :
        ( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X17,X3,X2),X2,X3)
        | c_Relation_OImage(X17,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f402,axiom,
    ! [X2,X3,X0,X4,X17] :
      ( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X17,X3,X2),X2,X3)
      | c_Relation_OImage(X17,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).

fof(f13702,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f364,f13700]) ).

fof(f13700,plain,
    ( spl0_557
  <=> ! [X38,X39,X6] :
        ( X38 = X39
        | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a)))
        | hBOOL(c_in(c_Pair(X38,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X38,X39,X6),t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f364,axiom,
    ! [X38,X39,X6] :
      ( X38 = X39
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(X38,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X38,X39,X6),t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).

fof(f13698,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f219,f13696]) ).

fof(f13696,plain,
    ( spl0_556
  <=> ! [X5,X3,X10,X11,X6,X2] :
        ( c_Recdef_Ocut(X10,X6,X5,X2,X3) = c_Recdef_Ocut(X11,X6,X5,X2,X3)
        | hAPP(X10,c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3)) != hAPP(X11,c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f219,axiom,
    ! [X2,X3,X10,X11,X6,X5] :
      ( c_Recdef_Ocut(X10,X6,X5,X2,X3) = c_Recdef_Ocut(X11,X6,X5,X2,X3)
      | hAPP(X10,c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3)) != hAPP(X11,c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).

fof(f13694,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f184,f13692]) ).

fof(f13692,plain,
    ( spl0_555
  <=> ! [X3,X18,X17,X31,X16,X2] : c_Relation_Orel__comp(X17,c_Lattices_Oupper__semilattice__class_Osup(X18,X31,tc_fun(tc_prod(X16,X3),tc_bool)),X2,X16,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X18,X2,X16,X3),c_Relation_Orel__comp(X17,X31,X2,X16,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f184,axiom,
    ! [X31,X2,X3,X18,X16,X17] : c_Relation_Orel__comp(X17,c_Lattices_Oupper__semilattice__class_Osup(X18,X31,tc_fun(tc_prod(X16,X3),tc_bool)),X2,X16,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X17,X18,X2,X16,X3),c_Relation_Orel__comp(X17,X31,X2,X16,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).

fof(f13690,plain,
    ( spl0_554
    | ~ spl0_124
    | ~ spl0_428 ),
    inference(avatar_split_clause,[],[f10281,f6882,f1432,f13688]) ).

fof(f13688,plain,
    ( spl0_554
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f10281,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 )
    | ~ spl0_124
    | ~ spl0_428 ),
    inference(resolution,[],[f6883,f1433]) ).

fof(f13686,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f183,f13684]) ).

fof(f13684,plain,
    ( spl0_553
  <=> ! [X17,X18,X3,X31,X16,X2] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X18,X31,tc_fun(tc_prod(X2,X16),tc_bool)),X17,X2,X16,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X18,X17,X2,X16,X3),c_Relation_Orel__comp(X31,X17,X2,X16,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f13418,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f606,f13416]) ).

fof(f13416,plain,
    ( spl0_552
  <=> ! [X5,X6,X10,X3,X11,X12,X2] :
        ( hAPP(X10,X12) = hAPP(X11,X12)
        | ~ hBOOL(c_in(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)))
        | c_Recdef_Ocut(X10,X6,X5,X2,X3) != c_Recdef_Ocut(X11,X6,X5,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f606,axiom,
    ! [X2,X3,X10,X11,X6,X5,X12] :
      ( hAPP(X10,X12) = hAPP(X11,X12)
      | ~ hBOOL(c_in(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)))
      | c_Recdef_Ocut(X10,X6,X5,X2,X3) != c_Recdef_Ocut(X11,X6,X5,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).

fof(f13414,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f568,f13412]) ).

fof(f13412,plain,
    ( spl0_551
  <=> ! [X5,X19,X6,X45] :
        ( hBOOL(hAPP(X19,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
        | hBOOL(c_in(X45,c_Wellfounded_Oacc(X6,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X45,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f568,axiom,
    ! [X19,X6,X45,X5] :
      ( hBOOL(hAPP(X19,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
      | hBOOL(c_in(X45,c_Wellfounded_Oacc(X6,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X45,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).

fof(f13410,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f563,f13408]) ).

fof(f13408,plain,
    ( spl0_550
  <=> ! [X5,X19,X6,X45] :
        ( hBOOL(hAPP(X19,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
        | hBOOL(c_in(X45,c_Wellfounded_Oacc(X6,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X45,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f563,axiom,
    ! [X19,X6,X45,X5] :
      ( hBOOL(hAPP(X19,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
      | hBOOL(c_in(X45,c_Wellfounded_Oacc(X6,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X45,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).

fof(f13406,plain,
    ( spl0_549
    | ~ spl0_124
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f9702,f6733,f1432,f13404]) ).

fof(f13404,plain,
    ( spl0_549
  <=> ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f6733,plain,
    ( spl0_424
  <=> ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f9702,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 )
    | ~ spl0_124
    | ~ spl0_424 ),
    inference(resolution,[],[f6734,f1433]) ).

fof(f6734,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_424 ),
    inference(avatar_component_clause,[],[f6733]) ).

fof(f13402,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f359,f13400]) ).

fof(f13400,plain,
    ( spl0_548
  <=> ! [X6,X13,X5,X2] :
        ( X5 = X13
        | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X6,X5,X13,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f359,axiom,
    ! [X2,X6,X5,X13] :
      ( X5 = X13
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X6,X5,X13,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).

fof(f13398,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f357,f13396]) ).

fof(f13396,plain,
    ( spl0_547
  <=> ! [X2,X6,X25,X26] :
        ( X25 = X26
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X25,X26,X6,X2),X26,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f357,axiom,
    ! [X2,X6,X26,X25] :
      ( X25 = X26
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X25,X26,X6,X2),X26,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).

fof(f13394,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f4,f13392]) ).

fof(f13392,plain,
    ( spl0_546
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | c_lessequals(X0,c_Set_Oinsert(X5,X4,X2),tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f4,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X0,X2))
      | c_lessequals(X0,c_Set_Oinsert(X5,X4,X2),tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

fof(f13167,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f702,f13165]) ).

fof(f13165,plain,
    ( spl0_545
  <=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f702,plain,
    ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),X2,X2),c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2,X2),tc_fun(X2,tc_bool)),
    inference(definition_unfolding,[],[f330,f678]) ).

fof(f330,axiom,
    ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__empty_0) ).

fof(f13163,plain,
    spl0_544,
    inference(avatar_split_clause,[],[f611,f13161]) ).

fof(f13161,plain,
    ( spl0_544
  <=> ! [X5,X3,X10,X12,X6,X2] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Oinv__image(X6,X10,X3,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(c_Pair(hAPP(X10,X5),hAPP(X10,X12),X3,X3),X6,tc_prod(X3,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f611,axiom,
    ! [X2,X3,X10,X6,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Oinv__image(X6,X10,X3,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(hAPP(X10,X5),hAPP(X10,X12),X3,X3),X6,tc_prod(X3,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).

fof(f13159,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f610,f13157]) ).

fof(f13157,plain,
    ( spl0_543
  <=> ! [X5,X2,X10,X12,X6,X3] :
        ( ~ hBOOL(c_in(c_Pair(hAPP(X10,X5),hAPP(X10,X12),X3,X3),X6,tc_prod(X3,X3)))
        | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Oinv__image(X6,X10,X3,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f610,axiom,
    ! [X2,X3,X10,X6,X5,X12] :
      ( ~ hBOOL(c_in(c_Pair(hAPP(X10,X5),hAPP(X10,X12),X3,X3),X6,tc_prod(X3,X3)))
      | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_Oinv__image(X6,X10,X3,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).

fof(f13155,plain,
    ( spl0_542
    | ~ spl0_124
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f8206,f6491,f1432,f13153]) ).

fof(f13153,plain,
    ( spl0_542
  <=> ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f8206,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | c_Set_Oinsert(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt) = X0 )
    | ~ spl0_124
    | ~ spl0_421 ),
    inference(resolution,[],[f6492,f1433]) ).

fof(f13151,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f394,f13149]) ).

fof(f13149,plain,
    ( spl0_541
  <=> ! [X5,X3,X10,X11,X6,X2] :
        ( c_Recdef_Ocut(X10,X6,X5,X2,X3) = c_Recdef_Ocut(X11,X6,X5,X2,X3)
        | hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3),X5,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f394,axiom,
    ! [X2,X3,X10,X11,X6,X5] :
      ( c_Recdef_Ocut(X10,X6,X5,X2,X3) = c_Recdef_Ocut(X11,X6,X5,X2,X3)
      | hBOOL(c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X10,X11,X6,X5,X2,X3),X5,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).

fof(f13147,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f366,f13145]) ).

fof(f13145,plain,
    ( spl0_540
  <=> ! [X38,X39,X6] :
        ( X38 = X39
        | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a)))
        | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X38,X39,X6),X39,t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f366,axiom,
    ! [X38,X39,X6] :
      ( X38 = X39
      | ~ hBOOL(c_in(c_Pair(X38,X39,t_a,t_a),c_Transitive__Closure_Ortrancl(X6,t_a),tc_prod(t_a,t_a)))
      | hBOOL(c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X38,X39,X6),X39,t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).

fof(f13022,plain,
    ( spl0_539
    | ~ spl0_301
    | ~ spl0_433
    | ~ spl0_538 ),
    inference(avatar_split_clause,[],[f12576,f12573,f6902,f3488,f13020]) ).

fof(f13020,plain,
    ( spl0_539
  <=> ! [X6,X2] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),c_Relation_Orel__comp(X6,X6,X2,X2,X2),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f3488,plain,
    ( spl0_301
  <=> ! [X6,X2] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2) = c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f6902,plain,
    ( spl0_433
  <=> ! [X3,X18,X42,X17,X31,X16,X2] : c_Relation_Orel__comp(c_Relation_Orel__comp(X17,X18,X2,X42,X16),X31,X2,X16,X3) = c_Relation_Orel__comp(X17,c_Relation_Orel__comp(X18,X31,X42,X16,X3),X2,X42,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f12573,plain,
    ( spl0_538
  <=> ! [X6,X2] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f12576,plain,
    ( ! [X2,X6] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),c_Relation_Orel__comp(X6,X6,X2,X2,X2),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ spl0_301
    | ~ spl0_433
    | ~ spl0_538 ),
    inference(forward_demodulation,[],[f12574,f7581]) ).

fof(f7581,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_301
    | ~ spl0_433 ),
    inference(superposition,[],[f6903,f3489]) ).

fof(f3489,plain,
    ( ! [X2,X6] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2) = c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2)
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f3488]) ).

fof(f6903,plain,
    ( ! [X2,X31,X3,X18,X16,X17,X42] : c_Relation_Orel__comp(c_Relation_Orel__comp(X17,X18,X2,X42,X16),X31,X2,X16,X3) = c_Relation_Orel__comp(X17,c_Relation_Orel__comp(X18,X31,X42,X16,X3),X2,X42,X3)
    | ~ spl0_433 ),
    inference(avatar_component_clause,[],[f6902]) ).

fof(f12574,plain,
    ( ! [X2,X6] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
    | ~ spl0_538 ),
    inference(avatar_component_clause,[],[f12573]) ).

fof(f12575,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f712,f12573]) ).

fof(f712,plain,
    ! [X2,X6] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(definition_unfolding,[],[f334,f538,f538]) ).

fof(f334,axiom,
    ! [X2,X6] : c_Transitive__Closure_Otrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X6,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).

fof(f12571,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f584,f12569]) ).

fof(f584,axiom,
    ! [X2,X3,X6,X5,X12,X13] :
      ( X12 = X13
      | ~ c_Relation_Osingle__valued(X6,X2,X3)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X6,tc_prod(X2,X3)))
      | ~ hBOOL(c_in(c_Pair(X5,X13,X2,X3),X6,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).

fof(f12567,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f569,f12565]) ).

fof(f569,axiom,
    ! [X2,X19,X6,X12,X25] :
      ( hBOOL(hAPP(X19,X12))
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).

fof(f12563,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f556,f12561]) ).

fof(f556,axiom,
    ! [X2,X19,X6,X12,X25] :
      ( hBOOL(hAPP(X19,X12))
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).

fof(f12559,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f367,f12557]) ).

fof(f12557,plain,
    ( spl0_534
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X26))
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X19,X26,X6,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f367,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X26))
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X19,X26,X6,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).

fof(f12555,plain,
    ( spl0_533
    | ~ spl0_90
    | ~ spl0_438 ),
    inference(avatar_split_clause,[],[f12326,f7080,f1221,f12553]) ).

fof(f12553,plain,
    ( spl0_533
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f12326,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_y)) )
    | ~ spl0_90
    | ~ spl0_438 ),
    inference(resolution,[],[f7081,f1222]) ).

fof(f12551,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f365,f12549]) ).

fof(f12549,plain,
    ( spl0_532
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X26))
        | hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f365,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X26))
      | hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X19,X25,X6,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).

fof(f12547,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f363,f12545]) ).

fof(f12545,plain,
    ( spl0_531
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X26))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X19,X25,X6,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f363,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X26))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X19,X25,X6,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).

fof(f12543,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f360,f12541]) ).

fof(f12541,plain,
    ( spl0_530
  <=> ! [X2,X19,X6,X25,X26] :
        ( ~ hBOOL(hAPP(X19,X26))
        | hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f360,axiom,
    ! [X2,X19,X26,X6,X25] :
      ( ~ hBOOL(hAPP(X19,X26))
      | hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X19,X26,X6,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).

fof(f12539,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f325,f12537]) ).

fof(f12537,plain,
    ( spl0_529
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( X0 = X4
        | ~ hBOOL(c_in(X5,X1,X2))
        | c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f325,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( X0 = X4
      | ~ hBOOL(c_in(X5,X1,X2))
      | c_Product__Type_OSigma(X0,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) != c_Product__Type_OSigma(X4,c_COMBK(X1,tc_fun(X2,tc_bool),X3),X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).

fof(f12535,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f84,f12533]) ).

fof(f12533,plain,
    ( spl0_528
  <=> ! [X2,X17,X18] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | ~ c_Wellfounded_Owf(X18,X2)
        | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_lessequals(c_Relation_Orel__comp(X17,X18,X2,X2,X2),X17,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f84,axiom,
    ! [X2,X18,X17] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | ~ c_Wellfounded_Owf(X18,X2)
      | c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_lessequals(c_Relation_Orel__comp(X17,X18,X2,X2,X2),X17,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).

fof(f12531,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f79,f12529]) ).

fof(f12529,plain,
    ( spl0_527
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f79,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

fof(f12527,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f78,f12525]) ).

fof(f12525,plain,
    ( spl0_526
  <=> ! [X4,X0,X2,X1] :
        ( c_lessequals(X1,X0,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f78,axiom,
    ! [X2,X0,X1,X4] :
      ( c_lessequals(X1,X0,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

fof(f10709,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f790,f10707]) ).

fof(f10707,plain,
    ( spl0_525
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f790,plain,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    inference(forward_demodulation,[],[f102,f294]) ).

fof(f294,axiom,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

fof(f102,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

fof(f10705,plain,
    ( spl0_524
    | ~ spl0_90
    | ~ spl0_428 ),
    inference(avatar_split_clause,[],[f10280,f6882,f1221,f10703]) ).

fof(f10703,plain,
    ( spl0_524
  <=> ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f10280,plain,
    ( ! [X0] :
        ( ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_x)) )
    | ~ spl0_90
    | ~ spl0_428 ),
    inference(resolution,[],[f6883,f1222]) ).

fof(f10701,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f603,f10699]) ).

fof(f603,axiom,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | X25 = X26
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).

fof(f10697,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f565,f10695]) ).

fof(f10695,plain,
    ( spl0_522
  <=> ! [X5,X12,X6,X19] :
        ( hBOOL(hAPP(X19,X12))
        | hBOOL(hAPP(X19,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f565,axiom,
    ! [X19,X6,X5,X12] :
      ( hBOOL(hAPP(X19,X12))
      | hBOOL(hAPP(X19,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).

fof(f10693,plain,
    spl0_521,
    inference(avatar_split_clause,[],[f557,f10691]) ).

fof(f10691,plain,
    ( spl0_521
  <=> ! [X5,X12,X6,X19] :
        ( hBOOL(hAPP(X19,X12))
        | hBOOL(hAPP(X19,X5))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
        | ~ hBOOL(c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f557,axiom,
    ! [X19,X6,X5,X12] :
      ( hBOOL(hAPP(X19,X12))
      | hBOOL(hAPP(X19,X5))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a))
      | ~ hBOOL(c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6),t_a,t_a),X6,tc_prod(t_a,t_a))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).

fof(f10689,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f407,f10687]) ).

fof(f10687,plain,
    ( spl0_520
  <=> ! [X5,X12,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
        | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f407,axiom,
    ! [X2,X6,X5,X12] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
      | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).

fof(f10685,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f313,f10683]) ).

fof(f10683,plain,
    ( spl0_519
  <=> ! [X5,X12,X6,X2] :
        ( ~ c_Wellfounded_Oacyclic(X6,X2)
        | c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
        | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f313,axiom,
    ! [X2,X6,X5,X12] :
      ( ~ c_Wellfounded_Oacyclic(X6,X2)
      | c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
      | hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).

fof(f10681,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f308,f10679]) ).

fof(f10679,plain,
    ( spl0_518
  <=> ! [X37,X0,X14,X6,X3,X2] :
        ( ~ c_lessequals(X37,X0,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X14,X6,tc_fun(tc_prod(X2,X3),tc_bool))
        | c_lessequals(c_Relation_OImage(X14,X37,X2,X3),c_Relation_OImage(X6,X0,X2,X3),tc_fun(X3,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f308,axiom,
    ! [X2,X3,X0,X37,X6,X14] :
      ( ~ c_lessequals(X37,X0,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X14,X6,tc_fun(tc_prod(X2,X3),tc_bool))
      | c_lessequals(c_Relation_OImage(X14,X37,X2,X3),c_Relation_OImage(X6,X0,X2,X3),tc_fun(X3,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).

fof(f10677,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f298,f10675]) ).

fof(f10675,plain,
    ( spl0_517
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f298,axiom,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

fof(f10673,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f293,f10671]) ).

fof(f10671,plain,
    ( spl0_516
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f293,axiom,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

fof(f10669,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f292,f10667]) ).

fof(f10667,plain,
    ( spl0_515
  <=> ! [X28,X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X28,tc_fun(X2,tc_bool))
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f292,axiom,
    ! [X2,X28,X0,X1,X4] :
      ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X28,tc_fun(X2,tc_bool))
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

fof(f10665,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f255,f10663]) ).

fof(f10663,plain,
    ( spl0_514
  <=> ! [X4,X0,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f255,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

fof(f10661,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f254,f10659]) ).

fof(f254,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

fof(f10657,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f195,f10655]) ).

fof(f10655,plain,
    ( spl0_512
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f195,axiom,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

fof(f10653,plain,
    spl0_511,
    inference(avatar_split_clause,[],[f138,f10651]) ).

fof(f10651,plain,
    ( spl0_511
  <=> ! [X28,X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X28,tc_fun(X2,tc_bool))
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f138,axiom,
    ! [X2,X28,X0,X1,X4] :
      ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X28,tc_fun(X2,tc_bool))
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

fof(f10649,plain,
    spl0_510,
    inference(avatar_split_clause,[],[f107,f10647]) ).

fof(f10647,plain,
    ( spl0_510
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f107,axiom,
    ! [X2,X0,X1,X4] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

fof(f10645,plain,
    spl0_509,
    inference(avatar_split_clause,[],[f105,f10643]) ).

fof(f10643,plain,
    ( spl0_509
  <=> ! [X28,X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X28,X4,tc_fun(X2,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f105,axiom,
    ! [X2,X28,X0,X1,X4] :
      ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X28,X4,tc_fun(X2,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X28,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

fof(f10534,plain,
    ( spl0_508
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f10530,f10527,f10532]) ).

fof(f10532,plain,
    ( spl0_508
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f10527,plain,
    ( spl0_507
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f10530,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool))
    | ~ spl0_507 ),
    inference(forward_demodulation,[],[f10528,f107]) ).

fof(f10528,plain,
    ( ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_507 ),
    inference(avatar_component_clause,[],[f10527]) ).

fof(f10529,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f103,f10527]) ).

fof(f103,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

fof(f10525,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f77,f10523]) ).

fof(f10523,plain,
    ( spl0_506
  <=> ! [X17,X4,X0,X3,X2] : c_lessequals(c_Relation_OImage(X17,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f77,axiom,
    ! [X2,X3,X0,X4,X17] : c_lessequals(c_Relation_OImage(X17,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).

fof(f10521,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f76,f10519]) ).

fof(f10519,plain,
    ( spl0_505
  <=> ! [X4,X10,X0,X3,X2] : c_lessequals(c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f76,axiom,
    ! [X2,X3,X10,X0,X4] : c_lessequals(c_Set_Oimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X3,tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

fof(f10517,plain,
    ( ~ spl0_504
    | ~ spl0_55
    | ~ spl0_428 ),
    inference(avatar_split_clause,[],[f10293,f6882,f1074,f10514]) ).

fof(f10514,plain,
    ( spl0_504
  <=> c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f10293,plain,
    ( ~ c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_55
    | ~ spl0_428 ),
    inference(resolution,[],[f6883,f1075]) ).

fof(f10512,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f55,f10510]) ).

fof(f10510,plain,
    ( spl0_503
  <=> ! [X2,X17,X18] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X18,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f55,axiom,
    ! [X2,X18,X17] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X18,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).

fof(f10508,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f30,f10506]) ).

fof(f10506,plain,
    ( spl0_502
  <=> ! [X4,X0,X3,X2,X10] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f30,axiom,
    ! [X2,X3,X10,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)),c_Set_Oimage(X10,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X3,tc_bool)),X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

fof(f10504,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f12,f10502]) ).

fof(f10502,plain,
    ( spl0_501
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f12,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

fof(f10500,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f11,f10498]) ).

fof(f11,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X0,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

fof(f9801,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f755,f9799]) ).

fof(f9799,plain,
    ( spl0_499
  <=> ! [X17,X12,X5,X2] :
        ( X5 = X12
        | hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X17,X2,X2),X2,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f755,plain,
    ! [X2,X17,X5,X12] :
      ( X5 = X12
      | hBOOL(c_in(X5,c_Relation_ORange(c_Relation_Oconverse(X17,X2,X2),X2,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f573,f514]) ).

