%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL839-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 07:55:26 EDT 2024

% Result   : Unsatisfiable 4.96s 1.14s
% Output   : Refutation 4.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  862
% Syntax   : Number of formulae    : 1981 ( 406 unt;   0 def)
%            Number of atoms       : 5092 ( 808 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 5777 (2666   ~;2533   |;   0   &)
%                                         ( 578 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :  605 ( 603 usr; 580 prp; 0-4 aty)
%            Number of functors    :   53 (  53 usr;  21 con; 0-5 aty)
%            Number of variables   : 3492 (3492   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14179,plain,
    $false,
    inference(avatar_sat_refutation,[],[f503,f508,f513,f518,f523,f528,f533,f538,f543,f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f602,f607,f612,f616,f621,f626,f631,f635,f639,f643,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f687,f691,f695,f699,f703,f707,f711,f715,f719,f723,f727,f731,f735,f739,f743,f747,f751,f757,f761,f765,f769,f773,f777,f781,f785,f789,f793,f797,f801,f805,f809,f813,f817,f839,f846,f850,f854,f858,f862,f866,f870,f874,f879,f896,f900,f904,f908,f912,f916,f920,f924,f928,f932,f936,f940,f945,f949,f953,f1029,f1033,f1037,f1041,f1046,f1050,f1054,f1058,f1062,f1066,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1178,f1183,f1188,f1192,f1199,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1544,f1615,f1619,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1707,f1823,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f2102,f2106,f2110,f2114,f2129,f2133,f2137,f2141,f2145,f2149,f2153,f2157,f2161,f2186,f2365,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2408,f2412,f2416,f2421,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2454,f2458,f2462,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2785,f2922,f2926,f2931,f2935,f2939,f2943,f2947,f2951,f2955,f2959,f2963,f2967,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3341,f3421,f3425,f3429,f3433,f3437,f3441,f3445,f3667,f3671,f3676,f3680,f3684,f3688,f3692,f3696,f3700,f3704,f3708,f3753,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f4260,f4264,f4268,f4272,f4276,f4280,f4287,f4291,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4630,f4637,f4651,f4655,f4659,f4663,f4667,f4950,f4954,f4958,f5062,f5076,f5080,f5084,f5090,f5140,f5144,f5154,f5163,f5167,f5181,f5185,f5194,f5198,f5202,f5206,f5210,f5299,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5370,f5374,f5378,f5382,f5468,f5527,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5615,f5619,f5992,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6072,f6164,f6420,f6542,f6546,f6550,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6587,f6595,f6604,f6608,f6612,f6616,f6620,f6624,f7027,f7081,f7085,f7089,f7093,f7097,f7101,f7105,f7115,f7119,f7159,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7554,f7869,f7873,f7877,f7881,f7885,f7889,f7893,f7897,f7901,f7905,f7909,f7913,f7917,f7921,f7925,f7929,f7933,f7937,f7941,f7945,f7949,f7953,f7958,f7962,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8026,f9283,f9287,f9291,f9295,f9299,f9303,f9307,f9311,f9315,f9320,f9324,f9328,f9332,f9336,f9340,f9344,f9348,f9352,f9356,f9360,f9364,f9368,f9372,f9376,f9380,f9705,f9903,f10073,f10077,f10081,f10085,f10089,f10093,f10097,f10101,f10105,f10109,f10113,f10117,f10121,f10125,f10129,f10133,f10137,f10141,f10145,f10149,f10153,f10157,f10161,f10165,f10169,f10173,f10177,f10186,f10190,f10194,f10198,f10202,f10206,f10210,f10214,f10218,f10222,f10231,f10235,f10239,f12021,f12025,f12029,f12033,f12037,f12041,f12045,f12049,f12053,f12057,f12154,f12269,f12366,f12420,f12424,f12428,f12432,f12436,f12440,f12444,f12448,f12452,f12456,f12460,f12464,f12468,f12472,f12476,f12480,f12484,f12489,f12493,f12497,f12502,f12551,f12555,f12559,f12563,f12567,f12571,f12575,f12579,f12583,f12587,f12591,f12595,f12599,f12603,f12613,f12617,f12621,f12625,f12629,f12633,f12637,f12641,f12645,f12649,f12659,f12663,f12667,f12671,f12675,f14178]) ).

fof(f14178,plain,
    ( ~ spl0_21
    | ~ spl0_546 ),
    inference(avatar_contradiction_clause,[],[f14175]) ).

fof(f14175,plain,
    ( $false
    | ~ spl0_21
    | ~ spl0_546 ),
    inference(resolution,[],[f12488,f601]) ).

fof(f601,plain,
    ( ! [X7] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X7)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f600]) ).

fof(f600,plain,
    ( spl0_21
  <=> ! [X7] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f12488,plain,
    ( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____))
    | ~ spl0_546 ),
    inference(avatar_component_clause,[],[f12486]) ).

fof(f12486,plain,
    ( spl0_546
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f12675,plain,
    ( spl0_578
    | ~ spl0_82
    | ~ spl0_290 ),
    inference(avatar_split_clause,[],[f4901,f4665,f872,f12673]) ).

fof(f12673,plain,
    ( spl0_578
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),X1) = c_Lambda_Olift(c_Lambda_Olift(X0,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f872,plain,
    ( spl0_82
  <=> ! [X7] : c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f4665,plain,
    ( spl0_290
  <=> ! [X13,X27,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X27,X13),X11) = c_Lambda_Olift(c_Lambda_Olift(X27,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f4901,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),X1) = c_Lambda_Olift(c_Lambda_Olift(X0,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_82
    | ~ spl0_290 ),
    inference(resolution,[],[f4666,f873]) ).

fof(f873,plain,
    ( ! [X7] : c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f872]) ).

fof(f4666,plain,
    ( ! [X11,X27,X13] :
        ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X27,X13),X11) = c_Lambda_Olift(c_Lambda_Olift(X27,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) )
    | ~ spl0_290 ),
    inference(avatar_component_clause,[],[f4665]) ).

fof(f12671,plain,
    ( spl0_577
    | ~ spl0_67
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f4882,f4661,f791,f12669]) ).

fof(f12669,plain,
    ( spl0_577
  <=> ! [X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f791,plain,
    ( spl0_67
  <=> ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f4661,plain,
    ( spl0_289
  <=> ! [X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)),c_HOL_Oone__class_Oone(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f4882,plain,
    ( ! [X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_67
    | ~ spl0_289 ),
    inference(forward_demodulation,[],[f4783,f792]) ).

fof(f792,plain,
    ( ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f791]) ).

fof(f4783,plain,
    ( ! [X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_67
    | ~ spl0_289 ),
    inference(superposition,[],[f4662,f792]) ).

fof(f4662,plain,
    ( ! [X2,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f4661]) ).

fof(f12667,plain,
    ( spl0_576
    | ~ spl0_101
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f3938,f3879,f1035,f12665]) ).

fof(f12665,plain,
    ( spl0_576
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f1035,plain,
    ( spl0_101
  <=> ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f3879,plain,
    ( spl0_263
  <=> ! [X7,X8,X42] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f3938,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)),tc_nat)
    | ~ spl0_101
    | ~ spl0_263 ),
    inference(superposition,[],[f1036,f3880]) ).

fof(f3880,plain,
    ( ! [X8,X7,X42] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42))
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f3879]) ).

fof(f1036,plain,
    ( ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat)
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f1035]) ).

fof(f12663,plain,
    ( spl0_575
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_161
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3648,f3443,f1661,f1136,f1064,f12661]) ).

fof(f12661,plain,
    ( spl0_575
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f1064,plain,
    ( spl0_108
  <=> ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1136,plain,
    ( spl0_111
  <=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1661,plain,
    ( spl0_161
  <=> ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f3443,plain,
    ( spl0_248
  <=> ! [X41,X40] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f3648,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat)
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_161
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3592,f1205]) ).

fof(f1205,plain,
    ( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(X0))
    | ~ spl0_108
    | ~ spl0_111 ),
    inference(superposition,[],[f1137,f1065]) ).

fof(f1065,plain,
    ( ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1064]) ).

fof(f1137,plain,
    ( ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1136]) ).

fof(f3592,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat)
    | ~ spl0_161
    | ~ spl0_248 ),
    inference(superposition,[],[f1662,f3444]) ).

fof(f3444,plain,
    ( ! [X40,X41] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f3443]) ).

fof(f1662,plain,
    ( ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X1)),tc_nat)
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1661]) ).

fof(f12659,plain,
    ( spl0_574
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3457,f3423,f795,f12657]) ).

fof(f12657,plain,
    ( spl0_574
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f795,plain,
    ( spl0_68
  <=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f3423,plain,
    ( spl0_243
  <=> ! [X13,X14,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X14) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f3457,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(superposition,[],[f3424,f796]) ).

fof(f796,plain,
    ( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f795]) ).

fof(f3424,plain,
    ( ! [X2,X1,X14,X13] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X14)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f3423]) ).

fof(f12649,plain,
    ( spl0_573
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3451,f3423,f795,f12647]) ).

fof(f12647,plain,
    ( spl0_573
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f3451,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
    | ~ spl0_68
    | ~ spl0_243 ),
    inference(superposition,[],[f3424,f796]) ).

fof(f12645,plain,
    ( spl0_572
    | ~ spl0_67
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3447,f3423,f791,f12643]) ).

fof(f12643,plain,
    ( spl0_572
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f3447,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X0
        | c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_67
    | ~ spl0_243 ),
    inference(superposition,[],[f3424,f792]) ).

fof(f12641,plain,
    ( spl0_571
    | ~ spl0_108
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f3410,f2994,f1064,f12639]) ).

fof(f12639,plain,
    ( spl0_571
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f2994,plain,
    ( spl0_240
  <=> ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f3410,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) )
    | ~ spl0_108
    | ~ spl0_240 ),
    inference(superposition,[],[f2995,f1065]) ).

fof(f2995,plain,
    ( ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f2994]) ).

fof(f12637,plain,
    ( spl0_570
    | ~ spl0_108
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f3405,f2994,f1064,f12635]) ).

fof(f12635,plain,
    ( spl0_570
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f3405,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_240 ),
    inference(superposition,[],[f2995,f1065]) ).

fof(f12633,plain,
    ( spl0_569
    | ~ spl0_46
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f3360,f2986,f705,f12631]) ).

fof(f12631,plain,
    ( spl0_569
  <=> ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(hAPP(c_Type_Otype_OFun,X0),X1,X0)
        | c_Type_Otyping(hAPP(c_Type_Otype_OFun,X0),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2)),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f705,plain,
    ( spl0_46
  <=> ! [X50,X7] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X7),hAPP(X50,X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f2986,plain,
    ( spl0_238
  <=> ! [X18,X50,X27,X25,X28] :
        ( ~ c_Type_Otyping(X50,X27,X18)
        | ~ c_Type_Otyping(X50,X25,hAPP(hAPP(c_Type_Otype_OFun,X18),X28))
        | c_Type_Otyping(X50,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X28) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f3360,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(hAPP(c_Type_Otype_OFun,X0),X1,X0)
        | c_Type_Otyping(hAPP(c_Type_Otype_OFun,X0),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2)),X1),X2) )
    | ~ spl0_46
    | ~ spl0_238 ),
    inference(resolution,[],[f2987,f706]) ).

fof(f706,plain,
    ( ! [X50,X7] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X7),hAPP(X50,X7))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f705]) ).

fof(f2987,plain,
    ( ! [X50,X28,X18,X27,X25] :
        ( ~ c_Type_Otyping(X50,X25,hAPP(hAPP(c_Type_Otype_OFun,X18),X28))
        | ~ c_Type_Otyping(X50,X27,X18)
        | c_Type_Otyping(X50,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X28) )
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f2986]) ).

fof(f12629,plain,
    ( spl0_568
    | ~ spl0_135
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3307,f2961,f1386,f12627]) ).

fof(f12627,plain,
    ( spl0_568
  <=> ! [X5,X4,X0,X3,X2,X1] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f1386,plain,
    ( spl0_135
  <=> ! [X2,X25,X27,X46] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f2961,plain,
    ( spl0_232
  <=> ! [X13,X25,X27] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X27),X25,X13) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X27,c_Lambda_Olift(X25,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f3307,plain,
    ( ! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X5,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2)),X3)
    | ~ spl0_135
    | ~ spl0_232 ),
    inference(superposition,[],[f1387,f2962]) ).

fof(f2962,plain,
    ( ! [X27,X25,X13] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X27),X25,X13) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X27,c_Lambda_Olift(X25,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))))
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2961]) ).

fof(f1387,plain,
    ( ! [X2,X46,X27,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1386]) ).

fof(f12625,plain,
    ( spl0_567
    | ~ spl0_108
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3293,f2961,f1064,f12623]) ).

fof(f12623,plain,
    ( spl0_567
  <=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,c_Lambda_OdB_OdB__size(X0)) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f3293,plain,
    ( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,c_Lambda_OdB_OdB__size(X0)) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))))
    | ~ spl0_108
    | ~ spl0_232 ),
    inference(superposition,[],[f2962,f1065]) ).

fof(f12621,plain,
    ( spl0_566
    | ~ spl0_126
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f2904,f2771,f1350,f12619]) ).

fof(f12619,plain,
    ( spl0_566
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X0,X1,X1),X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f1350,plain,
    ( spl0_126
  <=> ! [X7,X8,X6,X19] :
        ( ~ hBOOL(hAPP(hAPP(X19,X7),X8))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f2771,plain,
    ( spl0_218
  <=> ! [X7,X8,X6,X19] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X7))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X19,X6,X6),X6),X7),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f2904,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X0,X1,X1),X3),X2)) )
    | ~ spl0_126
    | ~ spl0_218 ),
    inference(resolution,[],[f2772,f1351]) ).

fof(f1351,plain,
    ( ! [X8,X19,X6,X7] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X8))
        | ~ hBOOL(hAPP(hAPP(X19,X7),X8)) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f1350]) ).

fof(f2772,plain,
    ( ! [X8,X19,X6,X7] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X19,X6,X6),X6),X7),X8))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X7)) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2771]) ).

fof(f12617,plain,
    ( spl0_565
    | ~ spl0_82
    | ~ spl0_85
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2890,f2763,f898,f872,f12615]) ).

fof(f12615,plain,
    ( spl0_565
  <=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_Type_Oshift(X0,X1,X2,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f898,plain,
    ( spl0_85
  <=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f2763,plain,
    ( spl0_216
  <=> ! [X6,X11,X18,X12,X17] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2890,plain,
    ( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_Type_Oshift(X0,X1,X2,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_82
    | ~ spl0_85
    | ~ spl0_216 ),
    inference(forward_demodulation,[],[f2858,f899]) ).

fof(f899,plain,
    ( ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f898]) ).

fof(f2858,plain,
    ( ! [X2,X3,X0,X1] : hAPP(c_Type_Oshift(X0,X1,X2,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) = hAPP(X0,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_82
    | ~ spl0_216 ),
    inference(resolution,[],[f2764,f873]) ).

fof(f2764,plain,
    ( ! [X11,X18,X6,X17,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2763]) ).

fof(f12613,plain,
    ( spl0_564
    | ~ spl0_46
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2686,f2443,f705,f12611]) ).

fof(f12611,plain,
    ( spl0_564
  <=> ! [X2,X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X1)),hAPP(hAPP(c_Type_Otype_OFun,X2),hAPP(c_Type_Oshift(X0,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f2443,plain,
    ( spl0_209
  <=> ! [X18,X50,X27,X28] :
        ( ~ c_Type_Otyping(c_Type_Oshift(X50,c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_Type_Otype),X27,X28)
        | c_Type_Otyping(X50,c_Lambda_OdB_OAbs(X27),hAPP(hAPP(c_Type_Otype_OFun,X18),X28)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f2686,plain,
    ( ! [X2,X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X1)),hAPP(hAPP(c_Type_Otype_OFun,X2),hAPP(c_Type_Oshift(X0,c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_Type_Otype),X1)))
    | ~ spl0_46
    | ~ spl0_209 ),
    inference(resolution,[],[f2444,f706]) ).