fof(f573,axiom,
    ! [X2,X17,X5,X12] :
      ( X5 = X12
      | hBOOL(c_in(X5,c_Relation_ODomain(X17,X2,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).

fof(f9797,plain,
    spl0_498,
    inference(avatar_split_clause,[],[f715,f9795]) ).

fof(f9795,plain,
    ( spl0_498
  <=> ! [X3,X6,X25,X2,X26] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X25,X26,X2,X3),X6,tc_prod(X2,X3)),X2,X3),X3,X2) = c_Set_Oinsert(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f9793,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f624,f9791]) ).

fof(f9791,plain,
    ( spl0_497
  <=> ! [X4,X0,X3,X25,X2,X26] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | ~ hBOOL(c_in(X26,hAPP(X4,X25),X3))
        | hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f624,axiom,
    ! [X2,X3,X0,X26,X4,X25] :
      ( ~ hBOOL(c_in(X25,X0,X2))
      | ~ hBOOL(c_in(X26,hAPP(X4,X25),X3))
      | hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).

fof(f9789,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f570,f9787]) ).

fof(f9787,plain,
    ( spl0_496
  <=> ! [X12,X21,X22,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(X22,X21,X2))
        | ~ hBOOL(c_in(X12,X21,X2))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X21,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f570,axiom,
    ! [X2,X21,X6,X22,X12] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(X22,X21,X2))
      | ~ hBOOL(c_in(X12,X21,X2))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X21,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).

fof(f9785,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f562,f9783]) ).

fof(f9783,plain,
    ( spl0_495
  <=> ! [X6,X25,X2,X26] :
        ( ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(c_in(X26,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(c_Pair(X26,X25,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f562,axiom,
    ! [X2,X6,X26,X25] :
      ( ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | hBOOL(c_in(X26,c_Wellfounded_Oacc(X6,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X26,X25,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).

fof(f9781,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f558,f9779]) ).

fof(f9779,plain,
    ( spl0_494
  <=> ! [X17,X21,X12,X5,X2] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | ~ hBOOL(c_in(X5,X21,X2))
        | ~ hBOOL(c_in(X12,X21,X2))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X21,X17,X2),X2,X2),X17,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f558,axiom,
    ! [X2,X21,X17,X5,X12] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | ~ hBOOL(c_in(X5,X21,X2))
      | ~ hBOOL(c_in(X12,X21,X2))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X21,X17,X2),X2,X2),X17,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).

fof(f9777,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f297,f9775]) ).

fof(f9775,plain,
    ( spl0_493
  <=> ! [X5,X2,X0] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
        | c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X0
        | ~ c_lessequals(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f297,axiom,
    ! [X2,X0,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
      | c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) = X0
      | ~ c_lessequals(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

fof(f9773,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f207,f9771]) ).

fof(f9771,plain,
    ( spl0_492
  <=> ! [X4,X0,X3,X2] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f207,axiom,
    ! [X2,X3,X0,X4] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).

fof(f9769,plain,
    ( spl0_491
    | ~ spl0_90
    | ~ spl0_424 ),
    inference(avatar_split_clause,[],[f9701,f6733,f1221,f9767]) ).

fof(f9767,plain,
    ( spl0_491
  <=> ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f9701,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_y)) )
    | ~ spl0_90
    | ~ spl0_424 ),
    inference(resolution,[],[f6734,f1222]) ).

fof(f9765,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f167,f9763]) ).

fof(f9763,plain,
    ( spl0_490
  <=> ! [X3,X8,X9,X2,X1] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f167,axiom,
    ! [X2,X3,X1,X8,X9] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).

fof(f9761,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f128,f9759]) ).

fof(f9759,plain,
    ( spl0_489
  <=> ! [X2,X30,X27,X25,X26] :
        ( X26 = X30
        | X25 = X30
        | c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X27,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f128,axiom,
    ! [X2,X26,X27,X25,X30] :
      ( X26 = X30
      | X25 = X30
      | c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X27,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

fof(f9757,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f127,f9755]) ).

fof(f9755,plain,
    ( spl0_488
  <=> ! [X2,X30,X27,X25,X26] :
        ( X25 = X27
        | X26 = X27
        | c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X27,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f127,axiom,
    ! [X2,X26,X27,X25,X30] :
      ( X25 = X27
      | X26 = X27
      | c_Set_Oinsert(X25,c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) != c_Set_Oinsert(X27,c_Set_Oinsert(X30,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

fof(f9753,plain,
    spl0_487,
    inference(avatar_split_clause,[],[f80,f9751]) ).

fof(f9751,plain,
    ( spl0_487
  <=> ! [X3,X8,X9,X2,X1] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f80,axiom,
    ! [X2,X3,X1,X8,X9] : c_Product__Type_OSigma(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_HOL_Ominus__class_Ominus(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).

fof(f9749,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f62,f9747]) ).

fof(f9747,plain,
    ( spl0_486
  <=> ! [X4,X0,X25,X2] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f62,axiom,
    ! [X2,X0,X4,X25] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

fof(f9745,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f61,f9743]) ).

fof(f9743,plain,
    ( spl0_485
  <=> ! [X4,X0,X25,X2] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f61,axiom,
    ! [X2,X0,X4,X25] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

fof(f9741,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f53,f9739]) ).

fof(f9739,plain,
    ( spl0_484
  <=> ! [X4,X0,X3,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f53,axiom,
    ! [X2,X3,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Relation_ORange(X0,X3,X2),c_Relation_ORange(X4,X3,X2),tc_fun(X2,tc_bool)),c_Relation_ORange(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).

fof(f9737,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f27,f9735]) ).

fof(f9735,plain,
    ( spl0_483
  <=> ! [X6,X4,X0,X3,X2,X1] :
        ( c_lessequals(c_Relation_OImage(X6,X1,X2,X3),X4,tc_fun(X3,tc_bool))
        | ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f27,axiom,
    ! [X2,X3,X0,X1,X6,X4] :
      ( c_lessequals(c_Relation_OImage(X6,X1,X2,X3),X4,tc_fun(X3,tc_bool))
      | ~ c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X4,tc_fun(X3,tc_bool),X2),X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).

fof(f9733,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f20,f9731]) ).

fof(f9731,plain,
    ( spl0_482
  <=> ! [X18,X0,X3,X17,X2] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X3,X2),tc_bool)),X0,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X18,X0,X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f20,axiom,
    ! [X2,X3,X0,X18,X17] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X3,X2),tc_bool)),X0,X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X18,X0,X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).

fof(f9729,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f7,f9727]) ).

fof(f9727,plain,
    ( spl0_481
  <=> ! [X3,X8,X9,X2,X1] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f7,axiom,
    ! [X2,X3,X1,X8,X9] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_fun(X2,tc_bool)),X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X8,X1,X2,X3),c_Product__Type_OSigma(X9,X1,X2,X3),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).

fof(f9181,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f785,f9179]) ).

fof(f9179,plain,
    ( spl0_480
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f785,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(forward_demodulation,[],[f784,f481]) ).

fof(f784,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(forward_demodulation,[],[f713,f697]) ).

fof(f697,plain,
    ! [X2,X6] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2) = c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),
    inference(definition_unfolding,[],[f537,f538]) ).

fof(f537,axiom,
    ! [X2,X6] : c_Transitive__Closure_Otrancl(X6,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

fof(f713,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(definition_unfolding,[],[f398,f500]) ).

fof(f398,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).

fof(f9177,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f781,f9175]) ).

fof(f9175,plain,
    ( spl0_479
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f781,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(forward_demodulation,[],[f707,f481]) ).

fof(f707,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(definition_unfolding,[],[f395,f538,f500]) ).

fof(f395,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X6,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).

fof(f9173,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f738,f9171]) ).

fof(f9171,plain,
    ( spl0_478
  <=> ! [X3,X7,X6,X2] :
        ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X3),tc_bool))
        | c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f738,plain,
    ! [X2,X3,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X3),tc_bool))
      | c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),c_Relation_ORange(c_Relation_Oconverse(X7,X2,X3),X3,X2),tc_fun(X2,tc_bool)) ),
    inference(definition_unfolding,[],[f296,f514,f514]) ).

fof(f296,axiom,
    ! [X2,X3,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X3),tc_bool))
      | c_lessequals(c_Relation_ODomain(X6,X2,X3),c_Relation_ODomain(X7,X2,X3),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).

fof(f9169,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f736,f9167]) ).

fof(f9167,plain,
    ( spl0_477
  <=> ! [X3,X6,X25,X2] :
        ( ~ hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f736,plain,
    ! [X2,X3,X6,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ),
    inference(definition_unfolding,[],[f567,f514]) ).

fof(f567,axiom,
    ! [X2,X3,X6,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ODomain(X6,X2,X3),X2))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).

fof(f9165,plain,
    spl0_476,
    inference(avatar_split_clause,[],[f735,f9163]) ).

fof(f9163,plain,
    ( spl0_476
  <=> ! [X3,X6,X25,X2] :
        ( ~ hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
        | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f735,plain,
    ! [X2,X3,X6,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ),
    inference(definition_unfolding,[],[f571,f514]) ).

fof(f571,axiom,
    ! [X2,X3,X6,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ODomain(X6,X2,X3),X2))
      | hBOOL(c_in(c_Pair(X25,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X25,X6,X2,X3),X2,X3),X6,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).

fof(f9160,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f703,f9158]) ).

fof(f9158,plain,
    ( spl0_475
  <=> ! [X6,X2] : c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X6,X2,X2),X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f703,plain,
    ! [X2,X6] : c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X6,X2,X2),X2),X2,X2,X2),
    inference(definition_unfolding,[],[f510,f538,f538]) ).

fof(f510,axiom,
    ! [X2,X6] : c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X6,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X6,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).

fof(f9156,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f621,f9153]) ).

fof(f9153,plain,
    ( spl0_474
  <=> hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(t_b,tc_bool))),v_x),v_y) = c_in(c_Pair(v_x,v_y,t_a,t_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(t_a,t_b),tc_bool)),tc_prod(t_a,t_b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f621,axiom,
    hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_fun(t_b,tc_bool))),v_x),v_y) = c_in(c_Pair(v_x,v_y,t_a,t_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(t_a,t_b),tc_bool)),tc_prod(t_a,t_b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq2_0) ).

fof(f9151,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f413,f9149]) ).

fof(f9149,plain,
    ( spl0_473
  <=> ! [X3,X6,X25,X2,X26] :
        ( hBOOL(c_in(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)))
        | ~ hBOOL(c_in(X26,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f413,axiom,
    ! [X2,X3,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)))
      | ~ hBOOL(c_in(X26,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).

fof(f9147,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f412,f9145]) ).

fof(f9145,plain,
    ( spl0_472
  <=> ! [X3,X6,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)))
        | hBOOL(c_in(X26,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f412,axiom,
    ! [X2,X3,X6,X26,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)))
      | hBOOL(c_in(X26,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).

fof(f9143,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f173,f9141]) ).

fof(f9141,plain,
    ( spl0_471
  <=> ! [X3,X7,X6,X2] : c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X6,X3,X2),c_Relation_Oconverse(X7,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f173,axiom,
    ! [X2,X3,X6,X7] : c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X6,X3,X2),c_Relation_Oconverse(X7,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).

fof(f9139,plain,
    ( spl0_470
    | ~ spl0_90
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f8205,f6491,f1221,f9137]) ).

fof(f9137,plain,
    ( spl0_470
  <=> ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_x)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f8205,plain,
    ( ! [X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt)
        | hBOOL(hAPP(X0,v_x)) )
    | ~ spl0_90
    | ~ spl0_421 ),
    inference(resolution,[],[f6492,f1222]) ).

fof(f9135,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f139,f9133]) ).

fof(f9133,plain,
    ( spl0_469
  <=> ! [X3,X7,X6,X2] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X6,X3,X2),c_Relation_Oconverse(X7,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f139,axiom,
    ! [X2,X3,X6,X7] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X6,X3,X2),c_Relation_Oconverse(X7,X3,X2),tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).

fof(f8415,plain,
    ( ~ spl0_468
    | ~ spl0_55
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f8218,f6491,f1074,f8412]) ).

fof(f8412,plain,
    ( spl0_468
  <=> c_Equiv__Relations_Oequiv(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f8218,plain,
    ( ~ c_Equiv__Relations_Oequiv(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_55
    | ~ spl0_421 ),
    inference(resolution,[],[f6492,f1075]) ).

fof(f8256,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f807,f8254]) ).

fof(f8254,plain,
    ( spl0_467
  <=> ! [X2,X35] :
        ( ~ hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_prod(X2,X2)))
        | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),X2,X2) = X35 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f807,plain,
    ! [X2,X35] :
      ( ~ hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_prod(X2,X2)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),X2,X2) = X35 ),
    inference(forward_demodulation,[],[f734,f481]) ).

fof(f734,plain,
    ! [X2,X35] :
      ( ~ hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),X2,X2) = X35 ),
    inference(definition_unfolding,[],[f387,f500]) ).

fof(f387,axiom,
    ! [X2,X35] :
      ( ~ hBOOL(c_in(X35,c_Relation_OId(X2),tc_prod(X2,X2)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X2),X2,X2) = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).

fof(f8252,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f628,f8250]) ).

fof(f628,axiom,
    ! [X2,X3,X0,X6,X26,X5] :
      ( ~ hBOOL(c_in(X5,X0,X3))
      | hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X5,X26,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).

fof(f8248,plain,
    spl0_465,
    inference(avatar_split_clause,[],[f626,f8246]) ).

fof(f626,axiom,
    ! [X2,X6,X25,X12] :
      ( ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | hBOOL(c_in(X12,c_Wellfounded_Oacc(X6,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X12,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).

fof(f8244,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f613,f8242]) ).

fof(f613,axiom,
    ! [X2,X6,X26,X25] :
      ( ~ c_Relation_Osym(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),X6,tc_prod(X2,X2)))
      | hBOOL(c_in(c_Pair(X26,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).

fof(f8240,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f601,f8238]) ).

fof(f601,axiom,
    ! [X2,X6,X5,X25] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X25,X5,X2,X2),X6,tc_prod(X2,X2)))
      | ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).

fof(f8236,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f591,f8234]) ).

fof(f8234,plain,
    ( spl0_462
  <=> ! [X3,X6,X25,X2,X26] :
        ( hBOOL(c_in(c_Pair(X26,X25,X3,X2),X6,tc_prod(X3,X2)))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Relation_Oconverse(X6,X3,X2),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f591,axiom,
    ! [X2,X3,X6,X26,X25] :
      ( hBOOL(c_in(c_Pair(X26,X25,X3,X2),X6,tc_prod(X3,X2)))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Relation_Oconverse(X6,X3,X2),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).

fof(f8232,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f589,f8230]) ).

fof(f8230,plain,
    ( spl0_461
  <=> ! [X3,X6,X25,X2,X26] :
        ( ~ hBOOL(c_in(c_Pair(X26,X25,X3,X2),X6,tc_prod(X3,X2)))
        | hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Relation_Oconverse(X6,X3,X2),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f589,axiom,
    ! [X2,X3,X6,X26,X25] :
      ( ~ hBOOL(c_in(c_Pair(X26,X25,X3,X2),X6,tc_prod(X3,X2)))
      | hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Relation_Oconverse(X6,X3,X2),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).

fof(f8204,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f572,f8202]) ).

fof(f8202,plain,
    ( spl0_460
  <=> ! [X3,X0,X6,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X26,X6,X3,X2),X26,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f572,axiom,
    ! [X2,X3,X0,X6,X26] :
      ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X26,X6,X3,X2),X26,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).

fof(f8200,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f554,f8198]) ).

fof(f8198,plain,
    ( spl0_459
  <=> ! [X3,X0,X6,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X26,X6,X3,X2),X26,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f554,axiom,
    ! [X2,X3,X0,X6,X26] :
      ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X26,X6,X3,X2),X26,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).

fof(f8196,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f406,f8194]) ).

fof(f8194,plain,
    ( spl0_458
  <=> ! [X5,X12,X6,X2] :
        ( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f406,axiom,
    ! [X2,X6,X5,X12] :
      ( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).

fof(f8192,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f372,f8190]) ).

fof(f8190,plain,
    ( spl0_457
  <=> ! [X19,X12,X6,X25,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X12))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f372,axiom,
    ! [X2,X6,X19,X25,X12] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X12))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).

fof(f8188,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f371,f8186]) ).

fof(f8186,plain,
    ( spl0_456
  <=> ! [X17,X40,X12,X19,X2] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | hBOOL(hAPP(X19,X40))
        | hBOOL(hAPP(X19,X12))
        | ~ hBOOL(c_in(c_Pair(X12,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X19,X17,X2),X2,X2),X17,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f371,axiom,
    ! [X2,X40,X19,X17,X12] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | hBOOL(hAPP(X19,X40))
      | hBOOL(hAPP(X19,X12))
      | ~ hBOOL(c_in(c_Pair(X12,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X19,X17,X2),X2,X2),X17,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).

fof(f8184,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f370,f8182]) ).

fof(f8182,plain,
    ( spl0_455
  <=> ! [X19,X12,X22,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X22))
        | hBOOL(hAPP(X19,X12))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f370,axiom,
    ! [X2,X6,X19,X22,X12] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X22))
      | hBOOL(hAPP(X19,X12))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).

fof(f8180,plain,
    spl0_454,
    inference(avatar_split_clause,[],[f369,f8178]) ).

fof(f8178,plain,
    ( spl0_454
  <=> ! [X19,X12,X6,X25,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X25))
        | hBOOL(hAPP(X19,X12))
        | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f369,axiom,
    ! [X2,X6,X19,X25,X12] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X25))
      | hBOOL(hAPP(X19,X12))
      | ~ hBOOL(c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X19,X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).

fof(f8176,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f328,f8174]) ).

fof(f8174,plain,
    ( spl0_453
  <=> ! [X17,X18,X5,X2] :
        ( ~ hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(X18,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f328,axiom,
    ! [X2,X18,X17,X5] :
      ( ~ hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(X18,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).

fof(f8172,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f327,f8170]) ).

fof(f8170,plain,
    ( spl0_452
  <=> ! [X17,X18,X5,X2] :
        ( ~ hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2)))
        | hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f327,axiom,
    ! [X2,X18,X17,X5] :
      ( ~ hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(X17,X2),tc_prod(X2,X2)))
      | hBOOL(c_in(X5,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).

fof(f8168,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f314,f8166]) ).

fof(f8166,plain,
    ( spl0_451
  <=> ! [X5,X12,X6,X2] :
        ( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f314,axiom,
    ! [X2,X6,X5,X12] :
      ( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X12,X5,X2,X2),X6,tc_prod(X2,X2)),X2)
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).

fof(f8164,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f307,f8162]) ).

fof(f8162,plain,
    ( spl0_450
  <=> ! [X4,X10,X0,X3,X2] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f307,axiom,
    ! [X2,X3,X10,X0,X4] : c_Set_Oimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X10,X0,X3,X2),c_Set_Oimage(X10,X4,X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

fof(f8160,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f300,f8158]) ).

fof(f8158,plain,
    ( spl0_449
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
        | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f300,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
      | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

fof(f8156,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f209,f8154]) ).

fof(f8154,plain,
    ( spl0_448
  <=> ! [X2,X17,X18] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X18,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f209,axiom,
    ! [X2,X18,X17] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X18,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).

fof(f8152,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f159,f8150]) ).

fof(f8150,plain,
    ( spl0_447
  <=> ! [X2,X17,X18] :
        ( c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(X18,X2)
        | ~ c_lessequals(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool))
        | ~ c_lessequals(X18,c_Transitive__Closure_Ortrancl(X17,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f159,axiom,
    ! [X2,X18,X17] :
      ( c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(X18,X2)
      | ~ c_lessequals(X17,X18,tc_fun(tc_prod(X2,X2),tc_bool))
      | ~ c_lessequals(X18,c_Transitive__Closure_Ortrancl(X17,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).

fof(f8148,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f21,f8146]) ).

fof(f21,axiom,
    ! [X2,X3,X0,X4,X17] : c_Relation_OImage(X17,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X3,tc_bool)),X3,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X17,X0,X3,X2),c_Relation_OImage(X17,X4,X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).

fof(f7795,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f410,f7793]) ).

fof(f7793,plain,
    ( spl0_445
  <=> ! [X0,X6,X25,X2] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | ~ hBOOL(c_in(X25,X0,X2))
        | hBOOL(c_in(X25,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f410,axiom,
    ! [X2,X0,X6,X25] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | ~ hBOOL(c_in(X25,X0,X2))
      | hBOOL(c_in(X25,c_Relation_OImage(X6,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).

fof(f7791,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f263,f7789]) ).

fof(f7787,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f210,f7785]) ).

fof(f210,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(c_in(X5,X4,X2))
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X5,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

fof(f7783,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f136,f7781]) ).

fof(f7781,plain,
    ( spl0_442
  <=> ! [X4,X0,X25,X2] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f136,axiom,
    ! [X2,X0,X4,X25] :
      ( ~ hBOOL(c_in(X25,X0,X2))
      | c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

fof(f7779,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f135,f7777]) ).

fof(f7777,plain,
    ( spl0_441
  <=> ! [X4,X25,X2,X1] :
        ( ~ hBOOL(c_in(X25,X1,X2))
        | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f135,axiom,
    ! [X2,X1,X4,X25] :
      ( ~ hBOOL(c_in(X25,X1,X2))
      | c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

fof(f7775,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f125,f7773]) ).

fof(f7773,plain,
    ( spl0_440
  <=> ! [X4,X0,X6,X2,X7] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | ~ c_Relation_Orefl__on(X4,X7,X2)
        | c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f125,axiom,
    ! [X2,X0,X6,X7,X4] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | ~ c_Relation_Orefl__on(X4,X7,X2)
      | c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).

fof(f7771,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f89,f7769]) ).

fof(f7769,plain,
    ( spl0_439
  <=> ! [X4,X0,X6,X2,X7] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | ~ c_Relation_Orefl__on(X4,X7,X2)
        | c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f89,axiom,
    ! [X2,X0,X6,X7,X4] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | ~ c_Relation_Orefl__on(X4,X7,X2)
      | c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).

fof(f7082,plain,
    ( spl0_438
    | ~ spl0_15
    | ~ spl0_371 ),
    inference(avatar_split_clause,[],[f5263,f4886,f909,f7080]) ).

fof(f5263,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_15
    | ~ spl0_371 ),
    inference(resolution,[],[f4887,f911]) ).

fof(f6920,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f824,f6918]) ).

fof(f6918,plain,
    ( spl0_437
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_Relation_Oantisym(X6,X2)
        | ~ c_Relation_Otrans(X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f824,plain,
    ! [X2,X6] :
      ( c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Relation_Oantisym(X6,X2)
      | ~ c_Relation_Otrans(X6,X2) ),
    inference(forward_demodulation,[],[f754,f481]) ).

fof(f754,plain,
    ! [X2,X6] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(definition_unfolding,[],[f403,f500]) ).

fof(f403,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_HOL_Ominus__class_Ominus(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).

fof(f6916,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f586,f6914]) ).

fof(f586,axiom,
    ! [X2,X3,X10,X6,X5,X25] :
      ( ~ hBOOL(c_in(c_Pair(X5,X25,X2,X2),X6,tc_prod(X2,X2)))
      | hAPP(X10,X5) = hAPP(c_Recdef_Ocut(X10,X6,X25,X2,X3),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).

fof(f6912,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f574,f6910]) ).

fof(f6910,plain,
    ( spl0_435
  <=> ! [X3,X6,X25,X2] :
        ( ~ hBOOL(c_in(X25,c_Relation_ORange(X6,X3,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X25,X6,X2,X3),X25,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f574,axiom,
    ! [X2,X3,X6,X25] :
      ( ~ hBOOL(c_in(X25,c_Relation_ORange(X6,X3,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X25,X6,X2,X3),X25,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).

fof(f6908,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f559,f6906]) ).

fof(f6906,plain,
    ( spl0_434
  <=> ! [X3,X6,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_ORange(X6,X3,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X26,X6,X2,X3),X26,X3,X2),X6,tc_prod(X3,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f559,axiom,
    ! [X2,X3,X6,X26] :
      ( ~ hBOOL(c_in(X26,c_Relation_ORange(X6,X3,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X26,X6,X2,X3),X26,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).

fof(f6904,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f508,f6902]) ).

fof(f508,axiom,
    ! [X2,X31,X3,X18,X16,X17,X42] : c_Relation_Orel__comp(c_Relation_Orel__comp(X17,X18,X2,X42,X16),X31,X2,X16,X3) = c_Relation_Orel__comp(X17,c_Relation_Orel__comp(X18,X31,X42,X16,X3),X2,X42,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).

fof(f6900,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f294,f6898]) ).

fof(f6898,plain,
    ( spl0_432
  <=> ! [X4,X0,X2,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f6896,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f250,f6894]) ).

fof(f6894,plain,
    ( spl0_431
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
        | c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f250,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X1,X0,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X1,X4,tc_fun(X2,tc_bool))
      | c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

fof(f6892,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f95,f6890]) ).

fof(f6890,plain,
    ( spl0_430
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f95,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

fof(f6888,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f94,f6886]) ).

fof(f6886,plain,
    ( spl0_429
  <=> ! [X4,X0,X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f94,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

fof(f6884,plain,
    ( spl0_428
    | ~ spl0_14
    | ~ spl0_371 ),
    inference(avatar_split_clause,[],[f5262,f4886,f904,f6882]) ).

fof(f5262,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Relation_Orefl__on(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_14
    | ~ spl0_371 ),
    inference(resolution,[],[f4887,f906]) ).

fof(f6880,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f45,f6878]) ).

fof(f6878,plain,
    ( spl0_427
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f45,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X0,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

fof(f6876,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f32,f6874]) ).

fof(f32,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

fof(f6872,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f31,f6870]) ).

fof(f6870,plain,
    ( spl0_425
  <=> ! [X4,X0,X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f31,axiom,
    ! [X2,X0,X1,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

fof(f6735,plain,
    ( spl0_424
    | ~ spl0_15
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f5204,f4874,f909,f6733]) ).

fof(f5204,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_y,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_15
    | ~ spl0_368 ),
    inference(resolution,[],[f4875,f911]) ).

fof(f6501,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f804,f6499]) ).

fof(f6499,plain,
    ( spl0_423
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | c_Relation_Ototal__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f804,plain,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | c_Relation_Ototal__on(X0,X6,X2) ),
    inference(forward_demodulation,[],[f730,f481]) ).

fof(f730,plain,
    ! [X2,X0,X6] :
      ( c_Relation_Ototal__on(X0,X6,X2)
      | ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(definition_unfolding,[],[f348,f500]) ).

fof(f348,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Ototal__on(X0,X6,X2)
      | ~ c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).

fof(f6497,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f803,f6495]) ).

fof(f6495,plain,
    ( spl0_422
  <=> ! [X6,X2,X0] :
        ( c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_Relation_Ototal__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f803,plain,
    ! [X2,X0,X6] :
      ( c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Relation_Ototal__on(X0,X6,X2) ),
    inference(forward_demodulation,[],[f729,f481]) ).

fof(f729,plain,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Ototal__on(X0,X6,X2)
      | c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(definition_unfolding,[],[f349,f500]) ).

fof(f349,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Ototal__on(X0,X6,X2)
      | c_Relation_Ototal__on(X0,c_HOL_Ominus__class_Ominus(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).

fof(f6493,plain,
    ( spl0_421
    | ~ spl0_14
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f5203,f4874,f904,f6491]) ).

fof(f5203,plain,
    ( ! [X0] :
        ( hBOOL(c_in(v_x,X0,tc_Arrow__Order__Mirabelle_Oalt))
        | ~ c_Equiv__Relations_Oequiv(X0,v_L,tc_Arrow__Order__Mirabelle_Oalt) )
    | ~ spl0_14
    | ~ spl0_368 ),
    inference(resolution,[],[f4875,f906]) ).

fof(f6489,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f740,f6487]) ).

fof(f740,plain,
    ! [X2,X3,X6,X5,X25] :
      ( hBOOL(c_in(X25,c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X25,X5,X2,X3),X6,tc_prod(X2,X3))) ),
    inference(definition_unfolding,[],[f635,f514]) ).

fof(f635,axiom,
    ! [X2,X3,X6,X5,X25] :
      ( hBOOL(c_in(X25,c_Relation_ODomain(X6,X2,X3),X2))
      | ~ hBOOL(c_in(c_Pair(X25,X5,X2,X3),X6,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).

fof(f6485,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f695,f6483]) ).

fof(f6483,plain,
    ( spl0_419
  <=> ! [X6,X2] : c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f695,plain,
    ! [X2,X6] : c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2),X2,X2),
    inference(definition_unfolding,[],[f464,f514,f514,f538]) ).

fof(f464,axiom,
    ! [X2,X6] : c_Relation_ODomain(X6,X2,X2) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

fof(f6481,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f637,f6479]) ).

fof(f6479,plain,
    ( spl0_418
  <=> ! [X2,X4,X0,X3,X25,X26] :
        ( hBOOL(c_in(X26,hAPP(X4,X25),X3))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f637,axiom,
    ! [X2,X3,X0,X26,X4,X25] :
      ( hBOOL(c_in(X26,hAPP(X4,X25),X3))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).

fof(f6477,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f493,f6475]) ).

fof(f6475,plain,
    ( spl0_417
  <=> ! [X16,X3,X7,X6,X2] : c_Relation_Oconverse(c_Relation_Orel__comp(X6,X7,X3,X16,X2),X3,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X7,X16,X2),c_Relation_Oconverse(X6,X3,X16),X2,X16,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f493,axiom,
    ! [X2,X3,X6,X7,X16] : c_Relation_Oconverse(c_Relation_Orel__comp(X6,X7,X3,X16,X2),X3,X2) = c_Relation_Orel__comp(c_Relation_Oconverse(X7,X16,X2),c_Relation_Oconverse(X6,X3,X16),X2,X16,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).

fof(f6473,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f411,f6471]) ).

fof(f6471,plain,
    ( spl0_416
  <=> ! [X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | ~ c_Relation_Otrans(X6,X2)
        | c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2),X6,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f411,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | ~ c_Relation_Otrans(X6,X2)
      | c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2),X6,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).

fof(f6469,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f393,f6467]) ).

fof(f6467,plain,
    ( spl0_415
  <=> ! [X2,X0,X27] :
        ( ~ hBOOL(c_in(X27,c_Relation_OId__on(X0,X2),tc_prod(X2,X2)))
        | c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),X2,X2) = X27 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f393,axiom,
    ! [X2,X0,X27] :
      ( ~ hBOOL(c_in(X27,c_Relation_OId__on(X0,X2),tc_prod(X2,X2)))
      | c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),X2,X2) = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).

fof(f6465,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f323,f6463]) ).

fof(f6463,plain,
    ( spl0_414
  <=> ! [X3,X4,X0,X5,X2,X10] :
        ( ~ hBOOL(c_in(X5,X0,X3))
        | hBOOL(c_in(hAPP(X10,X5),X4,X2))
        | ~ c_lessequals(c_Set_Oimage(X10,X0,X3,X2),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f323,axiom,
    ! [X2,X3,X10,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X0,X3))
      | hBOOL(c_in(hAPP(X10,X5),X4,X2))
      | ~ c_lessequals(c_Set_Oimage(X10,X0,X3,X2),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

fof(f6461,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f243,f6459]) ).

fof(f6459,plain,
    ( spl0_413
  <=> ! [X4,X0,X5,X2] :
        ( X0 = X4
        | hBOOL(c_in(X5,X0,X2))
        | hBOOL(c_in(X5,X4,X2))
        | c_Set_Oinsert(X5,X4,X2) != c_Set_Oinsert(X5,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f243,axiom,
    ! [X2,X0,X4,X5] :
      ( X0 = X4
      | hBOOL(c_in(X5,X0,X2))
      | hBOOL(c_in(X5,X4,X2))
      | c_Set_Oinsert(X5,X4,X2) != c_Set_Oinsert(X5,X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

fof(f6457,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f218,f6455]) ).

fof(f6455,plain,
    ( spl0_412
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
        | c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f218,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool))
      | c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

fof(f6453,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f217,f6451]) ).

fof(f6451,plain,
    ( spl0_411
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f217,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
      | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

fof(f6449,plain,
    ( spl0_410
    | ~ spl0_13
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f5167,f4870,f900,f6447]) ).

fof(f6447,plain,
    ( spl0_410
  <=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f4870,plain,
    ( spl0_367
  <=> ! [X3,X17,X12,X5,X2] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12))
        | hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f5167,plain,
    ( ! [X0] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X0))
    | ~ spl0_13
    | ~ spl0_367 ),
    inference(resolution,[],[f4871,f901]) ).

fof(f4871,plain,
    ( ! [X2,X3,X17,X5,X12] :
        ( hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3)))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12)) )
    | ~ spl0_367 ),
    inference(avatar_component_clause,[],[f4870]) ).

fof(f6381,plain,
    ( spl0_409
    | ~ spl0_51
    | ~ spl0_380
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f6377,f6374,f5359,f1058,f6379]) ).

fof(f1058,plain,
    ( spl0_51
  <=> ! [X2,X5,X4] : hBOOL(c_in(X5,c_Set_Oinsert(X5,X4,X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f6374,plain,
    ( spl0_408
  <=> ! [X5,X2,X0] :
        ( hBOOL(c_in(X5,X0,X2))
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f6377,plain,
    ( ! [X2,X0,X5] :
        ( c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0
        | hBOOL(c_in(X5,X0,X2)) )
    | ~ spl0_51
    | ~ spl0_380
    | ~ spl0_408 ),
    inference(forward_demodulation,[],[f6375,f5487]) ).

fof(f5487,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X0,X3),c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool))
    | ~ spl0_51
    | ~ spl0_380 ),
    inference(resolution,[],[f5360,f1059]) ).

fof(f1059,plain,
    ( ! [X2,X4,X5] : hBOOL(c_in(X5,c_Set_Oinsert(X5,X4,X2),X2))
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f1058]) ).

fof(f6375,plain,
    ( ! [X2,X0,X5] :
        ( hBOOL(c_in(X5,X0,X2))
        | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0 )
    | ~ spl0_408 ),
    inference(avatar_component_clause,[],[f6374]) ).

fof(f6376,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f216,f6374]) ).

fof(f216,axiom,
    ! [X2,X0,X5] :
      ( hBOOL(c_in(X5,X0,X2))
      | c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

fof(f6372,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f131,f6370]) ).

fof(f6370,plain,
    ( spl0_407
  <=> ! [X6,X2,X7] :
        ( ~ c_lessequals(X6,c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f131,axiom,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).

fof(f6368,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f104,f6366]) ).

fof(f6366,plain,
    ( spl0_406
  <=> ! [X3,X0,X27,X2] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0
        | c_Set_Oimage(c_COMBK(X27,X2,X3),X0,X3,X2) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f104,axiom,
    ! [X2,X3,X0,X27] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0
      | c_Set_Oimage(c_COMBK(X27,X2,X3),X0,X3,X2) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

fof(f6364,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f64,f6362]) ).

fof(f6362,plain,
    ( spl0_405
  <=> ! [X4,X0,X25,X2] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X0,X2),c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f64,axiom,
    ! [X2,X0,X4,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X0,X2),c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

fof(f6238,plain,
    ( spl0_404
    | ~ spl0_15
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f5153,f4866,f909,f6235]) ).

fof(f6235,plain,
    ( spl0_404
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f5153,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x),v_y))
    | ~ spl0_15
    | ~ spl0_366 ),
    inference(resolution,[],[f4867,f911]) ).

fof(f6017,plain,
    ( spl0_403
    | ~ spl0_14
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f5152,f4866,f904,f6014]) ).

fof(f6014,plain,
    ( spl0_403
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f5152,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y),v_x))
    | ~ spl0_14
    | ~ spl0_366 ),
    inference(resolution,[],[f4867,f906]) ).

fof(f5455,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f800,f5453]) ).

fof(f5453,plain,
    ( spl0_402
  <=> ! [X2,X25,X26] :
        ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_prod(X2,X2)))
        | X25 = X26 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f800,plain,
    ! [X2,X26,X25] :
      ( ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_prod(X2,X2)))
      | X25 = X26 ),
    inference(forward_demodulation,[],[f727,f481]) ).

fof(f727,plain,
    ! [X2,X26,X25] :
      ( X25 = X26
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f607,f500]) ).

fof(f607,axiom,
    ! [X2,X26,X25] :
      ( X25 = X26
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).

fof(f5451,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f783,f5449]) ).

fof(f5449,plain,
    ( spl0_401
  <=> ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f783,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(forward_demodulation,[],[f709,f481]) ).

fof(f709,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    inference(definition_unfolding,[],[f337,f500]) ).

fof(f337,axiom,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X17,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).

fof(f5447,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f780,f5445]) ).

fof(f780,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    inference(forward_demodulation,[],[f706,f481]) ).

fof(f706,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    inference(definition_unfolding,[],[f338,f500]) ).

fof(f338,axiom,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).

fof(f5443,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f779,f5441]) ).

fof(f5441,plain,
    ( spl0_399
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f779,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    inference(forward_demodulation,[],[f705,f481]) ).

fof(f705,plain,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    inference(definition_unfolding,[],[f339,f500]) ).

fof(f339,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_HOL_Ominus__class_Ominus(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).

fof(f5439,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f733,f5437]) ).

fof(f5437,plain,
    ( spl0_398
  <=> ! [X6,X2] :
        ( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),X6,X2)
        | c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2) != X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f733,plain,
    ! [X2,X6] :
      ( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X6,X2,X2),X2,X2),X6,X2)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2) != X6 ),
    inference(definition_unfolding,[],[f512,f514]) ).

fof(f512,axiom,
    ! [X2,X6] :
      ( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X6,X2,X2),X6,X2)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2) != X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).

fof(f5435,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f732,f5433]) ).

fof(f5433,plain,
    ( spl0_397
  <=> ! [X6,X2,X35] :
        ( ~ hBOOL(c_in(X35,X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X35,c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f732,plain,
    ! [X2,X6,X35] :
      ( ~ hBOOL(c_in(X35,X6,tc_prod(X2,X2)))
      | hBOOL(c_in(X35,c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f443,f538]) ).

fof(f443,axiom,
    ! [X2,X6,X35] :
      ( ~ hBOOL(c_in(X35,X6,tc_prod(X2,X2)))
      | hBOOL(c_in(X35,c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).

fof(f5431,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f721,f5429]) ).

fof(f5429,plain,
    ( spl0_396
  <=> ! [X6,X2,X5] :
        ( ~ c_Wellfounded_Oacyclic(X6,X2)
        | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f721,plain,
    ! [X2,X6,X5] :
      ( ~ c_Wellfounded_Oacyclic(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),tc_prod(X2,X2))) ),
    inference(definition_unfolding,[],[f377,f538]) ).

fof(f377,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Wellfounded_Oacyclic(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Transitive__Closure_Otrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).

fof(f5427,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f560,f5425]) ).

fof(f5425,plain,
    ( spl0_395
  <=> ! [X6,X2,X5] :
        ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X6,X5,X2),X5,X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f560,axiom,
    ! [X2,X6,X5] :
      ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X6,X5,X2),X5,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).

fof(f5423,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f555,f5421]) ).

fof(f5421,plain,
    ( spl0_394
  <=> ! [X2,X5,X17] :
        ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X17,X2),X2))
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X17,X5,X2),X5,X2,X2),X17,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f555,axiom,
    ! [X2,X17,X5] :
      ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X17,X2),X2))
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X17,X5,X2),X5,X2,X2),X17,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).

fof(f5419,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f543,f5417]) ).

fof(f5417,plain,
    ( spl0_393
  <=> ! [X2,X19,X6,X25] :
        ( hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f543,axiom,
    ! [X2,X19,X6,X25] :
      ( hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).

fof(f5415,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f461,f5413]) ).

fof(f5413,plain,
    ( spl0_392
  <=> ! [X2,X19,X6,X25] :
        ( hBOOL(hAPP(X19,X25))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f461,axiom,
    ! [X2,X19,X6,X25] :
      ( hBOOL(hAPP(X19,X25))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).

fof(f5411,plain,
    ( spl0_391
    | ~ spl0_90
    | ~ spl0_364 ),
    inference(avatar_split_clause,[],[f5366,f4857,f1221,f5408]) ).

fof(f5408,plain,
    ( spl0_391
  <=> hBOOL(hAPP(c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f4857,plain,
    ( spl0_364
  <=> hBOOL(c_in(v_y,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f5366,plain,
    ( hBOOL(hAPP(c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_y))
    | ~ spl0_90
    | ~ spl0_364 ),
    inference(resolution,[],[f4859,f1222]) ).

fof(f4859,plain,
    ( hBOOL(c_in(v_y,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_364 ),
    inference(avatar_component_clause,[],[f4857]) ).

fof(f5406,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f356,f5404]) ).

fof(f5404,plain,
    ( spl0_390
  <=> ! [X3,X4,X0,X27,X2] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X0,X4,X27,X2,X3),X0,X2))
        | ~ hBOOL(c_in(X27,c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f356,axiom,
    ! [X2,X3,X0,X27,X4] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X0,X4,X27,X2,X3),X0,X2))
      | ~ hBOOL(c_in(X27,c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).

fof(f5402,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f322,f5400]) ).

fof(f322,axiom,
    ! [X2,X3,X10,X0,X5] :
      ( ~ hBOOL(c_in(X5,X0,X2))
      | c_Set_Oimage(X10,X0,X2,X3) = c_Set_Oinsert(hAPP(X10,X5),c_Set_Oimage(X10,X0,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

fof(f5398,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f320,f5396]) ).

fof(f5396,plain,
    ( spl0_388
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X4,X2))
        | ~ hBOOL(c_in(X5,X0,X2))
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f320,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X2))
      | ~ hBOOL(c_in(X5,X0,X2))
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

fof(f5394,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f311,f5392]) ).

fof(f311,axiom,
    ! [X2,X3,X0,X27,X5] :
      ( ~ hBOOL(c_in(X5,X0,X2))
      | c_Set_Oimage(c_COMBK(X27,X3,X2),X0,X2,X3) = c_Set_Oinsert(X27,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

fof(f5390,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f309,f5388]) ).

fof(f5388,plain,
    ( spl0_386
  <=> ! [X6,X2,X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f309,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).

fof(f5386,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f214,f5384]) ).

fof(f5384,plain,
    ( spl0_385
  <=> ! [X3,X6,X25,X2,X26] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X25,X26,X3,X2),X6,tc_prod(X3,X2)),X3,X2) = c_Set_Oinsert(X26,c_Relation_ORange(X6,X3,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f5382,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f175,f5380]) ).

fof(f175,axiom,
    ! [X2,X1,X4,X25] :
      ( hBOOL(c_in(X25,X1,X2))
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X25,X4,X2),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

fof(f5378,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f174,f5376]) ).

fof(f174,axiom,
    ! [X2,X0,X4,X25] :
      ( hBOOL(c_in(X25,X0,X2))
      | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

fof(f5374,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f158,f5372]) ).

fof(f5372,plain,
    ( spl0_382
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f158,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

fof(f5370,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f106,f5368]) ).

fof(f5368,plain,
    ( spl0_381
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f106,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

fof(f5361,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f50,f5359]) ).

fof(f50,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X2))
      | c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

fof(f5357,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f16,f5355]) ).

fof(f5355,plain,
    ( spl0_379
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f16,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | c_lessequals(X6,c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).

fof(f5044,plain,
    ( spl0_378
    | ~ spl0_90
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f4905,f4812,f1221,f5041]) ).

fof(f5041,plain,
    ( spl0_378
  <=> hBOOL(hAPP(c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f4812,plain,
    ( spl0_353
  <=> hBOOL(c_in(v_x,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f4905,plain,
    ( hBOOL(hAPP(c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_x))
    | ~ spl0_90
    | ~ spl0_353 ),
    inference(resolution,[],[f4814,f1222]) ).

fof(f4814,plain,
    ( hBOOL(c_in(v_x,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f4812]) ).

fof(f4917,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f799,f4915]) ).

fof(f4915,plain,
    ( spl0_377
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_Relation_Otrans(X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f799,plain,
    ! [X2,X6] :
      ( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Relation_Otrans(X6,X2) ),
    inference(forward_demodulation,[],[f726,f481]) ).

fof(f726,plain,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(definition_unfolding,[],[f344,f500]) ).

fof(f344,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).

fof(f4913,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f798,f4911]) ).

fof(f4911,plain,
    ( spl0_376
  <=> ! [X6,X2] :
        ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
        | ~ c_Relation_Oantisym(X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f798,plain,
    ! [X2,X6] :
      ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
      | ~ c_Relation_Oantisym(X6,X2) ),
    inference(forward_demodulation,[],[f722,f481]) ).

fof(f722,plain,
    ! [X2,X6] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    inference(definition_unfolding,[],[f347,f500]) ).

fof(f347,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).

fof(f4909,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f739,f4907]) ).