fof(f2444,plain,
    ( ! [X50,X28,X18,X27] :
        ( ~ c_Type_Otyping(c_Type_Oshift(X50,c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_Type_Otype),X27,X28)
        | c_Type_Otyping(X50,c_Lambda_OdB_OAbs(X27),hAPP(hAPP(c_Type_Otype_OFun,X18),X28)) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f2443]) ).

fof(f12603,plain,
    ( spl0_563
    | ~ spl0_53
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2657,f2423,f733,f12601]) ).

fof(f12601,plain,
    ( spl0_563
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X3,X2,X1)),X0))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),c_Lambda_Olift(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f733,plain,
    ( spl0_53
  <=> ! [X13,X25,X27] : c_Lambda_Osubst(c_Lambda_Olift(X27,X13),X25,X13) = X27 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f2423,plain,
    ( spl0_204
  <=> ! [X19,X11,X27,X25] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X19,X27,X11)),c_Lambda_Osubst(X25,X27,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f2657,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X3,X2,X1)),X0))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),c_Lambda_Olift(X0,X1))) )
    | ~ spl0_53
    | ~ spl0_204 ),
    inference(superposition,[],[f2424,f734]) ).

fof(f734,plain,
    ( ! [X27,X25,X13] : c_Lambda_Osubst(c_Lambda_Olift(X27,X13),X25,X13) = X27
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f733]) ).

fof(f2424,plain,
    ( ! [X11,X19,X27,X25] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X19,X27,X11)),c_Lambda_Osubst(X25,X27,X11)))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25)) )
    | ~ spl0_204 ),
    inference(avatar_component_clause,[],[f2423]) ).

fof(f12599,plain,
    ( spl0_562
    | ~ spl0_53
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2655,f2423,f733,f12597]) ).

fof(f12597,plain,
    ( spl0_562
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),c_Lambda_Osubst(X3,X2,X1)))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X0,X1)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f2655,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),c_Lambda_Osubst(X3,X2,X1)))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X0,X1)),X3)) )
    | ~ spl0_53
    | ~ spl0_204 ),
    inference(superposition,[],[f2424,f734]) ).

fof(f12595,plain,
    ( spl0_561
    | ~ spl0_108
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f2589,f2375,f1064,f12593]) ).

fof(f12593,plain,
    ( spl0_561
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f2375,plain,
    ( spl0_195
  <=> ! [X13,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f2589,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_108
    | ~ spl0_195 ),
    inference(superposition,[],[f2376,f1065]) ).

fof(f2376,plain,
    ( ! [X2,X1,X13] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f2375]) ).

fof(f12591,plain,
    ( spl0_560
    | ~ spl0_108
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f2583,f2375,f1064,f12589]) ).

fof(f12589,plain,
    ( spl0_560
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f2583,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_195 ),
    inference(superposition,[],[f2376,f1065]) ).

fof(f12587,plain,
    ( spl0_559
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2552,f2371,f1064,f12585]) ).

fof(f12585,plain,
    ( spl0_559
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f2371,plain,
    ( spl0_194
  <=> ! [X13,X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f2552,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(superposition,[],[f2372,f1065]) ).

fof(f2372,plain,
    ( ! [X2,X1,X13] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f2371]) ).

fof(f12583,plain,
    ( spl0_558
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2546,f2371,f1064,f12581]) ).

fof(f12581,plain,
    ( spl0_558
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f2546,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(superposition,[],[f2372,f1065]) ).

fof(f12579,plain,
    ( spl0_557
    | ~ spl0_108
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2524,f2367,f1064,f12577]) ).

fof(f12577,plain,
    ( spl0_557
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f2367,plain,
    ( spl0_193
  <=> ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f2524,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) )
    | ~ spl0_108
    | ~ spl0_193 ),
    inference(superposition,[],[f2368,f1065]) ).

fof(f2368,plain,
    ( ! [X11,X12,X13] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f2367]) ).

fof(f12575,plain,
    ( spl0_556
    | ~ spl0_108
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2518,f2367,f1064,f12573]) ).

fof(f12573,plain,
    ( spl0_556
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f2518,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_193 ),
    inference(superposition,[],[f2368,f1065]) ).

fof(f12571,plain,
    ( spl0_555
    | ~ spl0_111
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2315,f2143,f1136,f12569]) ).

fof(f12569,plain,
    ( spl0_555
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f2143,plain,
    ( spl0_186
  <=> ! [X2,X1] :
        ( X1 = X2
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f2315,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 )
    | ~ spl0_111
    | ~ spl0_186 ),
    inference(superposition,[],[f2144,f1137]) ).

fof(f2144,plain,
    ( ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f2143]) ).

fof(f12567,plain,
    ( spl0_554
    | ~ spl0_46
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2294,f2139,f705,f12565]) ).

fof(f12565,plain,
    ( spl0_554
  <=> ! [X2,X0,X1] : c_Type_Otyping(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X0,X1)),c_Lambda_OdB_OVar(c_Lambda_Olift(X2,X1)),c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f2139,plain,
    ( spl0_185
  <=> ! [X13,X25,X27] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X25,X13)),c_Lambda_Olift(X27,X13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f2294,plain,
    ( ! [X2,X0,X1] : c_Type_Otyping(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X0,X1)),c_Lambda_OdB_OVar(c_Lambda_Olift(X2,X1)),c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1))
    | ~ spl0_46
    | ~ spl0_185 ),
    inference(superposition,[],[f706,f2140]) ).

fof(f2140,plain,
    ( ! [X27,X25,X13] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X25,X13)),c_Lambda_Olift(X27,X13))
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f2139]) ).

fof(f12563,plain,
    ( spl0_553
    | ~ spl0_235
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f7106,f7025,f2974,f12561]) ).

fof(f12561,plain,
    ( spl0_553
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f2974,plain,
    ( spl0_235
  <=> ! [X18,X17,X36,X27] :
        ( ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18)
        | c_Type_Otyping(X17,X27,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)),X18)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f7025,plain,
    ( spl0_389
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f7106,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)
    | ~ spl0_235
    | ~ spl0_389 ),
    inference(resolution,[],[f7026,f2975]) ).

fof(f2975,plain,
    ( ! [X36,X18,X27,X17] :
        ( c_Type_Otyping(X17,X27,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)),X18))
        | ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18) )
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2974]) ).

fof(f7026,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f7025]) ).

fof(f12559,plain,
    ( spl0_552
    | ~ spl0_111
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2198,f2108,f1136,f12557]) ).

fof(f12557,plain,
    ( spl0_552
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f2108,plain,
    ( spl0_180
  <=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f2198,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat)
    | ~ spl0_111
    | ~ spl0_180 ),
    inference(superposition,[],[f2109,f1137]) ).

fof(f2109,plain,
    ( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat)
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f2108]) ).

fof(f12555,plain,
    ( spl0_551
    | ~ spl0_147
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2057,f1888,f1434,f12553]) ).

fof(f12553,plain,
    ( spl0_551
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)
        | c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f1434,plain,
    ( spl0_147
  <=> ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1888,plain,
    ( spl0_172
  <=> ! [X13,X2,X1] :
        ( X1 = X2
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f2057,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)
        | c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) = X1 )
    | ~ spl0_147
    | ~ spl0_172 ),
    inference(superposition,[],[f1889,f1435]) ).

fof(f1435,plain,
    ( ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1434]) ).

fof(f1889,plain,
    ( ! [X2,X1,X13] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13)
        | X1 = X2 )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1888]) ).

fof(f12551,plain,
    ( spl0_550
    | ~ spl0_147
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2044,f1884,f1434,f12549]) ).