fof(f4907,plain,
    ( spl0_375
  <=> ! [X6,X2,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f739,plain,
    ! [X2,X3,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(c_Relation_Oconverse(X6,X2,X3),X3,X2) ),
    inference(definition_unfolding,[],[f467,f514]) ).

fof(f467,axiom,
    ! [X2,X3,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ODomain(X6,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).

fof(f4900,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f686,f4898]) ).

fof(f4898,plain,
    ( spl0_374
  <=> ! [X2] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f686,plain,
    ! [X2] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),
    inference(definition_unfolding,[],[f505,f500,f500]) ).

fof(f505,axiom,
    ! [X2] : c_Relation_OId(X2) = c_Relation_Oconverse(c_Relation_OId(X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).

fof(f4896,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f643,f4894]) ).

fof(f643,axiom,
    ! [X2,X0,X6,X25] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | ~ hBOOL(c_in(X25,X0,X2))
      | hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).

fof(f4892,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f642,f4890]) ).

fof(f642,axiom,
    ! [X2,X0,X6,X5,X12] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | hBOOL(c_in(X5,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).

fof(f4888,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f641,f4886]) ).

fof(f641,axiom,
    ! [X2,X0,X6,X5,X12] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | hBOOL(c_in(X12,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).

fof(f4884,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f638,f4882]) ).

fof(f4882,plain,
    ( spl0_370
  <=> ! [X4,X0,X3,X25,X2,X26] :
        ( hBOOL(c_in(X25,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f638,axiom,
    ! [X2,X3,X0,X26,X4,X25] :
      ( hBOOL(c_in(X25,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X25,X26,X2,X3),c_Product__Type_OSigma(X0,X4,X2,X3),tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).

fof(f4880,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f632,f4878]) ).

fof(f632,axiom,
    ! [X2,X0,X6,X5,X12] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | hBOOL(c_in(X5,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).

fof(f4876,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f631,f4874]) ).

fof(f631,axiom,
    ! [X2,X0,X6,X5,X12] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | hBOOL(c_in(X12,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).

fof(f4872,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f588,f4870]) ).

fof(f588,axiom,
    ! [X2,X3,X17,X5,X12] :
      ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12))
      | hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).

fof(f4868,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f587,f4866]) ).

fof(f587,axiom,
    ! [X2,X3,X17,X5,X12] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X17,X2,X3),X5),X12))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X3),X17,tc_prod(X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).

fof(f4864,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f399,f4862]) ).

fof(f4862,plain,
    ( spl0_365
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | c_lessequals(X6,c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f399,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | c_lessequals(X6,c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).

fof(f4860,plain,
    ( spl0_364
    | ~ spl0_15
    | ~ spl0_347 ),
    inference(avatar_split_clause,[],[f4770,f4518,f909,f4857]) ).

fof(f4770,plain,
    ( hBOOL(c_in(v_y,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_15
    | ~ spl0_347 ),
    inference(resolution,[],[f4519,f911]) ).

fof(f4855,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f389,f4853]) ).

fof(f4853,plain,
    ( spl0_363
  <=> ! [X2,X0,X3] : c_Product__Type_OSigma(X0,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X2),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f389,axiom,
    ! [X2,X3,X0] : c_Product__Type_OSigma(X0,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool),X2),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).

fof(f4851,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f304,f4849]) ).

fof(f4849,plain,
    ( spl0_362
  <=> ! [X3,X10,X0,X5,X2] :
        ( ~ c_lessequals(X5,X0,tc_fun(X3,tc_bool))
        | c_lessequals(c_Set_Oimage(X10,X5,X3,X2),c_Set_Oimage(X10,X0,X3,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f304,axiom,
    ! [X2,X3,X10,X0,X5] :
      ( ~ c_lessequals(X5,X0,tc_fun(X3,tc_bool))
      | c_lessequals(c_Set_Oimage(X10,X5,X3,X2),c_Set_Oimage(X10,X0,X3,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

fof(f4847,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f257,f4845]) ).

fof(f4845,plain,
    ( spl0_361
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X4,X2))
        | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f257,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X4,X2))
      | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

fof(f4843,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f253,f4841]) ).

fof(f4841,plain,
    ( spl0_360
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Odistrib__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f253,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Odistrib__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

fof(f4839,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f252,f4837]) ).

fof(f4837,plain,
    ( spl0_359
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Odistrib__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X5,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2),c_Lattices_Oupper__semilattice__class_Osup(X13,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f252,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Odistrib__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X5,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2),c_Lattices_Oupper__semilattice__class_Osup(X13,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

fof(f4835,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f241,f4833]) ).

fof(f4833,plain,
    ( spl0_358
  <=> ! [X4,X0,X27,X2] :
        ( ~ hBOOL(c_in(X27,X0,X2))
        | hBOOL(c_in(X27,X4,X2))
        | hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f241,axiom,
    ! [X2,X0,X27,X4] :
      ( ~ hBOOL(c_in(X27,X0,X2))
      | hBOOL(c_in(X27,X4,X2))
      | hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

fof(f4831,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f233,f4829]) ).

fof(f4829,plain,
    ( spl0_357
  <=> ! [X4,X0,X27,X2] :
        ( hBOOL(c_in(X27,X4,X2))
        | hBOOL(c_in(X27,X0,X2))
        | ~ hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f233,axiom,
    ! [X2,X0,X27,X4] :
      ( hBOOL(c_in(X27,X4,X2))
      | hBOOL(c_in(X27,X0,X2))
      | ~ hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

fof(f4827,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f223,f4825]) ).

fof(f4825,plain,
    ( spl0_356
  <=> ! [X4,X0,X27,X2] :
        ( ~ hBOOL(c_in(X27,X0,X2))
        | ~ hBOOL(c_in(X27,X4,X2))
        | hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f223,axiom,
    ! [X2,X0,X27,X4] :
      ( ~ hBOOL(c_in(X27,X0,X2))
      | ~ hBOOL(c_in(X27,X4,X2))
      | hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

fof(f4823,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f170,f4821]) ).

fof(f4821,plain,
    ( spl0_355
  <=> ! [X4,X0,X5,X2] :
        ( hBOOL(c_in(X5,X0,X2))
        | c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X0,c_Set_Oinsert(X5,X4,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f170,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(c_in(X5,X0,X2))
      | c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X0,c_Set_Oinsert(X5,X4,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

fof(f4819,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f161,f4817]) ).

fof(f4817,plain,
    ( spl0_354
  <=> ! [X2,X0,X25] : c_Set_Oinsert(X25,X0,X2) = c_Set_Oinsert(X25,c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f161,axiom,
    ! [X2,X0,X25] : c_Set_Oinsert(X25,X0,X2) = c_Set_Oinsert(X25,c_HOL_Ominus__class_Ominus(X0,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

fof(f4815,plain,
    ( spl0_353
    | ~ spl0_14
    | ~ spl0_347 ),
    inference(avatar_split_clause,[],[f4769,f4518,f904,f4812]) ).

fof(f4769,plain,
    ( hBOOL(c_in(v_x,c_Relation_ORange(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_14
    | ~ spl0_347 ),
    inference(resolution,[],[f4519,f906]) ).

fof(f4810,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f69,f4808]) ).

fof(f4808,plain,
    ( spl0_352
  <=> ! [X6,X2,X7] :
        ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f69,axiom,
    ! [X2,X6,X7] :
      ( ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Transitive__Closure_Ortrancl(X6,X2),c_Transitive__Closure_Ortrancl(X7,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).

fof(f4806,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f14,f4804]) ).

fof(f4804,plain,
    ( spl0_351
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Odistrib__lattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X5,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2),c_Lattices_Olower__semilattice__class_Oinf(X13,X5,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f14,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Odistrib__lattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X5,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2),c_Lattices_Olower__semilattice__class_Oinf(X13,X5,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

fof(f4802,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f13,f4800]) ).

fof(f4800,plain,
    ( spl0_350
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Odistrib__lattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f13,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Odistrib__lattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

fof(f4722,plain,
    ( spl0_349
    | ~ spl0_90
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f4511,f3957,f1221,f4720]) ).

fof(f4720,plain,
    ( spl0_349
  <=> ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(v_L,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f3957,plain,
    ( spl0_329
  <=> ! [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(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f4511,plain,
    ( ! [X0] :
        ( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
        | hBOOL(hAPP(v_L,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))) )
    | ~ spl0_90
    | ~ spl0_329 ),
    inference(resolution,[],[f3958,f1222]) ).

fof(f3958,plain,
    ( ! [X0] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,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_329 ),
    inference(avatar_component_clause,[],[f3957]) ).

fof(f4524,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f731,f4522]) ).

fof(f4522,plain,
    ( spl0_348
  <=> ! [X6,X2] :
        ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X6,X2,X2),X2)
        | c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f731,plain,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X6,X2,X2),X2)
      | c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2),X2) ),
    inference(definition_unfolding,[],[f477,f538]) ).

fof(f477,axiom,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X6,X2,X2),X2)
      | c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X6,X2),X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).

fof(f4520,plain,
    spl0_347,
    inference(avatar_split_clause,[],[f633,f4518]) ).

fof(f633,axiom,
    ! [X2,X3,X6,X5,X25] :
      ( hBOOL(c_in(X25,c_Relation_ORange(X6,X3,X2),X2))
      | ~ hBOOL(c_in(c_Pair(X5,X25,X3,X2),X6,tc_prod(X3,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).

fof(f4516,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f620,f4513]) ).

fof(f4513,plain,
    ( spl0_346
  <=> hAPP(hAPP(c_FunDef_Oin__rel(v_R,t_a,t_b),v_x),v_y) = c_in(c_Pair(v_x,v_y,t_a,t_b),v_R,tc_prod(t_a,t_b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f620,axiom,
    hAPP(hAPP(c_FunDef_Oin__rel(v_R,t_a,t_b),v_x),v_y) = c_in(c_Pair(v_x,v_y,t_a,t_b),v_R,tc_prod(t_a,t_b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def__raw_0) ).

fof(f4507,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f465,f4505]) ).

fof(f4505,plain,
    ( spl0_345
  <=> ! [X3,X0,X6,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X26,X6,X3,X2),X0,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f465,axiom,
    ! [X2,X3,X0,X6,X26] :
      ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X26,X6,X3,X2),X0,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).

fof(f4503,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f456,f4501]) ).

fof(f4501,plain,
    ( spl0_344
  <=> ! [X3,X0,X6,X2,X26] :
        ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X26,X6,X3,X2),X0,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f456,axiom,
    ! [X2,X3,X0,X6,X26] :
      ( ~ hBOOL(c_in(X26,c_Relation_OImage(X6,X0,X3,X2),X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X26,X6,X3,X2),X0,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).

fof(f4499,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f388,f4497]) ).

fof(f4497,plain,
    ( spl0_343
  <=> ! [X2,X0,X17] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
        | ~ c_lessequals(X0,c_Relation_OImage(X17,X0,X2,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f388,axiom,
    ! [X2,X0,X17] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
      | ~ c_lessequals(X0,c_Relation_OImage(X17,X0,X2,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).

fof(f4495,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f278,f4493]) ).

fof(f4493,plain,
    ( spl0_342
  <=> ! [X11,X3,X10] :
        ( ~ class_Lattices_Olattice(X3)
        | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X11,tc_fun(t_a,X3)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X10,v_x),hAPP(X11,v_x),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f278,axiom,
    ! [X3,X10,X11] :
      ( ~ class_Lattices_Olattice(X3)
      | hAPP(c_Lattices_Olower__semilattice__class_Oinf(X10,X11,tc_fun(t_a,X3)),v_x) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(X10,v_x),hAPP(X11,v_x),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

fof(f4491,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f186,f4489]) ).

fof(f4489,plain,
    ( spl0_341
  <=> ! [X4,X0,X3] :
        ( ~ class_HOL_Ominus(X3)
        | hAPP(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(t_a,X3)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),hAPP(X4,v_x),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f186,axiom,
    ! [X3,X0,X4] :
      ( ~ class_HOL_Ominus(X3)
      | hAPP(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(t_a,X3)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X0,v_x),hAPP(X4,v_x),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

fof(f4487,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f137,f4485]) ).

fof(f4485,plain,
    ( spl0_340
  <=> ! [X4,X10,X3,X25,X2] : c_Set_Oimage(X10,c_Set_Oinsert(X25,X4,X3),X3,X2) = c_Set_Oinsert(hAPP(X10,X25),c_Set_Oimage(X10,X4,X3,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f137,axiom,
    ! [X2,X3,X10,X4,X25] : c_Set_Oimage(X10,c_Set_Oinsert(X25,X4,X3),X3,X2) = c_Set_Oinsert(hAPP(X10,X25),c_Set_Oimage(X10,X4,X3,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

fof(f4483,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f57,f4481]) ).

fof(f4481,plain,
    ( spl0_339
  <=> ! [X4,X0,X25,X2] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f57,axiom,
    ! [X2,X0,X4,X25] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) = c_Set_Oinsert(X25,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

fof(f4479,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f56,f4477]) ).

fof(f4475,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f15,f4473]) ).

fof(f4473,plain,
    ( spl0_337
  <=> ! [X2,X0] : c_lessequals(c_Relation_OId__on(X0,X2),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f15,axiom,
    ! [X2,X0] : c_lessequals(c_Relation_OId__on(X0,X2),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).

fof(f4471,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f9,f4469]) ).

fof(f4469,plain,
    ( spl0_336
  <=> ! [X11,X3,X10] :
        ( ~ class_Lattices_Olattice(X3)
        | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X11,tc_fun(t_a,X3)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X10,v_x),hAPP(X11,v_x),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f9,axiom,
    ! [X3,X10,X11] :
      ( ~ class_Lattices_Olattice(X3)
      | hAPP(c_Lattices_Oupper__semilattice__class_Osup(X10,X11,tc_fun(t_a,X3)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X10,v_x),hAPP(X11,v_x),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

fof(f4467,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f8,f4465]) ).

fof(f4465,plain,
    ( spl0_335
  <=> ! [X2,X0,X4] :
        ( c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = X0
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f8,axiom,
    ! [X2,X0,X4] :
      ( c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = X0
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

fof(f4344,plain,
    ( spl0_334
    | ~ spl0_13
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f4269,f3900,f900,f4341]) ).

fof(f4341,plain,
    ( spl0_334
  <=> c_Relation_Oirrefl(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f4269,plain,
    ( c_Relation_Oirrefl(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_13
    | ~ spl0_316 ),
    inference(resolution,[],[f3901,f901]) ).

fof(f4158,plain,
    ( spl0_333
    | ~ spl0_14
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f3314,f3097,f904,f4156]) ).

fof(f4156,plain,
    ( spl0_333
  <=> ! [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(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f3097,plain,
    ( spl0_262
  <=> ! [X17,X21,X5,X2] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | ~ hBOOL(c_in(X5,X21,X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X21,X17,X2),X21,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f3314,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(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_14
    | ~ spl0_262 ),
    inference(resolution,[],[f3098,f906]) ).

fof(f3098,plain,
    ( ! [X2,X21,X17,X5] :
        ( ~ hBOOL(c_in(X5,X21,X2))
        | ~ c_Wellfounded_Owf(X17,X2)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X21,X17,X2),X21,X2)) )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f3097]) ).

fof(f3971,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f630,f3969]) ).

fof(f3969,plain,
    ( spl0_332
  <=> ! [X5,X2,X0] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f630,axiom,
    ! [X2,X0,X5] :
      ( ~ hBOOL(c_in(X5,X0,X2))
      | hBOOL(c_in(c_Pair(X5,X5,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).

fof(f3967,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f629,f3965]) ).

fof(f3965,plain,
    ( spl0_331
  <=> ! [X0,X12,X5,X2] :
        ( hBOOL(c_in(X5,X0,X2))
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f629,axiom,
    ! [X2,X0,X5,X12] :
      ( hBOOL(c_in(X5,X0,X2))
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).

fof(f3963,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f580,f3961]) ).

fof(f3961,plain,
    ( spl0_330
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f580,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_2) ).

fof(f3959,plain,
    ( spl0_329
    | ~ spl0_14
    | ~ spl0_261 ),
    inference(avatar_split_clause,[],[f3297,f3093,f904,f3957]) ).

fof(f3093,plain,
    ( spl0_261
  <=> ! [X21,X22,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(X22,X21,X2))
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X21,X6,X2),X21,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f3297,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(v_L,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_14
    | ~ spl0_261 ),
    inference(resolution,[],[f3094,f906]) ).

fof(f3094,plain,
    ( ! [X2,X21,X6,X22] :
        ( ~ hBOOL(c_in(X22,X21,X2))
        | ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X21,X6,X2),X21,X2)) )
    | ~ spl0_261 ),
    inference(avatar_component_clause,[],[f3093]) ).

fof(f3955,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f579,f3953]) ).

fof(f3953,plain,
    ( spl0_328
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__2(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f579,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__2(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_0) ).

fof(f3951,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f578,f3949]) ).

fof(f3949,plain,
    ( spl0_327
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f578,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_3) ).

fof(f3947,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f577,f3945]) ).

fof(f3945,plain,
    ( spl0_326
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f577,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_1) ).

fof(f3943,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f576,f3941]) ).

fof(f3941,plain,
    ( spl0_325
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__2(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f576,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__2(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_1) ).

fof(f3939,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f575,f3937]) ).

fof(f3937,plain,
    ( spl0_324
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f575,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | ~ hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XtransI__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__XtransI__1__3(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_2) ).

fof(f3935,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f545,f3933]) ).

fof(f3933,plain,
    ( spl0_323
  <=> ! [X6,X3,X10,X12,X5,X2] :
        ( hBOOL(c_Predicate_Oinv__imagep(X6,X10,X5,X12,X2,X3))
        | ~ hBOOL(hAPP(hAPP(X6,hAPP(X10,X5)),hAPP(X10,X12))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f545,axiom,
    ! [X2,X3,X10,X6,X5,X12] :
      ( hBOOL(c_Predicate_Oinv__imagep(X6,X10,X5,X12,X2,X3))
      | ~ hBOOL(hAPP(hAPP(X6,hAPP(X10,X5)),hAPP(X10,X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__imagep_1) ).

fof(f3931,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f544,f3929]) ).

fof(f3929,plain,
    ( spl0_322
  <=> ! [X6,X3,X10,X12,X5,X2] :
        ( ~ hBOOL(c_Predicate_Oinv__imagep(X6,X10,X5,X12,X2,X3))
        | hBOOL(hAPP(hAPP(X6,hAPP(X10,X5)),hAPP(X10,X12))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f544,axiom,
    ! [X2,X3,X10,X6,X5,X12] :
      ( ~ hBOOL(c_Predicate_Oinv__imagep(X6,X10,X5,X12,X2,X3))
      | hBOOL(hAPP(hAPP(X6,hAPP(X10,X5)),hAPP(X10,X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__imagep_0) ).

fof(f3927,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f504,f3925]) ).

fof(f3925,plain,
    ( spl0_321
  <=> ! [X17,X3,X16,X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(X17,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16,X3),tc_bool)),X2,X16,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f504,axiom,
    ! [X2,X3,X16,X17] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(X17,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X16,X3),tc_bool)),X2,X16,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).

fof(f3923,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f503,f3921]) ).

fof(f3921,plain,
    ( spl0_320
  <=> ! [X17,X3,X16,X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X16),tc_bool)),X17,X2,X16,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f503,axiom,
    ! [X2,X3,X16,X17] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X16),tc_bool)),X17,X2,X16,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).

fof(f3919,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f478,f3917]) ).

fof(f3917,plain,
    ( spl0_319
  <=> ! [X2,X19,X6,X25] :
        ( hBOOL(hAPP(X19,X25))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2)))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f478,axiom,
    ! [X2,X19,X6,X25] :
      ( hBOOL(hAPP(X19,X25))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X19,X6,X2)))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).

fof(f3910,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f458,f3908]) ).

fof(f3908,plain,
    ( spl0_318
  <=> ! [X2,X19,X6,X25] :
        ( hBOOL(hAPP(X19,X25))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2)))
        | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f458,axiom,
    ! [X2,X19,X6,X25] :
      ( hBOOL(hAPP(X19,X25))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X19,X6,X2)))
      | ~ hBOOL(c_in(X25,c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).

fof(f3906,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f404,f3904]) ).

fof(f404,axiom,
    ! [X2,X6] :
      ( c_Nitpick_Orefl_H(X6,X2)
      | ~ hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).

fof(f3902,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f401,f3900]) ).

fof(f401,axiom,
    ! [X2,X6] :
      ( c_Relation_Oirrefl(X6,X2)
      | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X6,X2),X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).

fof(f3898,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f305,f3896]) ).

fof(f3896,plain,
    ( spl0_315
  <=> ! [X28,X25,X2,X1] :
        ( ~ c_lessequals(X1,X28,tc_fun(X2,tc_bool))
        | c_lessequals(c_Set_Oinsert(X25,X1,X2),c_Set_Oinsert(X25,X28,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f305,axiom,
    ! [X2,X28,X1,X25] :
      ( ~ c_lessequals(X1,X28,tc_fun(X2,tc_bool))
      | c_lessequals(c_Set_Oinsert(X25,X1,X2),c_Set_Oinsert(X25,X28,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

fof(f3894,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f282,f3892]) ).

fof(f3892,plain,
    ( spl0_314
  <=> ! [X4,X0,X2,X1] :
        ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
        | c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f282,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X1,tc_fun(X2,tc_bool))
      | c_lessequals(X0,X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

fof(f3890,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f261,f3888]) ).

fof(f3888,plain,
    ( spl0_313
  <=> ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f261,axiom,
    ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

fof(f3886,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f203,f3884]) ).

fof(f3884,plain,
    ( spl0_312
  <=> ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f203,axiom,
    ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

fof(f3882,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f202,f3880]) ).

fof(f3880,plain,
    ( spl0_311
  <=> ! [X2,X32,X33] :
        ( ~ c_lessequals(X33,X32,tc_fun(tc_prod(X2,X2),tc_bool))
        | c_lessequals(c_Wellfounded_Oacc(X32,X2),c_Wellfounded_Oacc(X33,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f202,axiom,
    ! [X2,X32,X33] :
      ( ~ c_lessequals(X33,X32,tc_fun(tc_prod(X2,X2),tc_bool))
      | c_lessequals(c_Wellfounded_Oacc(X32,X2),c_Wellfounded_Oacc(X33,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).

fof(f3878,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f182,f3876]) ).

fof(f3876,plain,
    ( spl0_310
  <=> ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f182,axiom,
    ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

fof(f3874,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f181,f3872]) ).