fof(f12549,plain,
    ( spl0_550
  <=> ! [X0,X1] :
        ( c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)),X1)
        | c_HOL_Oone__class_Oone(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f1884,plain,
    ( spl0_171
  <=> ! [X8,X7,X42] :
        ( X8 = X42
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f2044,plain,
    ( ! [X0,X1] :
        ( c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)),X1)
        | c_HOL_Oone__class_Oone(tc_nat) = X1 )
    | ~ spl0_147
    | ~ spl0_171 ),
    inference(superposition,[],[f1885,f1435]) ).

fof(f1885,plain,
    ( ! [X8,X7,X42] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8)
        | X8 = X42 )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1884]) ).

fof(f12502,plain,
    ( spl0_549
    | ~ spl0_442
    | ~ spl0_548 ),
    inference(avatar_split_clause,[],[f12498,f12495,f7996,f12500]) ).

fof(f12500,plain,
    ( spl0_549
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f7996,plain,
    ( spl0_442
  <=> ! [X0] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f12495,plain,
    ( spl0_548
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f12498,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat))
    | ~ spl0_442
    | ~ spl0_548 ),
    inference(forward_demodulation,[],[f12496,f7997]) ).

fof(f7997,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_442 ),
    inference(avatar_component_clause,[],[f7996]) ).

fof(f12496,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat))
    | ~ spl0_548 ),
    inference(avatar_component_clause,[],[f12495]) ).

fof(f12497,plain,
    ( spl0_548
    | ~ spl0_85
    | ~ spl0_124
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2018,f1876,f1190,f898,f12495]) ).

fof(f1190,plain,
    ( spl0_124
  <=> ! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1876,plain,
    ( spl0_169
  <=> ! [X11,X36,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f2018,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat))
    | ~ spl0_85
    | ~ spl0_124
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f2006,f899]) ).

fof(f2006,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat))
    | ~ spl0_124
    | ~ spl0_169 ),
    inference(resolution,[],[f1877,f1191]) ).

fof(f1191,plain,
    ( ! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1190]) ).

fof(f1877,plain,
    ( ! [X11,X36,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f1876]) ).

fof(f12493,plain,
    ( spl0_547
    | ~ spl0_70
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f1998,f1876,f803,f12491]) ).

fof(f12491,plain,
    ( spl0_547
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Ozero__class_Ozero(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f803,plain,
    ( spl0_70
  <=> ! [X2] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f1998,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Ozero__class_Ozero(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_70
    | ~ spl0_169 ),
    inference(resolution,[],[f1877,f804]) ).

fof(f804,plain,
    ( ! [X2] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f803]) ).

fof(f12489,plain,
    ( spl0_546
    | ~ spl0_123
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1984,f1872,f1185,f12486]) ).

fof(f1185,plain,
    ( spl0_123
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1872,plain,
    ( spl0_168
  <=> ! [X18,X17,X36,X27] :
        ( ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18)
        | c_Type_Otyping(X17,X36,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1984,plain,
    ( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(v_Ua____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OAbs(v_r____),v_a____))
    | ~ spl0_123
    | ~ spl0_168 ),
    inference(resolution,[],[f1873,f1187]) ).

fof(f1187,plain,
    ( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____)
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1185]) ).

fof(f1873,plain,
    ( ! [X36,X18,X27,X17] :
        ( ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18)
        | c_Type_Otyping(X17,X36,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1872]) ).

fof(f12484,plain,
    ( spl0_545
    | ~ spl0_147
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1975,f1868,f1434,f12482]) ).

fof(f12482,plain,
    ( spl0_545
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f1868,plain,
    ( spl0_167
  <=> ! [X13,X12,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1975,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_147
    | ~ spl0_167 ),
    inference(superposition,[],[f1869,f1435]) ).

fof(f1869,plain,
    ( ! [X11,X12,X13] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1868]) ).

fof(f12480,plain,
    ( spl0_544
    | ~ spl0_73
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1963,f1868,f815,f12478]) ).

fof(f12478,plain,
    ( spl0_544
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f815,plain,
    ( spl0_73
  <=> ! [X2] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f1963,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) )
    | ~ spl0_73
    | ~ spl0_167 ),
    inference(resolution,[],[f1869,f816]) ).

fof(f816,plain,
    ( ! [X2] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f815]) ).

fof(f12476,plain,
    ( spl0_543
    | ~ spl0_256
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6784,f6418,f3694,f12474]) ).

fof(f12474,plain,
    ( spl0_543
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f3694,plain,
    ( spl0_256
  <=> ! [X18,X17,X27,X26] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26),X18,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f6418,plain,
    ( spl0_369
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f6784,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_369 ),
    inference(resolution,[],[f6419,f3695]) ).

fof(f3695,plain,
    ( ! [X18,X26,X27,X17] :
        ( c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26),X18,tc_Type_Otype,tc_Type_Otype))
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) )
    | ~ spl0_256 ),
    inference(avatar_component_clause,[],[f3694]) ).

fof(f6419,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3)
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f6418]) ).

fof(f12472,plain,
    ( spl0_542
    | ~ spl0_147
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1946,f1864,f1434,f12470]) ).

fof(f12470,plain,
    ( spl0_542
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f1864,plain,
    ( spl0_166
  <=> ! [X13,X12,X11] :
        ( c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f1946,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_147
    | ~ spl0_166 ),
    inference(superposition,[],[f1865,f1435]) ).

fof(f1865,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat)
        | c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1864]) ).

fof(f12468,plain,
    ( spl0_541
    | ~ spl0_70
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1810,f1657,f803,f12466]) ).

fof(f12466,plain,
    ( spl0_541
  <=> ! [X0,X3,X2,X1] :
        ( hAPP(X0,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(c_Type_Oshift(X0,X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f1657,plain,
    ( spl0_160
  <=> ! [X17,X11,X18,X12,X6] :
        ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
        | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f1810,plain,
    ( ! [X2,X3,X0,X1] :
        ( hAPP(X0,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(c_Type_Oshift(X0,X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_70
    | ~ spl0_160 ),
    inference(resolution,[],[f1658,f804]) ).

fof(f1658,plain,
    ( ! [X11,X18,X6,X17,X12] :
        ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
        | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,X12) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1657]) ).

fof(f12464,plain,
    ( spl0_540
    | ~ spl0_82
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1799,f1657,f872,f12462]) ).

fof(f12462,plain,
    ( spl0_540
  <=> ! [X0,X3,X2,X1] : hAPP(X0,X1) = hAPP(c_Type_Oshift(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,X3),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f1799,plain,
    ( ! [X2,X3,X0,X1] : hAPP(X0,X1) = hAPP(c_Type_Oshift(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,X3),X1)
    | ~ spl0_82
    | ~ spl0_160 ),
    inference(resolution,[],[f1658,f873]) ).

fof(f12460,plain,
    ( spl0_539
    | ~ spl0_127
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1795,f1653,f1354,f12458]) ).

fof(f12458,plain,
    ( spl0_539
  <=> ! [X2,X0,X1] :
        ( c_Wellfounded_Oaccp(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2)
        | ~ c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f1354,plain,
    ( spl0_127
  <=> ! [X4,X19,X6,X8] :
        ( ~ c_Wellfounded_Oaccp(X19,X4,X6)
        | c_Wellfounded_Oaccp(X19,X8,X6)
        | ~ hBOOL(hAPP(hAPP(X19,X8),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1653,plain,
    ( spl0_159
  <=> ! [X25,X27] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27)),c_Lambda_Osubst(X25,X27,c_HOL_Ozero__class_Ozero(tc_nat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1795,plain,
    ( ! [X2,X0,X1] :
        ( c_Wellfounded_Oaccp(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2)
        | ~ c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2) )
    | ~ spl0_127
    | ~ spl0_159 ),
    inference(resolution,[],[f1654,f1355]) ).

fof(f1355,plain,
    ( ! [X8,X19,X6,X4] :
        ( ~ hBOOL(hAPP(hAPP(X19,X8),X4))
        | c_Wellfounded_Oaccp(X19,X8,X6)
        | ~ c_Wellfounded_Oaccp(X19,X4,X6) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1354]) ).