fof(f3872,plain,
    ( spl0_309
  <=> ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f181,axiom,
    ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X4,X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

fof(f3864,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f162,f3862]) ).

fof(f3862,plain,
    ( spl0_308
  <=> ! [X25,X2,X26] :
        ( X25 = X26
        | c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f162,axiom,
    ! [X2,X26,X25] :
      ( X25 = X26
      | c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X26,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

fof(f3860,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f118,f3858]) ).

fof(f3858,plain,
    ( spl0_307
  <=> ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f118,axiom,
    ! [X2,X0,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

fof(f3856,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f25,f3854]) ).

fof(f3854,plain,
    ( spl0_306
  <=> ! [X2,X0,X4] : c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f25,axiom,
    ! [X2,X0,X4] : c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

fof(f3833,plain,
    ( spl0_305
    | ~ spl0_175
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f3486,f3483,f1821,f3831]) ).

fof(f3483,plain,
    ( spl0_300
  <=> ! [X6,X2] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f3486,plain,
    ( ! [X2,X6] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_175
    | ~ spl0_300 ),
    inference(forward_demodulation,[],[f3484,f1822]) ).

fof(f3484,plain,
    ( ! [X2,X6] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f3483]) ).

fof(f3807,plain,
    ( spl0_304
    | ~ spl0_108
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3429,f3223,f1367,f3805]) ).

fof(f3805,plain,
    ( spl0_304
  <=> ! [X0] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1367,plain,
    ( spl0_108
  <=> ! [X2,X0,X4] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f3223,plain,
    ( spl0_267
  <=> ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(hAPP(X0,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f3429,plain,
    ( ! [X0] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_108
    | ~ spl0_267 ),
    inference(resolution,[],[f3224,f1368]) ).

fof(f1368,plain,
    ( ! [X2,X0,X4] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1367]) ).

fof(f3224,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(hAPP(X0,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_267 ),
    inference(avatar_component_clause,[],[f3223]) ).

fof(f3716,plain,
    ( spl0_303
    | ~ spl0_107
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3428,f3223,f1363,f3714]) ).

fof(f3714,plain,
    ( spl0_303
  <=> ! [X0] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f1363,plain,
    ( spl0_107
  <=> ! [X2,X0,X4] : c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f3428,plain,
    ( ! [X0] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,v_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_107
    | ~ spl0_267 ),
    inference(resolution,[],[f3224,f1364]) ).

fof(f1364,plain,
    ( ! [X2,X0,X4] : c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1363]) ).

fof(f3494,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f704,f3492]) ).

fof(f3492,plain,
    ( spl0_302
  <=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f704,plain,
    ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),X3,X2),
    inference(definition_unfolding,[],[f491,f514]) ).

fof(f491,axiom,
    ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).

fof(f3490,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f697,f3488]) ).

fof(f3485,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f696,f3483]) ).

fof(f696,plain,
    ! [X2,X6] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    inference(definition_unfolding,[],[f353,f500]) ).

fof(f353,axiom,
    ! [X2,X6] : c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(X6,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).

fof(f3481,plain,
    ( spl0_299
    | ~ spl0_66
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f3436,f3223,f1125,f3479]) ).

fof(f3479,plain,
    ( spl0_299
  <=> ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f1125,plain,
    ( spl0_66
  <=> ! [X2,X25,X4] : c_lessequals(X4,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f3436,plain,
    ( ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_66
    | ~ spl0_267 ),
    inference(resolution,[],[f3224,f1126]) ).

fof(f1126,plain,
    ( ! [X2,X4,X25] : c_lessequals(X4,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool))
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1125]) ).

fof(f3477,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f622,f3475]) ).

fof(f3475,plain,
    ( spl0_298
  <=> ! [X6,X3,X10] : c_Predicate_Oinv__imagep(X6,X10,v_x,v_y,X3,t_a) = hAPP(hAPP(X6,hAPP(X10,v_x)),hAPP(X10,v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f622,axiom,
    ! [X3,X10,X6] : c_Predicate_Oinv__imagep(X6,X10,v_x,v_y,X3,t_a) = hAPP(hAPP(X6,hAPP(X10,v_x)),hAPP(X10,v_y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__imagep__def_0) ).

fof(f3473,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f547,f3471]) ).

fof(f3471,plain,
    ( spl0_297
  <=> ! [X6,X2,X3] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)) = X6
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(X6,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f547,axiom,
    ! [X2,X3,X6] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)) = X6
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Relation_ORange(X6,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).

fof(f3469,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f534,f3467]) ).

fof(f3467,plain,
    ( spl0_296
  <=> ! [X6,X2,X5] :
        ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2))
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X6,X5,X2),c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f534,axiom,
    ! [X2,X6,X5] :
      ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2))
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X6,X5,X2),c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).

fof(f3465,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f525,f3463]) ).

fof(f3463,plain,
    ( spl0_295
  <=> ! [X6,X5,X19] :
        ( hBOOL(hAPP(X19,X5))
        | ~ hBOOL(hAPP(X19,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6)))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f525,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(X19,X5))
      | ~ hBOOL(hAPP(X19,v_sko__Wellfounded__Xacc__Xinduct__1(X19,X6)))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).

fof(f3461,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f517,f3459]) ).

fof(f3459,plain,
    ( spl0_294
  <=> ! [X16,X3,X7,X6,X2] :
        ( ~ c_Relation_Osingle__valued(X6,X2,X3)
        | ~ c_Relation_Osingle__valued(X7,X3,X16)
        | c_Relation_Osingle__valued(c_Relation_Orel__comp(X6,X7,X2,X3,X16),X2,X16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f517,axiom,
    ! [X2,X3,X6,X7,X16] :
      ( ~ c_Relation_Osingle__valued(X6,X2,X3)
      | ~ c_Relation_Osingle__valued(X7,X3,X16)
      | c_Relation_Osingle__valued(c_Relation_Orel__comp(X6,X7,X2,X3,X16),X2,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).

fof(f3457,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f509,f3455]) ).

fof(f3455,plain,
    ( spl0_293
  <=> ! [X17,X10,X3,X2] : c_Relation_Oconverse(c_Relation_Oinv__image(X17,X10,X3,X2),X2,X2) = c_Relation_Oinv__image(c_Relation_Oconverse(X17,X3,X3),X10,X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f509,axiom,
    ! [X2,X3,X10,X17] : c_Relation_Oconverse(c_Relation_Oinv__image(X17,X10,X3,X2),X2,X2) = c_Relation_Oinv__image(c_Relation_Oconverse(X17,X3,X3),X10,X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).

fof(f3453,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f469,f3451]) ).

fof(f3451,plain,
    ( spl0_292
  <=> ! [X2,X5,X17] :
        ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X17,X2),X2))
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X17,X5,X2),c_Wellfounded_Oacc(X17,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f469,axiom,
    ! [X2,X17,X5] :
      ( hBOOL(c_in(X5,c_Wellfounded_Oacc(X17,X2),X2))
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X17,X5,X2),c_Wellfounded_Oacc(X17,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).

fof(f3449,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f459,f3447]) ).

fof(f3447,plain,
    ( spl0_291
  <=> ! [X6,X5,X19] :
        ( hBOOL(hAPP(X19,X5))
        | ~ hBOOL(hAPP(X19,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6)))
        | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f459,axiom,
    ! [X19,X6,X5] :
      ( hBOOL(hAPP(X19,X5))
      | ~ hBOOL(hAPP(X19,v_sko__Wellfounded__Xacc__Xinducts__1(X19,X6)))
      | ~ hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,t_a),t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).

fof(f3445,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f429,f3443]) ).

fof(f3443,plain,
    ( spl0_290
  <=> ! [X2,X3,X10,X16,X25,X26] : hAPP(hAPP(X10,X25),X26) = hAPP(c_split(X10,X3,X16,X2),c_Pair(X25,X26,X3,X16)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f429,axiom,
    ! [X2,X3,X10,X26,X16,X25] : hAPP(hAPP(X10,X25),X26) = hAPP(c_split(X10,X3,X16,X2),c_Pair(X25,X26,X3,X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).

fof(f3441,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f426,f3439]) ).

fof(f3439,plain,
    ( spl0_289
  <=> ! [X2,X3,X10,X16,X25,X26] : hAPP(hAPP(c_curry(X10,X3,X16,X2),X25),X26) = hAPP(X10,c_Pair(X25,X26,X3,X16)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f426,axiom,
    ! [X2,X3,X10,X26,X16,X25] : hAPP(hAPP(c_curry(X10,X3,X16,X2),X25),X26) = hAPP(X10,c_Pair(X25,X26,X3,X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__conv_0) ).

fof(f3424,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f392,f3422]) ).

fof(f3422,plain,
    ( spl0_288
  <=> ! [X2,X0,X27] :
        ( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),X0,X2))
        | ~ hBOOL(c_in(X27,c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f392,axiom,
    ! [X2,X0,X27] :
      ( hBOOL(c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X27,X2),X0,X2))
      | ~ hBOOL(c_in(X27,c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).

fof(f3420,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f299,f3418]) ).

fof(f3418,plain,
    ( spl0_287
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(hAPP(X0,X5))
        | ~ hBOOL(hAPP(X4,X5))
        | hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f299,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

fof(f3416,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f277,f3414]) ).

fof(f3414,plain,
    ( spl0_286
  <=> ! [X2,X0,X1,X4] :
        ( c_lessequals(X4,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f277,axiom,
    ! [X2,X0,X1,X4] :
      ( c_lessequals(X4,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

fof(f3412,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f276,f3410]) ).

fof(f3410,plain,
    ( spl0_285
  <=> ! [X4,X0,X2,X1] :
        ( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f276,axiom,
    ! [X2,X0,X1,X4] :
      ( c_lessequals(X0,X1,tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

fof(f3408,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f201,f3406]) ).

fof(f3406,plain,
    ( spl0_284
  <=> ! [X2,X0,X25] : c_Set_Oinsert(X25,X0,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f3404,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f188,f3402]) ).

fof(f3402,plain,
    ( spl0_283
  <=> ! [X4,X0,X2,X1] :
        ( c_lessequals(X1,X0,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f188,axiom,
    ! [X2,X0,X1,X4] :
      ( c_lessequals(X1,X0,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

fof(f3400,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f187,f3398]) ).

fof(f3398,plain,
    ( spl0_282
  <=> ! [X4,X0,X2,X1] :
        ( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f187,axiom,
    ! [X2,X0,X1,X4] :
      ( c_lessequals(X1,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

fof(f3396,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f178,f3394]) ).

fof(f3394,plain,
    ( spl0_281
  <=> ! [X2,X0,X4] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f178,axiom,
    ! [X2,X0,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

fof(f3392,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f177,f3390]) ).

fof(f3390,plain,
    ( spl0_280
  <=> ! [X4,X0,X2] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X4
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f177,axiom,
    ! [X2,X0,X4] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X4
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

fof(f3388,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f142,f3386]) ).

fof(f3386,plain,
    ( spl0_279
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X5,X12,X2)
        | ~ c_lessequals(X5,X13,X2)
        | c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f142,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X5,X12,X2)
      | ~ c_lessequals(X5,X13,X2)
      | c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

fof(f3384,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f93,f3382]) ).

fof(f3382,plain,
    ( spl0_278
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f93,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

fof(f3380,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f92,f3378]) ).

fof(f3378,plain,
    ( spl0_277
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f92,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

fof(f3376,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f91,f3374]) ).

fof(f3374,plain,
    ( spl0_276
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f91,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

fof(f3372,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f90,f3370]) ).

fof(f3370,plain,
    ( spl0_275
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f90,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X13,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

fof(f3368,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f85,f3366]) ).

fof(f3366,plain,
    ( spl0_274
  <=> ! [X4,X0,X5,X2] :
        ( hBOOL(hAPP(X4,X5))
        | hBOOL(hAPP(X0,X5))
        | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f85,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

fof(f3364,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f49,f3362]) ).

fof(f3362,plain,
    ( spl0_273
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X12,X5,X2)
        | ~ c_lessequals(X13,X5,X2)
        | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f49,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X12,X5,X2)
      | ~ c_lessequals(X13,X5,X2)
      | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

fof(f3360,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f36,f3358]) ).

fof(f3358,plain,
    ( spl0_272
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f36,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

fof(f3356,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f35,f3354]) ).

fof(f3354,plain,
    ( spl0_271
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f35,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

fof(f3352,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f34,f3350]) ).

fof(f3350,plain,
    ( spl0_270
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f34,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

fof(f3348,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f33,f3346]) ).

fof(f3346,plain,
    ( spl0_269
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f33,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

fof(f3344,plain,
    ( spl0_268
    | spl0_1
    | ~ spl0_226
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f3328,f3101,f2705,f840,f3342]) ).

fof(f3342,plain,
    ( spl0_268
  <=> ! [X0] : ~ c_lessequals(v_L,c_Relation_OId__on(X0,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_268])]) ).

fof(f2705,plain,
    ( spl0_226
  <=> ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f3101,plain,
    ( spl0_263
  <=> ! [X0,X12,X5,X2] :
        ( X5 = X12
        | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f3328,plain,
    ( ! [X0] :
        ( v_x = v_y
        | ~ c_lessequals(v_L,c_Relation_OId__on(X0,tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
    | ~ spl0_226
    | ~ spl0_263 ),
    inference(resolution,[],[f3102,f2706]) ).

fof(f2706,plain,
    ( ! [X0] :
        ( hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2705]) ).

fof(f3102,plain,
    ( ! [X2,X0,X5,X12] :
        ( ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2)))
        | X5 = X12 )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f3101]) ).

fof(f3225,plain,
    ( spl0_267
    | ~ spl0_90
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3009,f2705,f1221,f3223]) ).

fof(f3009,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(hAPP(X0,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_90
    | ~ spl0_226 ),
    inference(resolution,[],[f2706,f1222]) ).

fof(f3116,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f802,f3114]) ).

fof(f3114,plain,
    ( spl0_266
  <=> ! [X2,X17] :
        ( c_Relation_Orel__comp(X17,X17,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
        | c_Wellfounded_Owf(X17,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f802,plain,
    ! [X2,X17] :
      ( c_Relation_Orel__comp(X17,X17,X2,X2,X2) != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
      | c_Wellfounded_Owf(X17,X2) ),
    inference(forward_demodulation,[],[f460,f481]) ).

fof(f460,axiom,
    ! [X2,X17] :
      ( c_Wellfounded_Owf(X17,X2)
      | c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) != c_Relation_Orel__comp(X17,X17,X2,X2,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).

fof(f3112,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f694,f3110]) ).

fof(f3110,plain,
    ( spl0_265
  <=> ! [X6,X2] : c_Relation_ORange(X6,X2,X2) = c_Relation_ORange(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f694,plain,
    ! [X2,X6] : c_Relation_ORange(X6,X2,X2) = c_Relation_ORange(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2,X2),
    inference(definition_unfolding,[],[f492,f538]) ).

fof(f492,axiom,
    ! [X2,X6] : c_Relation_ORange(X6,X2,X2) = c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).

fof(f3107,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f689,f3105]) ).

fof(f3105,plain,
    ( spl0_264
  <=> ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X17,X2),X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f689,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X17,X2),X2),X2,X2,X2),
    inference(definition_unfolding,[],[f502,f538]) ).

fof(f502,axiom,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X17,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

fof(f3103,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f605,f3101]) ).

fof(f605,axiom,
    ! [X2,X0,X5,X12] :
      ( X5 = X12
      | ~ hBOOL(c_in(c_Pair(X5,X12,X2,X2),c_Relation_OId__on(X0,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).

fof(f3099,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f531,f3097]) ).

fof(f531,axiom,
    ! [X2,X21,X17,X5] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | ~ hBOOL(c_in(X5,X21,X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X21,X17,X2),X21,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).

fof(f3095,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f515,f3093]) ).

fof(f515,axiom,
    ! [X2,X21,X6,X22] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(X22,X21,X2))
      | hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X21,X6,X2),X21,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).

fof(f3091,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f501,f3089]) ).

fof(f3089,plain,
    ( spl0_260
  <=> ! [X10,X0,X3,X2] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0
        | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X10,X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f501,axiom,
    ! [X2,X3,X10,X0] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = X0
      | c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oimage(X10,X0,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

fof(f3087,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f444,f3085]) ).

fof(f3085,plain,
    ( spl0_259
  <=> ! [X6,X2,X35] :
        ( ~ hBOOL(c_in(X35,X6,tc_prod(X2,X2)))
        | hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f444,axiom,
    ! [X2,X6,X35] :
      ( ~ hBOOL(c_in(X35,X6,tc_prod(X2,X2)))
      | hBOOL(c_in(X35,c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).

fof(f3083,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f423,f3081]) ).

fof(f3081,plain,
    ( spl0_258
  <=> ! [X3,X10,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X0,X3))
        | hBOOL(c_in(hAPP(X10,X5),c_Set_Oimage(X10,X0,X3,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f423,axiom,
    ! [X2,X3,X10,X0,X5] :
      ( ~ hBOOL(c_in(X5,X0,X3))
      | hBOOL(c_in(hAPP(X10,X5),c_Set_Oimage(X10,X0,X3,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

fof(f3079,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f341,f3077]) ).

fof(f3077,plain,
    ( spl0_257
  <=> ! [X6,X2] :
        ( ~ c_Relation_Otrans(X6,X2)
        | c_lessequals(c_Relation_Orel__comp(X6,X6,X2,X2,X2),X6,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f341,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_lessequals(c_Relation_Orel__comp(X6,X6,X2,X2,X2),X6,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).

fof(f3075,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f290,f3073]) ).

fof(f3073,plain,
    ( spl0_256
  <=> ! [X3,X7,X6,X2] :
        ( ~ c_Relation_Osingle__valued(X7,X2,X3)
        | c_Relation_Osingle__valued(X6,X2,X3)
        | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X3),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f290,axiom,
    ! [X2,X3,X6,X7] :
      ( ~ c_Relation_Osingle__valued(X7,X2,X3)
      | c_Relation_Osingle__valued(X6,X2,X3)
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X3),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).

fof(f3071,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f249,f3069]) ).

fof(f3069,plain,
    ( spl0_255
  <=> ! [X6,X2,X7] :
        ( ~ c_Relation_Otrans(X6,X2)
        | ~ c_Relation_Otrans(X7,X2)
        | c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f249,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Relation_Otrans(X6,X2)
      | ~ c_Relation_Otrans(X7,X2)
      | c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).

fof(f3067,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f232,f3065]) ).

fof(f3065,plain,
    ( spl0_254
  <=> ! [X2,X0,X25,X26] :
        ( X25 = X26
        | hBOOL(c_in(X25,X0,X2))
        | ~ hBOOL(c_in(X25,c_Set_Oinsert(X26,X0,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f232,axiom,
    ! [X2,X0,X26,X25] :
      ( X25 = X26
      | hBOOL(c_in(X25,X0,X2))
      | ~ hBOOL(c_in(X25,c_Set_Oinsert(X26,X0,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

fof(f3063,plain,
    ( ~ spl0_253
    | ~ spl0_55
    | ~ spl0_175
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3017,f2705,f1821,f1074,f3060]) ).

fof(f3060,plain,
    ( spl0_253
  <=> c_lessequals(v_L,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),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_253])]) ).

fof(f3017,plain,
    ( ~ c_lessequals(v_L,c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_55
    | ~ spl0_175
    | ~ spl0_226 ),
    inference(forward_demodulation,[],[f3011,f1822]) ).

fof(f3011,plain,
    ( ~ c_lessequals(v_L,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_55
    | ~ spl0_226 ),
    inference(resolution,[],[f2706,f1075]) ).

fof(f3058,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f227,f3056]) ).

fof(f3056,plain,
    ( spl0_252
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(c_in(X5,X0,X2))
        | hBOOL(c_in(X5,X4,X2))
        | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f227,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(c_in(X5,X0,X2))
      | hBOOL(c_in(X5,X4,X2))
      | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

fof(f3054,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f221,f3052]) ).

fof(f3052,plain,
    ( spl0_251
  <=> ! [X5,X10,X11,X3,X2] :
        ( ~ class_HOL_Oord(X3)
        | ~ c_lessequals(X10,X11,tc_fun(X2,X3))
        | c_lessequals(hAPP(X10,X5),hAPP(X11,X5),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f221,axiom,
    ! [X2,X3,X10,X11,X5] :
      ( ~ class_HOL_Oord(X3)
      | ~ c_lessequals(X10,X11,tc_fun(X2,X3))
      | c_lessequals(hAPP(X10,X5),hAPP(X11,X5),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

fof(f3050,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f215,f3048]) ).

fof(f3048,plain,
    ( spl0_250
  <=> ! [X6,X2,X7] :
        ( ~ c_Relation_Osym(X6,X2)
        | ~ c_Relation_Osym(X7,X2)
        | c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f215,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Relation_Osym(X6,X2)
      | ~ c_Relation_Osym(X7,X2)
      | c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).

fof(f3046,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f206,f3044]) ).

fof(f3044,plain,
    ( spl0_249
  <=> ! [X2,X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f206,axiom,
    ! [X2,X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ominus__class_Ominus(X4,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

fof(f3042,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f68,f3040]) ).

fof(f3040,plain,
    ( spl0_248
  <=> ! [X6,X2,X7] :
        ( ~ c_Relation_Osym(X6,X2)
        | ~ c_Relation_Osym(X7,X2)
        | c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f68,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Relation_Osym(X6,X2)
      | ~ c_Relation_Osym(X7,X2)
      | c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).

fof(f3025,plain,
    ( spl0_247
    | ~ spl0_175
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2842,f2839,f1821,f3023]) ).

fof(f3023,plain,
    ( spl0_247
  <=> ! [X2,X17,X3] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X17,X2,X2,X3) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2839,plain,
    ( spl0_244
  <=> ! [X2,X17,X3] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X17,X2,X2,X3) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2842,plain,
    ( ! [X2,X3,X17] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X17,X2,X2,X3) = X17
    | ~ spl0_175
    | ~ spl0_244 ),
    inference(forward_demodulation,[],[f2840,f1822]) ).

fof(f2840,plain,
    ( ! [X2,X3,X17] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X17,X2,X2,X3) = X17
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f2839]) ).

fof(f3021,plain,
    ( spl0_246
    | ~ spl0_175
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f2837,f2834,f1821,f3019]) ).

fof(f3019,plain,
    ( spl0_246
  <=> ! [X2,X17,X3] : c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2,X3,X3) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2834,plain,
    ( spl0_243
  <=> ! [X2,X17,X3] : c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),X2,X3,X3) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2837,plain,
    ( ! [X2,X3,X17] : c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),X2,X3,X3) = X17
    | ~ spl0_175
    | ~ spl0_243 ),
    inference(forward_demodulation,[],[f2835,f1822]) ).