fof(f1654,plain,
    ( ! [X27,X25] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27)),c_Lambda_Osubst(X25,X27,c_HOL_Ozero__class_Ozero(tc_nat))))
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1653]) ).

fof(f12456,plain,
    ( spl0_538
    | ~ spl0_144
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1794,f1653,f1422,f12454]) ).

fof(f12454,plain,
    ( spl0_538
  <=> ! [X0,X3,X2,X1] :
        ( c_Type_Otyping(X0,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3)
        | ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f1422,plain,
    ( spl0_144
  <=> ! [X18,X33,X17,X27] :
        ( ~ c_Type_Otyping(X17,X27,X18)
        | c_Type_Otyping(X17,X33,X18)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X33)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1794,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Type_Otyping(X0,c_Lambda_Osubst(X1,X2,c_HOL_Ozero__class_Ozero(tc_nat)),X3)
        | ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1)),X2),X3) )
    | ~ spl0_144
    | ~ spl0_159 ),
    inference(resolution,[],[f1654,f1423]) ).

fof(f1423,plain,
    ( ! [X18,X27,X17,X33] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X33))
        | c_Type_Otyping(X17,X33,X18)
        | ~ c_Type_Otyping(X17,X27,X18) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1422]) ).

fof(f12452,plain,
    ( spl0_537
    | ~ spl0_151
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1792,f1649,f1621,f12450]) ).

fof(f12450,plain,
    ( spl0_537
  <=> ! [X2,X4,X0,X3,X1] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X4,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1621,plain,
    ( spl0_151
  <=> ! [X13,X25] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X25),X13) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1649,plain,
    ( spl0_158
  <=> ! [X2,X19,X46,X26] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1792,plain,
    ( ! [X2,X3,X0,X1,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X3,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X4,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_151
    | ~ spl0_158 ),
    inference(superposition,[],[f1650,f1622]) ).

fof(f1622,plain,
    ( ! [X25,X13] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X25),X13) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))))
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1621]) ).

fof(f1650,plain,
    ( ! [X2,X46,X19,X26] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X46,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1649]) ).

fof(f12448,plain,
    ( spl0_536
    | ~ spl0_119
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1756,f1621,f1168,f12446]) ).

fof(f12446,plain,
    ( spl0_536
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f1168,plain,
    ( spl0_119
  <=> ! [X25,X46,X19] :
        ( c_Lambda_OdB_OAbs(X19) = X25
        | c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1756,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) = X2 )
    | ~ spl0_119
    | ~ spl0_151 ),
    inference(superposition,[],[f1169,f1622]) ).

fof(f1169,plain,
    ( ! [X46,X19,X25] :
        ( c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_Lambda_OdB_OAbs(X19) = X25 )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f1168]) ).

fof(f12444,plain,
    ( spl0_535
    | ~ spl0_84
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1729,f1617,f894,f12442]) ).

fof(f12442,plain,
    ( spl0_535
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f894,plain,
    ( spl0_84
  <=> ! [X13,X2,X12] :
        ( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X2,tc_nat),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f1617,plain,
    ( spl0_150
  <=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1729,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_84
    | ~ spl0_150 ),
    inference(superposition,[],[f895,f1618]) ).

fof(f1618,plain,
    ( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat)
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1617]) ).

fof(f895,plain,
    ( ! [X2,X12,X13] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X2,tc_nat),X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f894]) ).

fof(f12440,plain,
    ( spl0_534
    | ~ spl0_86
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1715,f1617,f902,f12438]) ).

fof(f12438,plain,
    ( spl0_534
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f902,plain,
    ( spl0_86
  <=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f1715,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat),X0,tc_nat)
    | ~ spl0_86
    | ~ spl0_150 ),
    inference(superposition,[],[f1618,f903]) ).

fof(f903,plain,
    ( ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat) = X1
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f902]) ).

fof(f12436,plain,
    ( spl0_533
    | ~ spl0_85
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1714,f1617,f898,f12434]) ).

fof(f12434,plain,
    ( spl0_533
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f1714,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat),X1,tc_nat)
    | ~ spl0_85
    | ~ spl0_150 ),
    inference(superposition,[],[f1618,f899]) ).

fof(f12432,plain,
    ( spl0_532
    | ~ spl0_256
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f6597,f6162,f3694,f12430]) ).

fof(f12430,plain,
    ( spl0_532
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f6162,plain,
    ( spl0_368
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f6597,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_368 ),
    inference(resolution,[],[f6163,f3695]) ).

fof(f6163,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_368 ),
    inference(avatar_component_clause,[],[f6162]) ).

fof(f12428,plain,
    ( spl0_531
    | ~ spl0_73
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1673,f1613,f815,f12426]) ).

fof(f12426,plain,
    ( spl0_531
  <=> ! [X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f1613,plain,
    ( spl0_149
  <=> ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1673,plain,
    ( ! [X0] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_73
    | ~ spl0_149 ),
    inference(resolution,[],[f1614,f816]) ).

fof(f1614,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1613]) ).

fof(f12424,plain,
    ( spl0_530
    | ~ spl0_95
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1567,f1430,f938,f12422]) ).

fof(f12422,plain,
    ( spl0_530
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f938,plain,
    ( spl0_95
  <=> ! [X13,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1430,plain,
    ( spl0_146
  <=> ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1567,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) )
    | ~ spl0_95
    | ~ spl0_146 ),
    inference(resolution,[],[f1431,f939]) ).

fof(f939,plain,
    ( ! [X11,X13] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f938]) ).

fof(f1431,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1430]) ).

fof(f12420,plain,
    ( spl0_529
    | ~ spl0_84
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1559,f1426,f894,f12418]) ).

fof(f12418,plain,
    ( spl0_529
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f1426,plain,
    ( spl0_145
  <=> ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1559,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
    | ~ spl0_84
    | ~ spl0_145 ),
    inference(resolution,[],[f1427,f895]) ).

fof(f1427,plain,
    ( ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1426]) ).

fof(f12366,plain,
    ( ~ spl0_16
    | spl0_528
    | ~ spl0_84
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1535,f1394,f894,f12364,f575]) ).

fof(f575,plain,
    ( spl0_16
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f12364,plain,
    ( spl0_528
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f1394,plain,
    ( spl0_137
  <=> ! [X42,X7,X6,X8] :
        ( ~ class_Orderings_Opreorder(X6)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X6)
        | ~ c_HOL_Oord__class_Oless(X8,X42,X6)
        | c_HOL_Oord__class_Oless(X7,X42,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1535,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat) )
    | ~ spl0_84
    | ~ spl0_137 ),
    inference(resolution,[],[f1395,f895]) ).

fof(f1395,plain,
    ( ! [X8,X6,X7,X42] :
        ( ~ c_HOL_Oord__class_Oless(X8,X42,X6)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X6)
        | ~ class_Orderings_Opreorder(X6)
        | c_HOL_Oord__class_Oless(X7,X42,X6) )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1394]) ).

fof(f12269,plain,
    ( ~ spl0_16
    | spl0_527
    | ~ spl0_97
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1523,f1394,f947,f12267,f575]) ).

fof(f12267,plain,
    ( spl0_527
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | X1 = X2
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f947,plain,
    ( spl0_97
  <=> ! [X2,X1] :
        ( X1 = X2
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1523,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | X1 = X2 )
    | ~ spl0_97
    | ~ spl0_137 ),
    inference(resolution,[],[f1395,f948]) ).

fof(f948,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f947]) ).

fof(f12154,plain,
    ( ~ spl0_18
    | spl0_526
    | ~ spl0_84
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1517,f1390,f894,f12152,f585]) ).

fof(f585,plain,
    ( spl0_18
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f12152,plain,
    ( spl0_526
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f1390,plain,
    ( spl0_136
  <=> ! [X42,X7,X6,X8] :
        ( ~ class_Orderings_Oorder(X6)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X6)
        | ~ c_HOL_Oord__class_Oless(X42,X8,X6)
        | c_HOL_Oord__class_Oless(X42,X7,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1517,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_84
    | ~ spl0_136 ),
    inference(resolution,[],[f1391,f895]) ).