fof(f2835,plain,
    ( ! [X2,X3,X17] : c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),X2,X3,X3) = X17
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f2834]) ).

fof(f2897,plain,
    ( spl0_245
    | ~ spl0_146
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2527,f2219,f1575,f2895]) ).

fof(f2895,plain,
    ( spl0_245
  <=> ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f1575,plain,
    ( spl0_146
  <=> v_L = c_Set_Oinsert(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f2219,plain,
    ( spl0_197
  <=> ! [X4,X0,X5,X2] :
        ( hBOOL(c_in(X5,X4,X2))
        | ~ c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f2527,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_146
    | ~ spl0_197 ),
    inference(superposition,[],[f2220,f1577]) ).

fof(f1577,plain,
    ( v_L = c_Set_Oinsert(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1575]) ).

fof(f2220,plain,
    ( ! [X2,X0,X4,X5] :
        ( ~ c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool))
        | hBOOL(c_in(X5,X4,X2)) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f2219]) ).

fof(f2841,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f692,f2839]) ).

fof(f692,plain,
    ! [X2,X3,X17] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X17,X2,X2,X3) = X17,
    inference(definition_unfolding,[],[f472,f500]) ).

fof(f472,axiom,
    ! [X2,X3,X17] : c_Relation_Orel__comp(c_Relation_OId(X2),X17,X2,X2,X3) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).

fof(f2836,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f691,f2834]) ).

fof(f691,plain,
    ! [X2,X3,X17] : c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)),X3),X2,X3,X3) = X17,
    inference(definition_unfolding,[],[f473,f500]) ).

fof(f473,axiom,
    ! [X2,X3,X17] : c_Relation_Orel__comp(X17,c_Relation_OId(X3),X2,X3,X3) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).

fof(f2832,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f679,f2830]) ).

fof(f2830,plain,
    ( spl0_242
  <=> ! [X6,X2,X3] : c_Relation_ORange(X6,X3,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X6,X3,X2),X2,X3),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f679,plain,
    ! [X2,X3,X6] : c_Relation_ORange(X6,X3,X2) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X6,X3,X2),X2,X3),X3,X2),
    inference(definition_unfolding,[],[f536,f514]) ).

fof(f536,axiom,
    ! [X2,X3,X6] : c_Relation_ORange(X6,X3,X2) = c_Relation_ODomain(c_Relation_Oconverse(X6,X3,X2),X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

fof(f2828,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f519,f2826]) ).

fof(f2826,plain,
    ( spl0_241
  <=> ! [X6,X2,X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f519,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | c_Relation_Orel__comp(c_Relation_Oconverse(X6,X2,X2),X6,X2,X2,X2) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).

fof(f2824,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f468,f2822]) ).

fof(f2822,plain,
    ( spl0_240
  <=> ! [X2,X4,X3] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f468,axiom,
    ! [X2,X3,X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,X2,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).

fof(f2820,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f240,f2818]) ).

fof(f2818,plain,
    ( spl0_239
  <=> ! [X4,X0,X27,X2] :
        ( hBOOL(c_in(X27,X0,X2))
        | ~ hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f240,axiom,
    ! [X2,X0,X27,X4] :
      ( hBOOL(c_in(X27,X0,X2))
      | ~ hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

fof(f2816,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f239,f2814]) ).

fof(f2814,plain,
    ( spl0_238
  <=> ! [X4,X0,X27,X2] :
        ( hBOOL(c_in(X27,X4,X2))
        | ~ hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f239,axiom,
    ! [X2,X0,X27,X4] :
      ( hBOOL(c_in(X27,X4,X2))
      | ~ hBOOL(c_in(X27,c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

fof(f2812,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f235,f2810]) ).

fof(f2810,plain,
    ( spl0_237
  <=> ! [X4,X0,X27,X2] :
        ( hBOOL(c_in(X27,X0,X2))
        | ~ hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f235,axiom,
    ! [X2,X0,X27,X4] :
      ( hBOOL(c_in(X27,X0,X2))
      | ~ hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

fof(f2808,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f234,f2806]) ).

fof(f2806,plain,
    ( spl0_236
  <=> ! [X4,X0,X27,X2] :
        ( ~ hBOOL(c_in(X27,X4,X2))
        | ~ hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f234,axiom,
    ! [X2,X0,X27,X4] :
      ( ~ hBOOL(c_in(X27,X4,X2))
      | ~ hBOOL(c_in(X27,c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

fof(f2804,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f231,f2802]) ).

fof(f2802,plain,
    ( spl0_235
  <=> ! [X4,X0,X27,X2] :
        ( ~ hBOOL(c_in(X27,X4,X2))
        | hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f231,axiom,
    ! [X2,X0,X27,X4] :
      ( ~ hBOOL(c_in(X27,X4,X2))
      | hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

fof(f2800,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f230,f2798]) ).

fof(f2798,plain,
    ( spl0_234
  <=> ! [X4,X0,X27,X2] :
        ( ~ hBOOL(c_in(X27,X0,X2))
        | hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f230,axiom,
    ! [X2,X0,X27,X4] :
      ( ~ hBOOL(c_in(X27,X0,X2))
      | hBOOL(c_in(X27,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

fof(f2796,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f132,f2794]) ).

fof(f2794,plain,
    ( spl0_233
  <=> ! [X2,X0] :
        ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
        | ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f132,axiom,
    ! [X2,X0] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = X0
      | ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

fof(f2792,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f113,f2790]) ).

fof(f2790,plain,
    ( spl0_232
  <=> ! [X4,X0,X2] :
        ( X0 = X4
        | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f113,axiom,
    ! [X2,X0,X4] :
      ( X0 = X4
      | ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

fof(f2788,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f52,f2786]) ).

fof(f2786,plain,
    ( spl0_231
  <=> ! [X4,X0,X2,X26] :
        ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | c_lessequals(X0,c_Set_Oinsert(X26,X4,X2),tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f52,axiom,
    ! [X2,X0,X26,X4] :
      ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | c_lessequals(X0,c_Set_Oinsert(X26,X4,X2),tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

fof(f2784,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f51,f2782]) ).

fof(f2782,plain,
    ( spl0_230
  <=> ! [X5,X2,X0,X4] :
        ( c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | ~ c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f51,axiom,
    ! [X2,X0,X4,X5] :
      ( c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | ~ c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

fof(f2780,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f23,f2778]) ).

fof(f2778,plain,
    ( spl0_229
  <=> ! [X0,X12,X5,X2] : c_Set_Oinsert(X5,c_Set_Oinsert(X12,X0,X2),X2) = c_Set_Oinsert(X12,c_Set_Oinsert(X5,X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f23,axiom,
    ! [X2,X0,X5,X12] : c_Set_Oinsert(X5,c_Set_Oinsert(X12,X0,X2),X2) = c_Set_Oinsert(X12,c_Set_Oinsert(X5,X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

fof(f2752,plain,
    ( ~ spl0_228
    | ~ spl0_13
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2725,f2303,f900,f2749]) ).

fof(f2749,plain,
    ( spl0_228
  <=> c_Nitpick_Orefl_H(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f2725,plain,
    ( ~ c_Nitpick_Orefl_H(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_13
    | ~ spl0_217 ),
    inference(resolution,[],[f2304,f901]) ).

fof(f2747,plain,
    ( spl0_227
    | ~ spl0_175
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2342,f2339,f1821,f2745]) ).

fof(f2745,plain,
    ( spl0_227
  <=> ! [X2,X0] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X0,X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f2339,plain,
    ( spl0_224
  <=> ! [X2,X0] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X0,X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f2342,plain,
    ( ! [X2,X0] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X0,X2,X2) = X0
    | ~ spl0_175
    | ~ spl0_224 ),
    inference(forward_demodulation,[],[f2340,f1822]) ).

fof(f2340,plain,
    ( ! [X2,X0] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X0,X2,X2) = X0
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2339]) ).

fof(f2707,plain,
    ( spl0_226
    | ~ spl0_139
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2526,f2219,f1540,f2705]) ).

fof(f1540,plain,
    ( spl0_139
  <=> v_L = c_Set_Oinsert(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f2526,plain,
    ( ! [X0] :
        ( ~ c_lessequals(v_L,X0,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
        | hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_139
    | ~ spl0_197 ),
    inference(superposition,[],[f2220,f1542]) ).

fof(f1542,plain,
    ( v_L = c_Set_Oinsert(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1540]) ).

fof(f2346,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f690,f2344]) ).

fof(f2344,plain,
    ( spl0_225
  <=> ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f690,plain,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X17,c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),X2),
    inference(definition_unfolding,[],[f548,f538]) ).

fof(f548,axiom,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X17,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

fof(f2341,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f688,f2339]) ).

fof(f688,plain,
    ! [X2,X0] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X0,X2,X2) = X0,
    inference(definition_unfolding,[],[f485,f500]) ).

fof(f485,axiom,
    ! [X2,X0] : c_Relation_OImage(c_Relation_OId(X2),X0,X2,X2) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).

fof(f2337,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f645,f2335]) ).

fof(f2335,plain,
    ( spl0_223
  <=> ! [X51,X50,X3,X25,X2,X26] :
        ( X25 = X50
        | c_Pair(X25,X26,X2,X3) != c_Pair(X50,X51,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f645,axiom,
    ! [X50,X2,X51,X3,X26,X25] :
      ( X25 = X50
      | c_Pair(X25,X26,X2,X3) != c_Pair(X50,X51,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

fof(f2333,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f644,f2331]) ).

fof(f2331,plain,
    ( spl0_222
  <=> ! [X51,X50,X3,X25,X2,X26] :
        ( X26 = X51
        | c_Pair(X25,X26,X2,X3) != c_Pair(X50,X51,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f644,axiom,
    ! [X50,X2,X51,X3,X26,X25] :
      ( X26 = X51
      | c_Pair(X25,X26,X2,X3) != c_Pair(X50,X51,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

fof(f2329,plain,
    ( ~ spl0_221
    | ~ spl0_55
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2321,f2317,f1074,f2326]) ).

fof(f2326,plain,
    ( spl0_221
  <=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f2317,plain,
    ( spl0_220
  <=> 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_220])]) ).

fof(f2321,plain,
    ( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
    | ~ spl0_55
    | ~ spl0_220 ),
    inference(superposition,[],[f1075,f2319]) ).

fof(f2319,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_220 ),
    inference(avatar_component_clause,[],[f2317]) ).

fof(f2320,plain,
    ( spl0_220
    | ~ spl0_10
    | ~ spl0_132
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2315,f2311,f1464,f885,f2317]) ).

fof(f885,plain,
    ( spl0_10
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f1464,plain,
    ( spl0_132
  <=> ! [X3] :
        ( ~ class_Orderings_Obot(X3)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X3)),v_x) = c_Orderings_Obot__class_Obot(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f2311,plain,
    ( spl0_219
  <=> 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_219])]) ).

fof(f2315,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_10
    | ~ spl0_132
    | ~ spl0_219 ),
    inference(forward_demodulation,[],[f2313,f1537]) ).

fof(f1537,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
    | ~ spl0_10
    | ~ spl0_132 ),
    inference(resolution,[],[f1465,f887]) ).

fof(f887,plain,
    ( class_Orderings_Obot(tc_bool)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f885]) ).

fof(f1465,plain,
    ( ! [X3] :
        ( ~ class_Orderings_Obot(X3)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X3)),v_x) = c_Orderings_Obot__class_Obot(X3) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1464]) ).

fof(f2313,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_219 ),
    inference(avatar_component_clause,[],[f2311]) ).

fof(f2314,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f619,f2311]) ).

fof(f619,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(f2309,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f609,f2307]) ).

fof(f609,axiom,
    ! [X2,X6,X25] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X25,X25,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).

fof(f2305,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f608,f2303]) ).

fof(f608,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Nitpick_Orefl_H(X6,X2)
      | hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).

fof(f2301,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f592,f2299]) ).

fof(f592,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Relation_Oirrefl(X6,X2)
      | ~ hBOOL(c_in(c_Pair(X5,X5,X2,X2),X6,tc_prod(X2,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).

fof(f2297,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f528,f2295]) ).

fof(f2295,plain,
    ( spl0_215
  <=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f528,axiom,
    ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).

fof(f2293,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f520,f2291]) ).

fof(f2291,plain,
    ( spl0_214
  <=> ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f520,axiom,
    ! [X2,X17] : c_Transitive__Closure_Ortrancl(X17,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X17,X2),c_Transitive__Closure_Ortrancl(X17,X2),X2,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).

fof(f2289,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f405,f2287]) ).

fof(f2287,plain,
    ( spl0_213
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Oirrefl(X6,X2)
        | ~ c_Relation_Otrans(X6,X2)
        | ~ c_Relation_Ototal__on(X0,X6,X2)
        | c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f405,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Oirrefl(X6,X2)
      | ~ c_Relation_Otrans(X6,X2)
      | ~ c_Relation_Ototal__on(X0,X6,X2)
      | c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).

fof(f2285,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f350,f2283]) ).

fof(f2283,plain,
    ( spl0_212
  <=> ! [X2,X17,X3] : c_Set_Oimage(c_snd(X3,X2),X17,tc_prod(X3,X2),X2) = c_Relation_ORange(X17,X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f350,axiom,
    ! [X2,X3,X17] : c_Set_Oimage(c_snd(X3,X2),X17,tc_prod(X3,X2),X2) = c_Relation_ORange(X17,X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).

fof(f2278,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f345,f2276]) ).

fof(f2276,plain,
    ( spl0_211
  <=> ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X0,X2),X4,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f345,axiom,
    ! [X2,X0,X4] : c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X0,X2),X4,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).

fof(f2274,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f319,f2272]) ).

fof(f2272,plain,
    ( spl0_210
  <=> ! [X25,X2,X26] :
        ( X25 = X26
        | ~ hBOOL(c_in(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f319,axiom,
    ! [X2,X26,X25] :
      ( X25 = X26
      | ~ hBOOL(c_in(X26,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

fof(f2270,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f291,f2268]) ).

fof(f2268,plain,
    ( spl0_209
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Orderings_Opreorder(X2)
        | ~ c_lessequals(X5,X12,X2)
        | ~ c_lessequals(X12,X13,X2)
        | c_lessequals(X5,X13,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f291,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Orderings_Opreorder(X2)
      | ~ c_lessequals(X5,X12,X2)
      | ~ c_lessequals(X12,X13,X2)
      | c_lessequals(X5,X13,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f2266,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f289,f2264]) ).

fof(f2264,plain,
    ( spl0_208
  <=> ! [X6,X2,X7] :
        ( ~ c_Wellfounded_Oacyclic(X7,X2)
        | c_Wellfounded_Oacyclic(X6,X2)
        | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f289,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Wellfounded_Oacyclic(X7,X2)
      | c_Wellfounded_Oacyclic(X6,X2)
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).

fof(f2262,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f287,f2260]) ).

fof(f2260,plain,
    ( spl0_207
  <=> ! [X6,X2,X7] :
        ( ~ c_Relation_Oantisym(X7,X2)
        | c_Relation_Oantisym(X6,X2)
        | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f287,axiom,
    ! [X2,X6,X7] :
      ( ~ c_Relation_Oantisym(X7,X2)
      | c_Relation_Oantisym(X6,X2)
      | ~ c_lessequals(X6,X7,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).

fof(f2258,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f284,f2256]) ).

fof(f2256,plain,
    ( spl0_206
  <=> ! [X6,X2,X35] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(X35,X2)
        | ~ c_lessequals(X35,X6,tc_fun(tc_prod(X2,X2),tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f284,axiom,
    ! [X2,X6,X35] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(X35,X2)
      | ~ c_lessequals(X35,X6,tc_fun(tc_prod(X2,X2),tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).

fof(f2254,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f283,f2252]) ).

fof(f2252,plain,
    ( spl0_205
  <=> ! [X19,X21,X5,X2] :
        ( ~ hBOOL(hAPP(X19,X5))
        | hBOOL(hAPP(X21,X5))
        | ~ c_lessequals(X19,X21,tc_fun(X2,tc_bool)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f283,axiom,
    ! [X2,X21,X19,X5] :
      ( ~ hBOOL(hAPP(X19,X5))
      | hBOOL(hAPP(X21,X5))
      | ~ c_lessequals(X19,X21,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

fof(f2250,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f279,f2248]) ).

fof(f2248,plain,
    ( spl0_204
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Orderings_Oorder(X2)
        | ~ c_lessequals(X12,X5,X2)
        | ~ c_lessequals(X13,X12,X2)
        | c_lessequals(X13,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f279,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Orderings_Oorder(X2)
      | ~ c_lessequals(X12,X5,X2)
      | ~ c_lessequals(X13,X12,X2)
      | c_lessequals(X13,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f2246,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f260,f2244]) ).

fof(f2244,plain,
    ( spl0_203
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f260,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

fof(f2242,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f259,f2240]) ).

fof(f2240,plain,
    ( spl0_202
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f259,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

fof(f2238,plain,
    ( spl0_201
    | ~ spl0_2
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2167,f1855,f845,f2235]) ).

fof(f2235,plain,
    ( spl0_201
  <=> v_L = c_Relation_Orel__comp(v_L,c_Transitive__Closure_Ortrancl(v_L,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_201])]) ).

fof(f1855,plain,
    ( spl0_182
  <=> ! [X6,X2] :
        ( ~ c_Relation_Otrans(X6,X2)
        | c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f2167,plain,
    ( v_L = c_Relation_Orel__comp(v_L,c_Transitive__Closure_Ortrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_2
    | ~ spl0_182 ),
    inference(resolution,[],[f1856,f847]) ).

fof(f847,plain,
    ( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f845]) ).

fof(f1856,plain,
    ( ! [X2,X6] :
        ( ~ c_Relation_Otrans(X6,X2)
        | c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = X6 )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f1855]) ).

fof(f2233,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f208,f2231]) ).

fof(f2231,plain,
    ( spl0_200
  <=> ! [X19,X6,X25,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X19,X6,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f208,axiom,
    ! [X2,X6,X19,X25] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X19,X6,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).

fof(f2229,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f205,f2227]) ).

fof(f2227,plain,
    ( spl0_199
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f205,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

fof(f2225,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f204,f2223]) ).

fof(f2223,plain,
    ( spl0_198
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f204,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

fof(f2221,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f166,f2219]) ).

fof(f166,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(c_in(X5,X4,X2))
      | ~ c_lessequals(c_Set_Oinsert(X5,X0,X2),X4,tc_fun(X2,tc_bool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

fof(f2217,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f124,f2215]) ).

fof(f2215,plain,
    ( spl0_196
  <=> ! [X2,X0,X4] :
        ( c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) != X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f124,axiom,
    ! [X2,X0,X4] :
      ( c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

fof(f2213,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f123,f2211]) ).

fof(f2211,plain,
    ( spl0_195
  <=> ! [X2,X0,X4] :
        ( ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f123,axiom,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

fof(f2209,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f122,f2207]) ).

fof(f2207,plain,
    ( spl0_194
  <=> ! [X2,X0,X4] :
        ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f122,axiom,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

fof(f2205,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f109,f2203]) ).

fof(f2203,plain,
    ( spl0_193
  <=> ! [X29,X19,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X29))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X19,X6,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f109,axiom,
    ! [X2,X29,X6,X19] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X29))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X19,X6,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).

fof(f2201,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f100,f2199]) ).

fof(f2199,plain,
    ( spl0_192
  <=> ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f100,axiom,
    ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

fof(f2197,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f74,f2195]) ).

fof(f2195,plain,
    ( spl0_191
  <=> ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f74,axiom,
    ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

fof(f2193,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f73,f2191]) ).

fof(f2191,plain,
    ( spl0_190
  <=> ! [X2,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f73,axiom,
    ! [X2,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

fof(f2189,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f66,f2187]) ).

fof(f2187,plain,
    ( spl0_189
  <=> ! [X0,X12,X5,X2] :
        ( X5 = X12
        | hBOOL(hAPP(X0,X5))
        | ~ hBOOL(hAPP(c_Set_Oinsert(X12,X0,X2),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f66,axiom,
    ! [X2,X0,X5,X12] :
      ( X5 = X12
      | hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(c_Set_Oinsert(X12,X0,X2),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

fof(f2185,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f54,f2183]) ).

fof(f2183,plain,
    ( spl0_188
  <=> ! [X19,X6,X25,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(hAPP(X19,X25))
        | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X19,X6,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f54,axiom,
    ! [X2,X6,X19,X25] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(hAPP(X19,X25))
      | ~ hBOOL(hAPP(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X19,X6,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).

fof(f2181,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f38,f2179]) ).

fof(f2179,plain,
    ( spl0_187
  <=> ! [X2,X0,X4] :
        ( ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f38,axiom,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X4,X0,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

fof(f2177,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f37,f2175]) ).

fof(f2175,plain,
    ( spl0_186
  <=> ! [X2,X0,X4] :
        ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
        | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f37,axiom,
    ! [X2,X0,X4] :
      ( ~ c_lessequals(X0,X4,tc_fun(X2,tc_bool))
      | c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

fof(f2173,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f22,f2171]) ).

fof(f2171,plain,
    ( spl0_185
  <=> ! [X17,X19,X20,X2] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | hBOOL(hAPP(X19,X20))
        | ~ hBOOL(hAPP(X19,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X19,X17,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f22,axiom,
    ! [X2,X19,X17,X20] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | hBOOL(hAPP(X19,X20))
      | ~ hBOOL(hAPP(X19,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X19,X17,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).

fof(f2146,plain,
    ( ~ spl0_184
    | spl0_158
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2116,f1821,f1752,f2143]) ).

fof(f2143,plain,
    ( spl0_184
  <=> v_L = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f1752,plain,
    ( spl0_158
  <=> v_L = 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_158])]) ).

fof(f2116,plain,
    ( v_L != c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt)
    | spl0_158
    | ~ spl0_175 ),
    inference(superposition,[],[f1754,f1822]) ).

fof(f1754,plain,
    ( v_L != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | spl0_158 ),
    inference(avatar_component_clause,[],[f1752]) ).

fof(f2030,plain,
    ( spl0_183
    | ~ spl0_90
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1909,f1518,f1221,f2028]) ).

fof(f2028,plain,
    ( spl0_183
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(v_L,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1
        | hBOOL(hAPP(v_L,c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1518,plain,
    ( spl0_138
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(v_L,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1909,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(v_L,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1
        | hBOOL(hAPP(v_L,c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) )
    | ~ spl0_90
    | ~ spl0_138 ),
    inference(resolution,[],[f1519,f1222]) ).