fof(f1391,plain,
    ( ! [X8,X6,X7,X42] :
        ( ~ c_HOL_Oord__class_Oless(X42,X8,X6)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X6)
        | ~ class_Orderings_Oorder(X6)
        | c_HOL_Oord__class_Oless(X42,X7,X6) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1390]) ).

fof(f12057,plain,
    ( spl0_525
    | ~ spl0_256
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f6552,f6038,f3694,f12055]) ).

fof(f12055,plain,
    ( spl0_525
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f6038,plain,
    ( spl0_359
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f6552,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_359 ),
    inference(resolution,[],[f6039,f3695]) ).

fof(f6039,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_359 ),
    inference(avatar_component_clause,[],[f6038]) ).

fof(f12053,plain,
    ( ~ spl0_18
    | spl0_524
    | ~ spl0_97
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1505,f1390,f947,f12051,f585]) ).

fof(f12051,plain,
    ( spl0_524
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | X0 = X2
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f1505,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | X0 = X2 )
    | ~ spl0_97
    | ~ spl0_136 ),
    inference(resolution,[],[f1391,f948]) ).

fof(f12049,plain,
    ( spl0_523
    | ~ spl0_111
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1448,f1354,f1136,f12047]) ).

fof(f12047,plain,
    ( spl0_523
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0))
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X2)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f1448,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0))
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X2)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X1,X2) )
    | ~ spl0_111
    | ~ spl0_127 ),
    inference(superposition,[],[f1355,f1137]) ).

fof(f12045,plain,
    ( spl0_522
    | ~ spl0_62
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1310,f1176,f771,f12043]) ).

fof(f12043,plain,
    ( spl0_522
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X1)
        | c_Nat_Osemiring__1__class_Oof__nat(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f771,plain,
    ( spl0_62
  <=> ! [X6,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_HOL_Ozero__class_Ozero(X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1176,plain,
    ( spl0_121
  <=> ! [X6,X8,X7] :
        ( ~ class_Orderings_Olinorder(X6)
        | X7 = X8
        | c_HOL_Oord__class_Oless(X8,X7,X6)
        | c_HOL_Oord__class_Oless(X7,X8,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1310,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X1)
        | c_Nat_Osemiring__1__class_Oof__nat(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_62
    | ~ spl0_121 ),
    inference(resolution,[],[f1177,f772]) ).

fof(f772,plain,
    ( ! [X1,X6] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_HOL_Ozero__class_Ozero(X6),X6)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f771]) ).

fof(f1177,plain,
    ( ! [X8,X6,X7] :
        ( c_HOL_Oord__class_Oless(X8,X7,X6)
        | c_HOL_Oord__class_Oless(X7,X8,X6)
        | X7 = X8
        | ~ class_Orderings_Olinorder(X6) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1176]) ).

fof(f12041,plain,
    ( spl0_521
    | ~ spl0_106
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1261,f1144,f1056,f12039]) ).

fof(f12039,plain,
    ( spl0_521
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f1056,plain,
    ( spl0_106
  <=> ! [X12,X36,X11] :
        ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
        | c_Lambda_OdB_OVar(X12) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1144,plain,
    ( spl0_113
  <=> ! [X11,X12,X1] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1261,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)) )
    | ~ spl0_106
    | ~ spl0_113 ),
    inference(resolution,[],[f1145,f1057]) ).

fof(f1057,plain,
    ( ! [X11,X36,X12] :
        ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
        | c_Lambda_OdB_OVar(X12) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1056]) ).

fof(f1145,plain,
    ( ! [X11,X1,X12] :
        ( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat) )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f1144]) ).

fof(f12037,plain,
    ( spl0_520
    | ~ spl0_106
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1244,f1140,f1056,f12035]) ).

fof(f12035,plain,
    ( spl0_520
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1140,plain,
    ( spl0_112
  <=> ! [X11,X12,X1] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X12),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1244,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)) )
    | ~ spl0_106
    | ~ spl0_112 ),
    inference(resolution,[],[f1141,f1057]) ).

fof(f1141,plain,
    ( ! [X11,X1,X12] :
        ( c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X12),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f1140]) ).

fof(f12033,plain,
    ( spl0_519
    | ~ spl0_99
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1102,f1056,f1027,f12031]) ).

fof(f12031,plain,
    ( spl0_519
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f1027,plain,
    ( spl0_99
  <=> ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1102,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_99
    | ~ spl0_106 ),
    inference(resolution,[],[f1057,f1028]) ).

fof(f1028,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f1027]) ).

fof(f12029,plain,
    ( spl0_518
    | ~ spl0_61
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1003,f947,f767,f12027]) ).

fof(f12027,plain,
    ( spl0_518
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f767,plain,
    ( spl0_61
  <=> ! [X12,X11] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X11),X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f1003,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = X1 )
    | ~ spl0_61
    | ~ spl0_97 ),
    inference(resolution,[],[f948,f768]) ).

fof(f768,plain,
    ( ! [X11,X12] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X11),X11,tc_nat)
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f12025,plain,
    ( spl0_517
    | ~ spl0_60
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1002,f947,f763,f12023]) ).

fof(f12023,plain,
    ( spl0_517
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f763,plain,
    ( spl0_60
  <=> ! [X12,X11] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f1002,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) = X0 )
    | ~ spl0_60
    | ~ spl0_97 ),
    inference(resolution,[],[f948,f764]) ).

fof(f764,plain,
    ( ! [X11,X12] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X11,tc_nat)
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f763]) ).

fof(f12021,plain,
    ( spl0_516
    | ~ spl0_84
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f991,f938,f894,f12019]) ).

fof(f12019,plain,
    ( spl0_516
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f991,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_84
    | ~ spl0_95 ),
    inference(resolution,[],[f939,f895]) ).

fof(f10239,plain,
    ( spl0_515
    | ~ spl0_108
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f4252,f3899,f1064,f10237]) ).

fof(f10237,plain,
    ( spl0_515
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) = X1
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f3899,plain,
    ( spl0_268
  <=> ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f4252,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) = X1
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_268 ),
    inference(superposition,[],[f3900,f1065]) ).

fof(f3900,plain,
    ( ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_268 ),
    inference(avatar_component_clause,[],[f3899]) ).

fof(f10235,plain,
    ( spl0_514
    | ~ spl0_108
    | ~ spl0_248
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f4184,f3883,f3443,f1064,f10233]) ).

fof(f10233,plain,
    ( spl0_514
  <=> ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f3883,plain,
    ( spl0_264
  <=> ! [X13,X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f4184,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)))
    | ~ spl0_108
    | ~ spl0_248
    | ~ spl0_264 ),
    inference(forward_demodulation,[],[f4089,f1065]) ).

fof(f4089,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_248
    | ~ spl0_264 ),
    inference(superposition,[],[f3884,f3444]) ).

fof(f3884,plain,
    ( ! [X2,X1,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13))
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f3883]) ).

fof(f10231,plain,
    ( spl0_513
    | ~ spl0_98
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f4168,f3883,f951,f10229]) ).

fof(f10229,plain,
    ( spl0_513
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f951,plain,
    ( spl0_98
  <=> ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f4168,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))),tc_nat)
    | ~ spl0_98
    | ~ spl0_264 ),
    inference(superposition,[],[f952,f3884]) ).

fof(f952,plain,
    ( ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f951]) ).

fof(f10222,plain,
    ( spl0_512
    | ~ spl0_60
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3579,f3443,f763,f10220]) ).

fof(f10220,plain,
    ( spl0_512
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f3579,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),tc_nat)
    | ~ spl0_60
    | ~ spl0_248 ),
    inference(superposition,[],[f764,f3444]) ).

fof(f10218,plain,
    ( spl0_511
    | ~ spl0_82
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3568,f3443,f872,f10216]) ).