fof(f1519,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(hAPP(v_L,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1518]) ).

fof(f1857,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f725,f1855]) ).

fof(f725,plain,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2) = X6 ),
    inference(definition_unfolding,[],[f553,f538]) ).

fof(f553,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Transitive__Closure_Otrancl(X6,X2) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

fof(f1853,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f724,f1851]) ).

fof(f1851,plain,
    ( spl0_181
  <=> ! [X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f724,plain,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2) ),
    inference(definition_unfolding,[],[f506,f538]) ).

fof(f506,axiom,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X6,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

fof(f1849,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f723,f1847]) ).

fof(f1847,plain,
    ( spl0_180
  <=> ! [X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | c_Relation_Osym(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f723,plain,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Osym(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2) ),
    inference(definition_unfolding,[],[f457,f538]) ).

fof(f457,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Osym(c_Transitive__Closure_Otrancl(X6,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

fof(f1845,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f599,f1843]) ).

fof(f599,axiom,
    ! [X2,X6,X25] : hBOOL(c_in(c_Pair(X25,X25,X2,X2),c_Transitive__Closure_Ortrancl(X6,X2),tc_prod(X2,X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).

fof(f1835,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f529,f1833]) ).

fof(f529,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X6,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X6,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).

fof(f1831,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f507,f1829]) ).

fof(f1829,plain,
    ( spl0_177
  <=> ! [X2,X17,X3] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OImage(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f507,axiom,
    ! [X2,X3,X17] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Relation_OImage(X17,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).

fof(f1827,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f486,f1825]) ).

fof(f1825,plain,
    ( spl0_176
  <=> ! [X2,X3,X10] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f486,axiom,
    ! [X2,X3,X10] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_Set_Oimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

fof(f1823,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f481,f1821]) ).

fof(f1819,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f343,f1817]) ).

fof(f1817,plain,
    ( spl0_174
  <=> ! [X6,X2] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f343,axiom,
    ! [X2,X6] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).

fof(f1815,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f342,f1813]) ).

fof(f1813,plain,
    ( spl0_173
  <=> ! [X6,X2] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f342,axiom,
    ! [X2,X6] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Oconverse(X6,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).

fof(f1811,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f274,f1809]) ).

fof(f1809,plain,
    ( spl0_172
  <=> ! [X2,X5,X25,X26] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X26,X5,X2)
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f274,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X26,X5,X2)
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

fof(f1807,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f273,f1805]) ).

fof(f1805,plain,
    ( spl0_171
  <=> ! [X5,X25,X2,X26] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X5,X25,X2)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f273,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X5,X25,X2)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

fof(f1803,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f272,f1801]) ).

fof(f1801,plain,
    ( spl0_170
  <=> ! [X5,X25,X2,X26] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X5,X26,X2)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f272,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X5,X26,X2)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

fof(f1799,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f271,f1797]) ).

fof(f1797,plain,
    ( spl0_169
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X5,X13,X2)
        | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f271,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X5,X13,X2)
      | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X13,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

fof(f1795,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f265,f1793]) ).

fof(f1793,plain,
    ( spl0_168
  <=> ! [X6,X2,X14] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X14,X6,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f265,axiom,
    ! [X2,X6,X14] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X14,X6,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).

fof(f1791,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f264,f1789]) ).

fof(f1789,plain,
    ( spl0_167
  <=> ! [X6,X2,X14] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X6,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f264,axiom,
    ! [X2,X6,X14] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X6,X14,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).

fof(f1787,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f224,f1785]) ).

fof(f1785,plain,
    ( spl0_166
  <=> ! [X0,X25,X2,X26] :
        ( ~ hBOOL(c_in(X25,X0,X2))
        | hBOOL(c_in(X25,c_Set_Oinsert(X26,X0,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f224,axiom,
    ! [X2,X0,X26,X25] :
      ( ~ hBOOL(c_in(X25,X0,X2))
      | hBOOL(c_in(X25,c_Set_Oinsert(X26,X0,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

fof(f1783,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f213,f1781]) ).

fof(f1781,plain,
    ( spl0_165
  <=> ! [X4,X0,X5,X2] :
        ( hBOOL(hAPP(X0,X5))
        | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f213,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(hAPP(X0,X5))
      | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

fof(f1779,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f212,f1777]) ).

fof(f1777,plain,
    ( spl0_164
  <=> ! [X4,X5,X2,X0] :
        ( hBOOL(hAPP(X4,X5))
        | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f212,axiom,
    ! [X2,X0,X4,X5] :
      ( hBOOL(hAPP(X4,X5))
      | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

fof(f1775,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f197,f1773]) ).

fof(f1771,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f193,f1769]) ).

fof(f1769,plain,
    ( spl0_162
  <=> ! [X13,X12,X5,X2] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X5,X12,X2)
        | ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f193,axiom,
    ! [X2,X5,X12,X13] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X5,X12,X2)
      | ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

fof(f1767,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f192,f1765]) ).

fof(f1765,plain,
    ( spl0_161
  <=> ! [X2,X5,X25,X26] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X26,X5,X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f192,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X26,X5,X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

fof(f1763,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f191,f1761]) ).

fof(f1761,plain,
    ( spl0_160
  <=> ! [X5,X25,X2,X26] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X25,X5,X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f191,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X25,X5,X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

fof(f1759,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f190,f1757]) ).

fof(f1757,plain,
    ( spl0_159
  <=> ! [X5,X25,X2,X26] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X5,X26,X2)
        | ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f190,axiom,
    ! [X2,X26,X5,X25] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X5,X26,X2)
      | ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

fof(f1755,plain,
    ( ~ spl0_158
    | ~ spl0_71
    | ~ spl0_139 ),
    inference(avatar_split_clause,[],[f1686,f1540,f1145,f1752]) ).

fof(f1145,plain,
    ( spl0_71
  <=> ! [X2,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X25,X0,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f1686,plain,
    ( v_L != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
    | ~ spl0_71
    | ~ spl0_139 ),
    inference(superposition,[],[f1146,f1542]) ).

fof(f1146,plain,
    ( ! [X2,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X25,X0,X2)
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f1145]) ).

fof(f1750,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f180,f1748]) ).

fof(f1748,plain,
    ( spl0_157
  <=> ! [X2,X0,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = X4
        | c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f180,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = X4
      | c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

fof(f1746,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f179,f1744]) ).

fof(f1744,plain,
    ( spl0_156
  <=> ! [X2,X0,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = X0
        | c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f179,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = X0
      | c_Orderings_Obot__class_Obot(X2) != c_Lattices_Oupper__semilattice__class_Osup(X0,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

fof(f1742,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f153,f1740]) ).

fof(f1738,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f115,f1736]) ).

fof(f1736,plain,
    ( spl0_154
  <=> ! [X2,X5,X12] :
        ( ~ class_Orderings_Oorder(X2)
        | X5 = X12
        | ~ c_lessequals(X5,X12,X2)
        | ~ c_lessequals(X12,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f115,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Orderings_Oorder(X2)
      | X5 = X12
      | ~ c_lessequals(X5,X12,X2)
      | ~ c_lessequals(X12,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

fof(f1734,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f87,f1732]) ).

fof(f1732,plain,
    ( spl0_153
  <=> ! [X4,X0,X5,X2] :
        ( ~ hBOOL(hAPP(X0,X5))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f87,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

fof(f1730,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f86,f1728]) ).

fof(f1728,plain,
    ( spl0_152
  <=> ! [X4,X5,X2,X0] :
        ( ~ hBOOL(hAPP(X4,X5))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f86,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ hBOOL(hAPP(X4,X5))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

fof(f1598,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f530,f1596]) ).

fof(f1596,plain,
    ( spl0_151
  <=> ! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f530,axiom,
    ! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).

fof(f1594,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f391,f1592]) ).

fof(f1592,plain,
    ( spl0_150
  <=> ! [X6,X2] :
        ( c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f391,axiom,
    ! [X2,X6] :
      ( c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

fof(f1590,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f390,f1588]) ).

fof(f1588,plain,
    ( spl0_149
  <=> ! [X6,X2] :
        ( c_Wellfounded_Owf(X6,X2)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f390,axiom,
    ! [X2,X6] :
      ( c_Wellfounded_Owf(X6,X2)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X6,X2),c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

fof(f1586,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f121,f1584]) ).

fof(f1584,plain,
    ( spl0_148
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X5,X12,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f121,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X5,X12,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

fof(f1582,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f120,f1580]) ).

fof(f1580,plain,
    ( spl0_147
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X5,X12,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) != X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f120,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X5,X12,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) != X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

fof(f1578,plain,
    ( spl0_146
    | ~ spl0_15
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1524,f1432,f909,f1575]) ).

fof(f1524,plain,
    ( v_L = c_Set_Oinsert(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_15
    | ~ spl0_124 ),
    inference(resolution,[],[f1433,f911]) ).

fof(f1573,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f119,f1571]) ).

fof(f1571,plain,
    ( spl0_145
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X12,X5,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f119,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X12,X5,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

fof(f1569,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f65,f1567]) ).

fof(f1567,plain,
    ( spl0_144
  <=> ! [X5,X2,X0] : c_Set_Oinsert(X5,X0,X2) = c_Set_Oinsert(X5,c_Set_Oinsert(X5,X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f65,axiom,
    ! [X2,X0,X5] : c_Set_Oinsert(X5,X0,X2) = c_Set_Oinsert(X5,c_Set_Oinsert(X5,X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f1565,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f41,f1563]) ).

fof(f1563,plain,
    ( spl0_143
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X12,X5,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f41,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X12,X5,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

fof(f1561,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f40,f1559]) ).

fof(f1559,plain,
    ( spl0_142
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X5,X12,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) != X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f40,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X5,X12,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

fof(f1557,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f39,f1555]) ).

fof(f1555,plain,
    ( spl0_141
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X5,X12,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f39,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X5,X12,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

fof(f1553,plain,
    ( spl0_140
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1483,f1480,f1551]) ).

fof(f1551,plain,
    ( spl0_140
  <=> ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1480,plain,
    ( spl0_136
  <=> ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1483,plain,
    ( ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2,X2)
    | ~ spl0_136 ),
    inference(forward_demodulation,[],[f1481,f481]) ).

fof(f1481,plain,
    ( ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2)
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1480]) ).

fof(f1543,plain,
    ( spl0_139
    | ~ spl0_14
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1523,f1432,f904,f1540]) ).

fof(f1523,plain,
    ( v_L = c_Set_Oinsert(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
    | ~ spl0_14
    | ~ spl0_124 ),
    inference(resolution,[],[f1433,f906]) ).

fof(f1520,plain,
    ( spl0_138
    | ~ spl0_37
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f1278,f1221,f998,f1518]) ).

fof(f1278,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(v_L,c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X1,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X0 = X1 )
    | ~ spl0_37
    | ~ spl0_90 ),
    inference(resolution,[],[f1222,f999]) ).

fof(f1487,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f687,f1485]) ).

fof(f1485,plain,
    ( spl0_137
  <=> ! [X2,X0] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X2),X2,X2),X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f687,plain,
    ! [X2,X0] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X2),X2,X2),X2,X2) = X0,
    inference(definition_unfolding,[],[f488,f514]) ).

fof(f488,axiom,
    ! [X2,X0] : c_Relation_ODomain(c_Relation_OId__on(X0,X2),X2,X2) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

fof(f1482,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f685,f1480]) ).

fof(f685,plain,
    ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),
    inference(definition_unfolding,[],[f487,f500]) ).

fof(f487,axiom,
    ! [X2] : c_Relation_Osingle__valued(c_Relation_OId(X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

fof(f1478,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f542,f1476]) ).

fof(f1476,plain,
    ( spl0_135
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Ototal__on(X0,X6,X2)
        | c_Relation_Ototal__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f542,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Ototal__on(X0,X6,X2)
      | c_Relation_Ototal__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

fof(f1474,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f541,f1472]) ).

fof(f1472,plain,
    ( spl0_134
  <=> ! [X6,X2,X0] :
        ( c_Relation_Ototal__on(X0,X6,X2)
        | ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f541,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Ototal__on(X0,X6,X2)
      | ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

fof(f1470,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f524,f1468]) ).

fof(f1468,plain,
    ( spl0_133
  <=> ! [X2,X5,X12,X3] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_fun(X3,tc_bool))),X5),X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f524,axiom,
    ! [X2,X3,X5,X12] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_fun(X3,tc_bool))),X5),X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot2E_0) ).

fof(f1466,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f498,f1464]) ).

fof(f498,axiom,
    ! [X3] :
      ( ~ class_Orderings_Obot(X3)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X3)),v_x) = c_Orderings_Obot__class_Obot(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f1462,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f484,f1460]) ).

fof(f1460,plain,
    ( spl0_131
  <=> ! [X2,X17] :
        ( c_Wellfounded_Owf(X17,X2)
        | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X17,X17,X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f484,axiom,
    ! [X2,X17] :
      ( c_Wellfounded_Owf(X17,X2)
      | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X17,X17,X2,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

fof(f1458,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f483,f1456]) ).

fof(f1456,plain,
    ( spl0_130
  <=> ! [X2,X17] :
        ( ~ c_Wellfounded_Owf(X17,X2)
        | c_Wellfounded_Owf(c_Relation_Orel__comp(X17,X17,X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f483,axiom,
    ! [X2,X17] :
      ( ~ c_Wellfounded_Owf(X17,X2)
      | c_Wellfounded_Owf(c_Relation_Orel__comp(X17,X17,X2,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

fof(f1454,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f480,f1452]) ).

fof(f1452,plain,
    ( spl0_129
  <=> ! [X6,X2,X0] :
        ( ~ c_Relation_Orefl__on(X0,X6,X2)
        | c_Relation_Orefl__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f480,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Relation_Orefl__on(X0,X6,X2)
      | c_Relation_Orefl__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

fof(f1450,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f479,f1448]) ).

fof(f1448,plain,
    ( spl0_128
  <=> ! [X6,X2,X0] :
        ( c_Relation_Orefl__on(X0,X6,X2)
        | ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f479,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Orefl__on(X0,X6,X2)
      | ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

fof(f1446,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f475,f1444]) ).

fof(f1444,plain,
    ( spl0_127
  <=> ! [X3,X10,X16,X2] : c_split(c_curry(X10,X2,X3,X16),X2,X3,X16) = X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f475,axiom,
    ! [X2,X3,X10,X16] : c_split(c_curry(X10,X2,X3,X16),X2,X3,X16) = X10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__curry_0) ).

fof(f1442,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f471,f1440]) ).

fof(f1440,plain,
    ( spl0_126
  <=> ! [X3,X10,X16,X2] : c_curry(c_split(X10,X2,X3,X16),X2,X3,X16) = X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f471,axiom,
    ! [X2,X3,X10,X16] : c_curry(c_split(X10,X2,X3,X16),X2,X3,X16) = X10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_curry__split_0) ).

fof(f1438,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f246,f1436]) ).

fof(f1436,plain,
    ( spl0_125
  <=> ! [X3,X12,X5,X2] : hAPP(c_snd(X3,X2),c_Pair(X5,X12,X3,X2)) = X12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f246,axiom,
    ! [X2,X3,X5,X12] : hAPP(c_snd(X3,X2),c_Pair(X5,X12,X3,X2)) = X12,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).

fof(f1434,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f244,f1432]) ).

fof(f244,axiom,
    ! [X2,X0,X25] :
      ( ~ hBOOL(c_in(X25,X0,X2))
      | c_Set_Oinsert(X25,X0,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f1430,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f199,f1428]) ).

fof(f1428,plain,
    ( spl0_123
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f199,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f1426,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f198,f1424]) ).

fof(f1424,plain,
    ( spl0_122
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f198,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2) = c_Lattices_Oupper__semilattice__class_Osup(X12,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f1422,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f168,f1420]) ).

fof(f1420,plain,
    ( spl0_121
  <=> ! [X2,X5,X0,X12] :
        ( ~ hBOOL(hAPP(X0,X5))
        | hBOOL(hAPP(c_Set_Oinsert(X12,X0,X2),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f168,axiom,
    ! [X2,X0,X5,X12] :
      ( ~ hBOOL(hAPP(X0,X5))
      | hBOOL(hAPP(c_Set_Oinsert(X12,X0,X2),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f1418,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f160,f1416]) ).

fof(f1416,plain,
    ( spl0_120
  <=> ! [X2,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f160,axiom,
    ! [X2,X0,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X4,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f1414,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f155,f1412]) ).

fof(f1412,plain,
    ( spl0_119
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f155,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f1410,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f154,f1408]) ).

fof(f1408,plain,
    ( spl0_118
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f154,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2) = c_Lattices_Olower__semilattice__class_Oinf(X12,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f1406,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f148,f1404]) ).

fof(f1404,plain,
    ( spl0_117
  <=> ! [X2,X0,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f148,axiom,
    ! [X2,X0,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

fof(f1402,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f147,f1400]) ).

fof(f1400,plain,
    ( spl0_116
  <=> ! [X2,X0,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f147,axiom,
    ! [X2,X0,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X4,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

fof(f1398,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f117,f1396]) ).

fof(f1396,plain,
    ( spl0_115
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f117,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f1394,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f108,f1392]) ).

fof(f1392,plain,
    ( spl0_114
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f108,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f1390,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f99,f1388]) ).

fof(f1388,plain,
    ( spl0_113
  <=> ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f99,axiom,
    ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

fof(f1386,plain,
    ( spl0_112
    | ~ spl0_15
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f1277,f1221,f909,f1383]) ).

fof(f1383,plain,
    ( spl0_112
  <=> hBOOL(hAPP(v_L,c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1277,plain,
    ( hBOOL(hAPP(v_L,c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_15
    | ~ spl0_90 ),
    inference(resolution,[],[f1222,f911]) ).

fof(f1381,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f98,f1379]) ).

fof(f98,axiom,
    ! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4,tc_fun(X2,tc_bool)) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

fof(f1377,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f82,f1375]) ).

fof(f82,axiom,
    ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f1373,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f81,f1371]) ).

fof(f1371,plain,
    ( spl0_109
  <=> ! [X2,X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f81,axiom,
    ! [X2,X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f1369,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f44,f1367]) ).

fof(f44,axiom,
    ! [X2,X0,X4] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

fof(f1365,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f43,f1363]) ).

fof(f43,axiom,
    ! [X2,X0,X4] : c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X0,X4,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

fof(f1358,plain,
    ( spl0_106
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f1323,f1320,f1356]) ).

fof(f1356,plain,
    ( spl0_106
  <=> ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1320,plain,
    ( spl0_102
  <=> ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1323,plain,
    ( ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2)
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f1321,f481]) ).

fof(f1321,plain,
    ( ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f1320]) ).

fof(f1354,plain,
    ( spl0_105
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f1318,f1315,f1352]) ).

fof(f1352,plain,
    ( spl0_105
  <=> ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f1315,plain,
    ( spl0_101
  <=> ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1318,plain,
    ( ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2)
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f1316,f481]) ).

fof(f1316,plain,
    ( ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f1315]) ).

fof(f1350,plain,
    ( spl0_104
    | ~ spl0_14
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f1276,f1221,f904,f1347]) ).

fof(f1347,plain,
    ( spl0_104
  <=> hBOOL(hAPP(v_L,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f1276,plain,
    ( hBOOL(hAPP(v_L,c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_14
    | ~ spl0_90 ),
    inference(resolution,[],[f1222,f906]) ).

fof(f1327,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f684,f1325]) ).

fof(f1325,plain,
    ( spl0_103
  <=> ! [X6,X2] : c_Relation_Otrans(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f684,plain,
    ! [X2,X6] : c_Relation_Otrans(c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X2),X2,X2,X2),X2),
    inference(definition_unfolding,[],[f551,f538]) ).

fof(f551,axiom,
    ! [X2,X6] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X6,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

fof(f1322,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f682,f1320]) ).

fof(f682,plain,
    ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2),
    inference(definition_unfolding,[],[f470,f500]) ).

fof(f470,axiom,
    ! [X2] : c_Relation_Osym(c_Relation_OId(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

fof(f1317,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f681,f1315]) ).

fof(f681,plain,
    ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2),
    inference(definition_unfolding,[],[f513,f500]) ).

fof(f513,axiom,
    ! [X2] : c_Relation_Oantisym(c_Relation_OId(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

fof(f1313,plain,
    ( spl0_100
    | ~ spl0_13
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f1274,f1217,f900,f1311]) ).

fof(f1311,plain,
    ( spl0_100
  <=> ! [X0] : ~ hBOOL(hAPP(v_L,c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1274,plain,
    ( ! [X0] : ~ hBOOL(hAPP(v_L,c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_13
    | ~ spl0_89 ),
    inference(resolution,[],[f1218,f901]) ).

fof(f1309,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f511,f1307]) ).

fof(f1307,plain,
    ( spl0_99
  <=> ! [X2,X0] : c_Relation_OId__on(X0,X2) = c_Relation_Oconverse(c_Relation_OId__on(X0,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f511,axiom,
    ! [X2,X0] : c_Relation_OId__on(X0,X2) = c_Relation_Oconverse(c_Relation_OId__on(X0,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

fof(f1305,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f499,f1303]) ).

fof(f1303,plain,
    ( spl0_98
  <=> ! [X3,X10,X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | c_Relation_Osym(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f499,axiom,
    ! [X2,X3,X10,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Osym(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

fof(f1301,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f496,f1299]) ).

fof(f1299,plain,
    ( spl0_97
  <=> ! [X3,X10,X6,X2] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | c_Wellfounded_Owf(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f496,axiom,
    ! [X2,X3,X10,X6] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Owf(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

fof(f1297,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f454,f1295]) ).

fof(f1295,plain,
    ( spl0_96
  <=> ! [X6,X2,X5] :
        ( ~ c_Wellfounded_Owf(X6,X2)
        | hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f454,axiom,
    ! [X2,X6,X5] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | hBOOL(c_in(X5,c_Wellfounded_Oacc(X6,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

fof(f1293,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f447,f1291]) ).

fof(f1291,plain,
    ( spl0_95
  <=> ! [X3,X10,X6,X2] :
        ( ~ c_Relation_Otrans(X6,X2)
        | c_Relation_Otrans(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f447,axiom,
    ! [X2,X3,X10,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_Relation_Oinv__image(X6,X10,X2,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

fof(f1289,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f72,f1287]) ).

fof(f72,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f1285,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f71,f1283]) ).

fof(f71,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f1269,plain,
    ( spl0_92
    | ~ spl0_6
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f1232,f1129,f865,f1267]) ).