fof(f10216,plain,
    ( spl0_511
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f3568,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat)
    | ~ spl0_82
    | ~ spl0_248 ),
    inference(superposition,[],[f873,f3444]) ).

fof(f10214,plain,
    ( spl0_510
    | ~ spl0_60
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3483,f3439,f763,f10212]) ).

fof(f10212,plain,
    ( spl0_510
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f3439,plain,
    ( spl0_247
  <=> ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f3483,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1)),tc_nat)
    | ~ spl0_60
    | ~ spl0_247 ),
    inference(superposition,[],[f764,f3440]) ).

fof(f3440,plain,
    ( ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f3439]) ).

fof(f10210,plain,
    ( spl0_509
    | ~ spl0_82
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3472,f3439,f872,f10208]) ).

fof(f10208,plain,
    ( spl0_509
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f3472,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1)),c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat)
    | ~ spl0_82
    | ~ spl0_247 ),
    inference(superposition,[],[f873,f3440]) ).

fof(f10206,plain,
    ( spl0_508
    | ~ spl0_116
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3302,f2961,f1156,f10204]) ).

fof(f10204,plain,
    ( spl0_508
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X4,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_List_Olist_ONil(tc_Lambda_OdB) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f1156,plain,
    ( spl0_116
  <=> ! [X25,X19,X46] :
        ( c_List_Olist_ONil(tc_Lambda_OdB) = X46
        | c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f3302,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X4,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_List_Olist_ONil(tc_Lambda_OdB) = X4 )
    | ~ spl0_116
    | ~ spl0_232 ),
    inference(superposition,[],[f1157,f2962]) ).

fof(f1157,plain,
    ( ! [X46,X19,X25] :
        ( c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_List_Olist_ONil(tc_Lambda_OdB) = X46 )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1156]) ).

fof(f10202,plain,
    ( spl0_507
    | ~ spl0_68
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3292,f2961,f795,f10200]) ).

fof(f10200,plain,
    ( spl0_507
  <=> ! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f3292,plain,
    ( ! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_68
    | ~ spl0_232 ),
    inference(superposition,[],[f2962,f796]) ).

fof(f10198,plain,
    ( spl0_506
    | ~ spl0_123
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f2917,f2783,f1185,f10196]) ).

fof(f10196,plain,
    ( spl0_506
  <=> ! [X0] :
        ( c_Type_Otyping(v_e____,c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),X0,v_i____),v_Ua____)
        | ~ c_Type_Otyping(v_e____,X0,v_T____) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f2783,plain,
    ( spl0_221
  <=> ! [X18,X58,X11,X36,X27,X28] :
        ( ~ c_Type_Otyping(X58,X36,X28)
        | c_Type_Otyping(X58,c_Lambda_Osubst(X27,X36,X11),X18)
        | ~ c_Type_Otyping(c_Type_Oshift(X58,X11,X28,tc_Type_Otype),X27,X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f2917,plain,
    ( ! [X0] :
        ( c_Type_Otyping(v_e____,c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),X0,v_i____),v_Ua____)
        | ~ c_Type_Otyping(v_e____,X0,v_T____) )
    | ~ spl0_123
    | ~ spl0_221 ),
    inference(resolution,[],[f2784,f1187]) ).

fof(f2784,plain,
    ( ! [X58,X28,X11,X36,X18,X27] :
        ( ~ c_Type_Otyping(c_Type_Oshift(X58,X11,X28,tc_Type_Otype),X27,X18)
        | c_Type_Otyping(X58,c_Lambda_Osubst(X27,X36,X11),X18)
        | ~ c_Type_Otyping(X58,X36,X28) )
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f2783]) ).

fof(f10194,plain,
    ( spl0_505
    | ~ spl0_84
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2841,f2759,f894,f10192]) ).

fof(f10192,plain,
    ( spl0_505
  <=> ! [X2,X0,X1,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f2759,plain,
    ( spl0_215
  <=> ! [X13,X2,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f2841,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X3,tc_nat) )
    | ~ spl0_84
    | ~ spl0_215 ),
    inference(superposition,[],[f895,f2760]) ).

fof(f2760,plain,
    ( ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat)
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f2759]) ).

fof(f10190,plain,
    ( spl0_504
    | ~ spl0_84
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2806,f2755,f894,f10188]) ).

fof(f10188,plain,
    ( spl0_504
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f2755,plain,
    ( spl0_214
  <=> ! [X13,X2,X1] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f2806,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X3,tc_nat) )
    | ~ spl0_84
    | ~ spl0_214 ),
    inference(superposition,[],[f895,f2756]) ).

fof(f2756,plain,
    ( ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13),tc_nat)
    | ~ spl0_214 ),
    inference(avatar_component_clause,[],[f2755]) ).

fof(f10186,plain,
    ( spl0_503
    | ~ spl0_143
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2685,f2443,f1418,f10184]) ).

fof(f10184,plain,
    ( spl0_503
  <=> ! [X0,X3,X2,X1] :
        ( c_Type_Otyping(X0,c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Type_Otype_OFun,X2),X3))
        | ~ c_Type_Otyping(X0,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f1418,plain,
    ( spl0_143
  <=> ! [X18,X11,X27,X17,X28] :
        ( ~ c_Type_Otyping(X17,X27,X18)
        | c_Type_Otyping(c_Type_Oshift(X17,X11,X28,tc_Type_Otype),c_Lambda_Olift(X27,X11),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f2685,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Type_Otyping(X0,c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Type_Otype_OFun,X2),X3))
        | ~ c_Type_Otyping(X0,X1,X3) )
    | ~ spl0_143
    | ~ spl0_209 ),
    inference(resolution,[],[f2444,f1419]) ).

fof(f1419,plain,
    ( ! [X28,X11,X18,X27,X17] :
        ( c_Type_Otyping(c_Type_Oshift(X17,X11,X28,tc_Type_Otype),c_Lambda_Olift(X27,X11),X18)
        | ~ c_Type_Otyping(X17,X27,X18) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1418]) ).

fof(f10177,plain,
    ( spl0_502
    | ~ spl0_45
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2656,f2423,f701,f10175]) ).

fof(f10175,plain,
    ( spl0_502
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X2,X1,X0)),X1))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),c_Lambda_OdB_OVar(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f701,plain,
    ( spl0_45
  <=> ! [X13,X36] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X36,X13) = X36 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f2656,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X2,X1,X0)),X1))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X2),c_Lambda_OdB_OVar(X0))) )
    | ~ spl0_45
    | ~ spl0_204 ),
    inference(superposition,[],[f2424,f702]) ).

fof(f702,plain,
    ( ! [X36,X13] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X36,X13) = X36
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f701]) ).

fof(f10173,plain,
    ( spl0_501
    | ~ spl0_166
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f2561,f2375,f1864,f10171]) ).

fof(f10171,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f2561,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) )
    | ~ spl0_166
    | ~ spl0_195 ),
    inference(resolution,[],[f2376,f1865]) ).

fof(f10169,plain,
    ( spl0_500
    | ~ spl0_167
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2528,f2371,f1868,f10167]) ).

fof(f10167,plain,
    ( spl0_500
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f2528,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X0,tc_nat),tc_nat) )
    | ~ spl0_167
    | ~ spl0_194 ),
    inference(resolution,[],[f2372,f1869]) ).

fof(f10165,plain,
    ( spl0_499
    | ~ spl0_124
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2215,f2108,f1190,f10163]) ).

fof(f10163,plain,
    ( spl0_499
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f2215,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
    | ~ spl0_124
    | ~ spl0_180 ),
    inference(superposition,[],[f1191,f2109]) ).

fof(f10161,plain,
    ( spl0_498
    | ~ spl0_108
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2202,f2108,f1064,f10159]) ).

fof(f10159,plain,
    ( spl0_498
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Lambda_OdB_OdB__size(X0),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f2202,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_Lambda_OdB_OdB__size(X0),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
    | ~ spl0_108
    | ~ spl0_180 ),
    inference(superposition,[],[f2109,f1065]) ).

fof(f10157,plain,
    ( spl0_497
    | ~ spl0_150
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f2092,f1908,f1617,f10155]) ).