fof(f1267,plain,
    ( spl0_92
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f1129,plain,
    ( spl0_67
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(X2),X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f1232,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
    | ~ spl0_6
    | ~ spl0_67 ),
    inference(resolution,[],[f1130,f867]) ).

fof(f1130,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(X2),X2) = X5 )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1129]) ).

fof(f1231,plain,
    ( ~ spl0_3
    | spl0_91
    | ~ spl0_61
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f1225,f1113,f1102,f1229,f850]) ).

fof(f850,plain,
    ( spl0_3
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1229,plain,
    ( spl0_91
  <=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1102,plain,
    ( spl0_61
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f1113,plain,
    ( spl0_63
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1225,plain,
    ( ! [X0] :
        ( c_lessequals(X0,X0,tc_bool)
        | ~ class_Lattices_Oupper__semilattice(tc_bool) )
    | ~ spl0_61
    | ~ spl0_63 ),
    inference(superposition,[],[f1114,f1103]) ).

fof(f1103,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1102]) ).

fof(f1114,plain,
    ( ! [X2,X5,X12] :
        ( c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2)
        | ~ class_Lattices_Oupper__semilattice(X2) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1113]) ).

fof(f1223,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f649,f1221]) ).

fof(f649,axiom,
    ! [X2,X18,X5] :
      ( hBOOL(hAPP(X18,X5))
      | ~ hBOOL(c_in(X5,X18,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1219,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f648,f1217]) ).

fof(f648,axiom,
    ! [X2,X18,X5] :
      ( ~ hBOOL(hAPP(X18,X5))
      | hBOOL(c_in(X5,X18,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1215,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f549,f1213]) ).

fof(f1213,plain,
    ( spl0_88
  <=> ! [X6,X2] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f549,axiom,
    ! [X2,X6] : c_Transitive__Closure_Ortrancl(X6,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

fof(f1211,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f522,f1209]) ).

fof(f1209,plain,
    ( spl0_87
  <=> ! [X6,X2] :
        ( ~ c_Relation_Oantisym(X6,X2)
        | c_Relation_Oantisym(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f522,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Oantisym(X6,X2)
      | c_Relation_Oantisym(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

fof(f1207,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f521,f1205]) ).

fof(f1205,plain,
    ( spl0_86
  <=> ! [X6,X2] :
        ( c_Relation_Oantisym(X6,X2)
        | ~ c_Relation_Oantisym(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f521,axiom,
    ! [X2,X6] :
      ( c_Relation_Oantisym(X6,X2)
      | ~ c_Relation_Oantisym(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

fof(f1203,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f518,f1201]) ).

fof(f1201,plain,
    ( spl0_85
  <=> ! [X6,X2,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X6,X2,X3),X3,X2) = X6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f518,axiom,
    ! [X2,X3,X6] : c_Relation_Oconverse(c_Relation_Oconverse(X6,X2,X3),X3,X2) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

fof(f1199,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f490,f1197]) ).

fof(f1197,plain,
    ( spl0_84
  <=> ! [X6,X2] :
        ( c_Relation_Osym(X6,X2)
        | c_Relation_Oconverse(X6,X2,X2) != X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f490,axiom,
    ! [X2,X6] :
      ( c_Relation_Osym(X6,X2)
      | c_Relation_Oconverse(X6,X2,X2) != X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

fof(f1195,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f489,f1193]) ).

fof(f1193,plain,
    ( spl0_83
  <=> ! [X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | c_Relation_Oconverse(X6,X2,X2) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f489,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Oconverse(X6,X2,X2) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

fof(f1191,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f463,f1189]) ).

fof(f1189,plain,
    ( spl0_82
  <=> ! [X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | c_Relation_Osym(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f463,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Osym(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

fof(f1187,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f462,f1185]) ).

fof(f1185,plain,
    ( spl0_81
  <=> ! [X6,X2] :
        ( c_Relation_Osym(X6,X2)
        | ~ c_Relation_Osym(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f462,axiom,
    ! [X2,X6] :
      ( c_Relation_Osym(X6,X2)
      | ~ c_Relation_Osym(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

fof(f1183,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f449,f1181]) ).

fof(f1181,plain,
    ( spl0_80
  <=> ! [X6,X2] :
        ( c_Relation_Otrans(X6,X2)
        | ~ c_Relation_Otrans(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f449,axiom,
    ! [X2,X6] :
      ( c_Relation_Otrans(X6,X2)
      | ~ c_Relation_Otrans(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

fof(f1179,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f448,f1177]) ).

fof(f1177,plain,
    ( spl0_79
  <=> ! [X6,X2] :
        ( ~ c_Relation_Otrans(X6,X2)
        | c_Relation_Otrans(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f448,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Otrans(X6,X2)
      | c_Relation_Otrans(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

fof(f1175,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f152,f1173]) ).

fof(f1173,plain,
    ( spl0_78
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f152,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1171,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f151,f1169]) ).

fof(f1169,plain,
    ( spl0_77
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f151,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1167,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f146,f1165]) ).

fof(f1165,plain,
    ( spl0_76
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f146,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f1163,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f145,f1161]) ).

fof(f1161,plain,
    ( spl0_75
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X12,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f145,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X12,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f1159,plain,
    ( spl0_74
    | ~ spl0_4
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f1105,f1062,f855,f1157]) ).

fof(f1157,plain,
    ( spl0_74
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f855,plain,
    ( spl0_4
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1062,plain,
    ( spl0_52
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X5,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1105,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
    | ~ spl0_4
    | ~ spl0_52 ),
    inference(resolution,[],[f1063,f857]) ).

fof(f857,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f855]) ).

fof(f1063,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X5,X2) = X5 )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1062]) ).

fof(f1155,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f141,f1153]) ).

fof(f1153,plain,
    ( spl0_73
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X12,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f141,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X12,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f1151,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f140,f1149]) ).

fof(f1149,plain,
    ( spl0_72
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f140,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X12,X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f1147,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f134,f1145]) ).

fof(f134,axiom,
    ! [X2,X0,X25] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X25,X0,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

fof(f1143,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f111,f1141]) ).

fof(f1141,plain,
    ( spl0_70
  <=> ! [X6,X2] :
        ( ~ c_Wellfounded_Oacyclic(X6,X2)
        | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f111,axiom,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Oacyclic(X6,X2)
      | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

fof(f1139,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f110,f1137]) ).

fof(f1137,plain,
    ( spl0_69
  <=> ! [X6,X2] :
        ( c_Wellfounded_Oacyclic(X6,X2)
        | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X6,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f110,axiom,
    ! [X2,X6] :
      ( c_Wellfounded_Oacyclic(X6,X2)
      | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X6,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

fof(f1135,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f97,f1133]) ).

fof(f97,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X5,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1131,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f96,f1129]) ).

fof(f96,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(X2),X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1127,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f75,f1125]) ).

fof(f75,axiom,
    ! [X2,X4,X25] : c_lessequals(X4,c_Set_Oinsert(X25,X4,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1123,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f58,f1121]) ).

fof(f1121,plain,
    ( spl0_65
  <=> ! [X2,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f58,axiom,
    ! [X2,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1119,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f48,f1117]) ).

fof(f1117,plain,
    ( spl0_64
  <=> ! [X2,X5,X12] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f48,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1115,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f47,f1113]) ).

fof(f47,axiom,
    ! [X2,X5,X12] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X5,X12,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1110,plain,
    ( spl0_62
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f1081,f1078,f1108]) ).

fof(f1078,plain,
    ( spl0_56
  <=> ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1081,plain,
    ( ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
    | ~ spl0_56 ),
    inference(forward_demodulation,[],[f1079,f481]) ).

fof(f1079,plain,
    ( ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f1078]) ).

fof(f1104,plain,
    ( spl0_61
    | ~ spl0_3
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f1099,f1046,f850,f1102]) ).

fof(f1046,plain,
    ( spl0_48
  <=> ! [X2,X5] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X5,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1099,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_3
    | ~ spl0_48 ),
    inference(resolution,[],[f1047,f852]) ).

fof(f852,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f850]) ).

fof(f1047,plain,
    ( ! [X2,X5] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X5,X2) = X5 )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f1046]) ).

fof(f1097,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f527,f1095]) ).

fof(f1095,plain,
    ( spl0_60
  <=> ! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f527,axiom,
    ! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).

fof(f1093,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f526,f1091]) ).

fof(f1091,plain,
    ( spl0_59
  <=> ! [X6,X2,X0] :
        ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
        | c_Relation_Orefl__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f526,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Equiv__Relations_Oequiv(X0,X6,X2)
      | c_Relation_Orefl__on(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

fof(f1089,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f516,f1087]) ).

fof(f1087,plain,
    ( spl0_58
  <=> ! [X2,X0] : c_Relation_ORange(c_Relation_OId__on(X0,X2),X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f516,axiom,
    ! [X2,X0] : c_Relation_ORange(c_Relation_OId__on(X0,X2),X2,X2) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

fof(f1085,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f482,f1083]) ).

fof(f1083,plain,
    ( spl0_57
  <=> ! [X6,X2] :
        ( ~ c_Relation_Osym(X6,X2)
        | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X6,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f482,axiom,
    ! [X2,X6] :
      ( ~ c_Relation_Osym(X6,X2)
      | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X6,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

fof(f1080,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f476,f1078]) ).

fof(f476,axiom,
    ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).

fof(f1076,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f450,f1074]) ).

fof(f450,axiom,
    ! [X2,X25] : ~ hBOOL(c_in(X25,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

fof(f1072,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f340,f1070]) ).

fof(f1070,plain,
    ( spl0_54
  <=> ! [X6,X2] :
        ( ~ c_Wellfounded_Oacyclic(X6,X2)
        | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f340,axiom,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Oacyclic(X6,X2)
      | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

fof(f1068,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f268,f1066]) ).

fof(f1066,plain,
    ( spl0_53
  <=> ! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X2,tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f268,axiom,
    ! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X2,tc_bool)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1064,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f267,f1062]) ).

fof(f267,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X5,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1060,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f238,f1058]) ).

fof(f238,axiom,
    ! [X2,X4,X5] : hBOOL(c_in(X5,c_Set_Oinsert(X5,X4,X2),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

fof(f1056,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f176,f1054]) ).

fof(f1054,plain,
    ( spl0_50
  <=> ! [X6,X2,X0] :
        ( ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2)
        | c_Relation_Ototal__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f176,axiom,
    ! [X2,X0,X6] :
      ( ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2)
      | c_Relation_Ototal__on(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

fof(f1052,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f24,f1050]) ).

fof(f1050,plain,
    ( spl0_49
  <=> ! [X2,X19,X3,X21] : hAPP(c_COMBK(X19,X2,X3),X21) = X19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f24,axiom,
    ! [X2,X21,X3,X19] : hAPP(c_COMBK(X19,X2,X3),X21) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1048,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f18,f1046]) ).

fof(f18,axiom,
    ! [X2,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X5,X2) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1044,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f17,f1042]) ).

fof(f1042,plain,
    ( spl0_47
  <=> ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X2,tc_bool)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f17,axiom,
    ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X2,tc_bool)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f1039,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f677,f1037]) ).

fof(f1037,plain,
    ( spl0_46
  <=> ! [X54,X2,X55] :
        ( X54 = X55
        | ~ c_fequal(X54,X55,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f677,axiom,
    ! [X2,X54,X55] :
      ( X54 = X55
      | ~ c_fequal(X54,X55,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1035,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f533,f1033]) ).

fof(f1033,plain,
    ( spl0_45
  <=> ! [X6,X2,X0] :
        ( c_Relation_Osym(X6,X2)
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f533,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Osym(X6,X2)
      | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

fof(f1031,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f532,f1029]) ).

fof(f1029,plain,
    ( spl0_44
  <=> ! [X6,X2] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f532,axiom,
    ! [X2,X6] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

fof(f1027,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f523,f1025]) ).

fof(f1025,plain,
    ( spl0_43
  <=> ! [X2,X5] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f523,axiom,
    ! [X2,X5] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f1023,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f445,f1021]) ).

fof(f1021,plain,
    ( spl0_42
  <=> ! [X6,X2,X0] :
        ( c_Relation_Otrans(X6,X2)
        | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f445,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Otrans(X6,X2)
      | ~ c_Equiv__Relations_Oequiv(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

fof(f1019,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f312,f1017]) ).

fof(f1017,plain,
    ( spl0_41
  <=> ! [X6,X2,X0] :
        ( c_Relation_Oirrefl(X6,X2)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f312,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Oirrefl(X6,X2)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

fof(f1015,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f256,f1013]) ).

fof(f1013,plain,
    ( spl0_40
  <=> ! [X2,X5,X0] : hBOOL(hAPP(c_Set_Oinsert(X5,X0,X2),X5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f256,axiom,
    ! [X2,X0,X5] : hBOOL(hAPP(c_Set_Oinsert(X5,X0,X2),X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f1011,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f248,f1009]) ).

fof(f1009,plain,
    ( spl0_39
  <=> ! [X6,X2,X0] :
        ( c_Relation_Otrans(X6,X2)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f248,axiom,
    ! [X2,X0,X6] :
      ( c_Relation_Otrans(X6,X2)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X0,X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

fof(f1007,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f60,f1005]) ).

fof(f1005,plain,
    ( spl0_38
  <=> ! [X2,X5] :
        ( ~ class_Orderings_Obot(X2)
        | c_lessequals(c_Orderings_Obot__class_Obot(X2),X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f60,axiom,
    ! [X2,X5] :
      ( ~ class_Orderings_Obot(X2)
      | c_lessequals(c_Orderings_Obot__class_Obot(X2),X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f1000,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f655,f998]) ).

fof(f655,axiom,
    ! [X5,X12] :
      ( X5 = X12
      | hBOOL(c_in(c_Pair(X5,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X12,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f996,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f665,f994]) ).

fof(f994,plain,
    ( spl0_36
  <=> ! [X52,X53] :
        ( ~ class_HOL_Oord(X53)
        | class_HOL_Oord(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f665,axiom,
    ! [X52,X53] :
      ( ~ class_HOL_Oord(X53)
      | class_HOL_Oord(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f992,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f664,f990]) ).

fof(f990,plain,
    ( spl0_35
  <=> ! [X52,X53] :
        ( ~ class_HOL_Ominus(X53)
        | class_HOL_Ominus(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f664,axiom,
    ! [X52,X53] :
      ( ~ class_HOL_Ominus(X53)
      | class_HOL_Ominus(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f988,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f663,f986]) ).

fof(f986,plain,
    ( spl0_34
  <=> ! [X52,X53] :
        ( ~ class_Orderings_Obot(X53)
        | class_Orderings_Obot(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f663,axiom,
    ! [X52,X53] :
      ( ~ class_Orderings_Obot(X53)
      | class_Orderings_Obot(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f984,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f662,f982]) ).

fof(f982,plain,
    ( spl0_33
  <=> ! [X52,X53] :
        ( ~ class_Orderings_Oorder(X53)
        | class_Orderings_Oorder(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f662,axiom,
    ! [X52,X53] :
      ( ~ class_Orderings_Oorder(X53)
      | class_Orderings_Oorder(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f980,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f661,f978]) ).

fof(f978,plain,
    ( spl0_32
  <=> ! [X52,X53] :
        ( ~ class_Lattices_Olattice(X53)
        | class_Lattices_Olattice(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f661,axiom,
    ! [X52,X53] :
      ( ~ class_Lattices_Olattice(X53)
      | class_Lattices_Olattice(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f976,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f660,f974]) ).

fof(f974,plain,
    ( spl0_31
  <=> ! [X52,X53] :
        ( ~ class_Orderings_Opreorder(X53)
        | class_Orderings_Opreorder(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f660,axiom,
    ! [X52,X53] :
      ( ~ class_Orderings_Opreorder(X53)
      | class_Orderings_Opreorder(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f972,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f659,f970]) ).

fof(f970,plain,
    ( spl0_30
  <=> ! [X52,X53] :
        ( ~ class_Lattices_Obounded__lattice(X53)
        | class_Lattices_Obounded__lattice(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f659,axiom,
    ! [X52,X53] :
      ( ~ class_Lattices_Obounded__lattice(X53)
      | class_Lattices_Obounded__lattice(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f968,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f658,f966]) ).

fof(f966,plain,
    ( spl0_29
  <=> ! [X52,X53] :
        ( ~ class_Lattices_Odistrib__lattice(X53)
        | class_Lattices_Odistrib__lattice(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f658,axiom,
    ! [X52,X53] :
      ( ~ class_Lattices_Odistrib__lattice(X53)
      | class_Lattices_Odistrib__lattice(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f964,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f657,f962]) ).

fof(f962,plain,
    ( spl0_28
  <=> ! [X52,X53] :
        ( ~ class_Lattices_Olattice(X53)
        | class_Lattices_Olower__semilattice(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f657,axiom,
    ! [X52,X53] :
      ( ~ class_Lattices_Olattice(X53)
      | class_Lattices_Olower__semilattice(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f960,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f656,f958]) ).

fof(f958,plain,
    ( spl0_27
  <=> ! [X52,X53] :
        ( ~ class_Lattices_Olattice(X53)
        | class_Lattices_Oupper__semilattice(tc_fun(X52,X53)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f656,axiom,
    ! [X52,X53] :
      ( ~ class_Lattices_Olattice(X53)
      | class_Lattices_Oupper__semilattice(tc_fun(X52,X53)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f956,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f495,f954]) ).

fof(f954,plain,
    ( spl0_26
  <=> ! [X2,X0] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f495,axiom,
    ! [X2,X0] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

fof(f952,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f455,f950]) ).

fof(f950,plain,
    ( spl0_25
  <=> ! [X2,X0] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f455,axiom,
    ! [X2,X0] : c_Relation_Osingle__valued(c_Relation_OId__on(X0,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

fof(f948,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f286,f946]) ).

fof(f946,plain,
    ( spl0_24
  <=> ! [X2,X5] :
        ( ~ class_Orderings_Opreorder(X2)
        | c_lessequals(X5,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f286,axiom,
    ! [X2,X5] :
      ( ~ class_Orderings_Opreorder(X2)
      | c_lessequals(X5,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f944,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f285,f942]) ).

fof(f942,plain,
    ( spl0_23
  <=> ! [X2,X5] :
        ( ~ class_Orderings_Oorder(X2)
        | c_lessequals(X5,X5,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f285,axiom,
    ! [X2,X5] :
      ( ~ class_Orderings_Oorder(X2)
      | c_lessequals(X5,X5,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f940,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f280,f938]) ).

fof(f280,axiom,
    ! [X2,X5] : c_lessequals(X5,X5,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

fof(f936,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f156,f934]) ).

fof(f156,axiom,
    ! [X2,X6] :
      ( ~ c_Wellfounded_Owf(X6,X2)
      | c_Wellfounded_Oacyclic(X6,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

fof(f932,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f552,f930]) ).

fof(f930,plain,
    ( spl0_20
  <=> ! [X2,X0] : c_Relation_Otrans(c_Relation_OId__on(X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f552,axiom,
    ! [X2,X0] : c_Relation_Otrans(c_Relation_OId__on(X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

fof(f928,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f550,f926]) ).

fof(f550,axiom,
    ! [X2,X6] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X6,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

fof(f924,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f494,f922]) ).

fof(f922,plain,
    ( spl0_18
  <=> ! [X2,X0] : c_Relation_Osym(c_Relation_OId__on(X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f494,axiom,
    ! [X2,X0] : c_Relation_Osym(c_Relation_OId__on(X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

fof(f920,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f474,f918]) ).

fof(f918,plain,
    ( spl0_17
  <=> ! [X2,X0] : c_Relation_Oantisym(c_Relation_OId__on(X0,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f474,axiom,
    ! [X2,X0] : c_Relation_Oantisym(c_Relation_OId__on(X0,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

fof(f916,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f676,f914]) ).

fof(f914,plain,
    ( spl0_16
  <=> ! [X2,X5] : c_fequal(X5,X5,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f676,axiom,
    ! [X2,X5] : c_fequal(X5,X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f912,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f654,f909]) ).

fof(f654,axiom,
    hBOOL(c_in(c_Pair(v_x,v_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f907,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f653,f904]) ).

fof(f653,axiom,
    hBOOL(c_in(c_Pair(v_y,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f902,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f652,f900]) ).

fof(f652,axiom,
    ! [X5] : ~ hBOOL(c_in(c_Pair(X5,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f898,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f675,f895]) ).

fof(f895,plain,
    ( spl0_12
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f675,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f893,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f674,f890]) ).

fof(f890,plain,
    ( spl0_11
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f674,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f888,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f673,f885]) ).

fof(f673,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f883,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f672,f880]) ).

fof(f880,plain,
    ( spl0_9
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f672,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f878,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f671,f875]) ).

fof(f875,plain,
    ( spl0_8
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f671,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f873,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f670,f870]) ).

fof(f870,plain,
    ( spl0_7
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f670,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f868,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f669,f865]) ).

fof(f669,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f863,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f668,f860]) ).

fof(f860,plain,
    ( spl0_5
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f668,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f858,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f667,f855]) ).

fof(f667,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f853,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f666,f850]) ).

fof(f666,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f848,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f651,f845]) ).

fof(f651,axiom,
    c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f843,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f650,f840]) ).

fof(f650,axiom,
    v_x != v_y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SCT002-1 : TPTP v8.2.0. Released v4.1.0.
% 0.08/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n028.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 00:20:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (14422)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.40  % (14424)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41  % (14425)WARNING: value z3 for option sas not known
% 0.20/0.41  % (14427)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.41  % (14423)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.41  % (14426)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.41  % (14428)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.41  % (14425)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.41  % (14429)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.56  TRYING [1]
% 0.20/0.58  TRYING [2]
% 3.94/0.97  TRYING [1]
% 4.42/1.03  TRYING [2]
% 4.42/1.06  TRYING [3]
% 7.12/1.42  % (14427)First to succeed.
% 7.12/1.44  % (14427)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14422"
% 7.12/1.45  % (14427)Refutation found. Thanks to Tanya!
% 7.12/1.45  % SZS status Unsatisfiable for theBenchmark
% 7.12/1.45  % SZS output start Proof for theBenchmark
% See solution above
% 7.62/1.46  % (14427)------------------------------
% 7.62/1.46  % (14427)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 7.62/1.46  % (14427)Termination reason: Refutation
% 7.62/1.46  
% 7.62/1.46  % (14427)Memory used [KB]: 14696
% 7.62/1.46  % (14427)Time elapsed: 1.039 s
% 7.62/1.46  % (14427)Instructions burned: 2778 (million)
% 7.62/1.46  % (14422)Success in time 1.101 s
%------------------------------------------------------------------------------