fof(f10155,plain,
    ( spl0_497
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1908,plain,
    ( spl0_177
  <=> ! [X2,X11] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f2092,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_150
    | ~ spl0_177 ),
    inference(superposition,[],[f1909,f1618]) ).

fof(f1909,plain,
    ( ! [X2,X11] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1908]) ).

fof(f10153,plain,
    ( spl0_496
    | ~ spl0_111
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2042,f1884,f1136,f10151]) ).

fof(f10151,plain,
    ( spl0_496
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f2042,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)
        | X1 = X2 )
    | ~ spl0_111
    | ~ spl0_171 ),
    inference(superposition,[],[f1885,f1137]) ).

fof(f10149,plain,
    ( spl0_495
    | ~ spl0_111
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1973,f1868,f1136,f10147]) ).

fof(f10147,plain,
    ( spl0_495
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f1973,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_111
    | ~ spl0_167 ),
    inference(superposition,[],[f1869,f1137]) ).

fof(f10145,plain,
    ( spl0_494
    | ~ spl0_111
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1944,f1864,f1136,f10143]) ).

fof(f10143,plain,
    ( spl0_494
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f1944,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_111
    | ~ spl0_166 ),
    inference(superposition,[],[f1865,f1137]) ).

fof(f10141,plain,
    ( spl0_493
    | ~ spl0_67
    | ~ spl0_111
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1927,f1860,f1136,f791,f10139]) ).

fof(f10139,plain,
    ( spl0_493
  <=> ! [X2,X0,X1] :
        ( hBOOL(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X0))
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f1860,plain,
    ( spl0_165
  <=> ! [X4,X5,X3] :
        ( ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat)
        | hBOOL(hAPP(X3,c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ hBOOL(hAPP(X3,c_HOL_Ominus__class_Ominus(X4,X5,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f1927,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X0))
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_67
    | ~ spl0_111
    | ~ spl0_165 ),
    inference(forward_demodulation,[],[f1923,f792]) ).

fof(f1923,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),X0))
        | hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_111
    | ~ spl0_165 ),
    inference(superposition,[],[f1861,f1137]) ).

fof(f1861,plain,
    ( ! [X3,X4,X5] :
        ( ~ hBOOL(hAPP(X3,c_HOL_Ominus__class_Ominus(X4,X5,tc_nat)))
        | hBOOL(hAPP(X3,c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1860]) ).

fof(f10137,plain,
    ( spl0_492
    | ~ spl0_235
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f6783,f6418,f2974,f10135]) ).

fof(f10135,plain,
    ( spl0_492
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f6783,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)),X3),X4)
    | ~ spl0_235
    | ~ spl0_369 ),
    inference(resolution,[],[f6419,f2975]) ).

fof(f10133,plain,
    ( spl0_491
    | ~ spl0_52
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1912,f1860,f729,f10131]) ).

fof(f10131,plain,
    ( spl0_491
  <=> ! [X0,X3,X2,X1] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f729,plain,
    ( spl0_52
  <=> ! [X6,X7,X19] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1912,plain,
    ( ! [X2,X3,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) )
    | ~ spl0_52
    | ~ spl0_165 ),
    inference(resolution,[],[f1861,f730]) ).

fof(f730,plain,
    ( ! [X19,X6,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X7))
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f729]) ).

fof(f10129,plain,
    ( spl0_490
    | ~ spl0_135
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1760,f1621,f1386,f10127]) ).

fof(f10127,plain,
    ( spl0_490
  <=> ! [X4,X0,X3,X2,X1] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f1760,plain,
    ( ! [X2,X3,X0,X1,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X4,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)),X2)
    | ~ spl0_135
    | ~ spl0_151 ),
    inference(superposition,[],[f1387,f1622]) ).

fof(f10125,plain,
    ( spl0_489
    | ~ spl0_134
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1546,f1422,f1382,f10123]) ).

fof(f10123,plain,
    ( spl0_489
  <=> ! [X0,X3,X2,X1] :
        ( c_Type_Otyping(X0,c_Lambda_OdB_OAbs(X1),X2)
        | ~ c_Type_Otyping(X0,c_Lambda_OdB_OAbs(X3),X2)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f1382,plain,
    ( spl0_134
  <=> ! [X25,X27] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X25)),c_Lambda_OdB_OAbs(X27))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1546,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Type_Otyping(X0,c_Lambda_OdB_OAbs(X1),X2)
        | ~ c_Type_Otyping(X0,c_Lambda_OdB_OAbs(X3),X2)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X1)) )
    | ~ spl0_134
    | ~ spl0_144 ),
    inference(resolution,[],[f1423,f1383]) ).

fof(f1383,plain,
    ( ! [X27,X25] :
        ( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X25)),c_Lambda_OdB_OAbs(X27)))
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27)) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1382]) ).

fof(f10121,plain,
    ( spl0_488
    | ~ spl0_127
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1500,f1382,f1354,f10119]) ).

fof(f10119,plain,
    ( spl0_488
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
        | c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X0),X2)
        | ~ c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1500,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
        | c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X0),X2)
        | ~ c_Wellfounded_Oaccp(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X1),X2) )
    | ~ spl0_127
    | ~ spl0_134 ),
    inference(resolution,[],[f1383,f1355]) ).

fof(f10117,plain,
    ( spl0_487
    | ~ spl0_76
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1475,f1366,f848,f10115]) ).

fof(f10115,plain,
    ( spl0_487
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f848,plain,
    ( spl0_76
  <=> ! [X6,X4,X5] :
        ( ~ class_Orderings_Oorder(X6)
        | ~ c_HOL_Oord__class_Oless(X5,X4,X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1366,plain,
    ( spl0_130
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_HOL_Oone__class_Oone(X6)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1475,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_76
    | ~ spl0_130 ),
    inference(resolution,[],[f1367,f849]) ).

fof(f849,plain,
    ( ! [X6,X4,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X4,X6)
        | ~ class_Orderings_Oorder(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f848]) ).

fof(f1367,plain,
    ( ! [X6] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_HOL_Oone__class_Oone(X6)),X6)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1366]) ).

fof(f10113,plain,
    ( spl0_486
    | ~ spl0_77
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1474,f1366,f852,f10111]) ).

fof(f10111,plain,
    ( spl0_486
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f852,plain,
    ( spl0_77
  <=> ! [X6,X7,X8] :
        ( ~ class_Orderings_Olinorder(X6)
        | ~ c_HOL_Oord__class_Oless(X8,X7,X6)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1474,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_77
    | ~ spl0_130 ),
    inference(resolution,[],[f1367,f853]) ).

fof(f853,plain,
    ( ! [X8,X6,X7] :
        ( ~ c_HOL_Oord__class_Oless(X8,X7,X6)
        | ~ class_Orderings_Olinorder(X6)
        | ~ c_HOL_Oord__class_Oless(X7,X8,X6) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f852]) ).

fof(f10109,plain,
    ( spl0_485
    | ~ spl0_78
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1473,f1366,f856,f10107]) ).

fof(f10107,plain,
    ( spl0_485
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f856,plain,
    ( spl0_78
  <=> ! [X6,X4,X5] :
        ( ~ class_Orderings_Opreorder(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ c_HOL_Oord__class_Oless(X5,X4,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1473,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_78
    | ~ spl0_130 ),
    inference(resolution,[],[f1367,f857]) ).

fof(f857,plain,
    ( ! [X6,X4,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X4,X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ class_Orderings_Opreorder(X6) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f856]) ).

fof(f10105,plain,
    ( spl0_484
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1460,f1358,f848,f10103]) ).

fof(f10103,plain,
    ( spl0_484
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f1358,plain,
    ( spl0_128
  <=> ! [X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1460,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) )
    | ~ spl0_76
    | ~ spl0_128 ),
    inference(resolution,[],[f1359,f849]) ).

fof(f1359,plain,
    ( ! [X2,X1,X6] :
        ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1358]) ).

fof(f10101,plain,
    ( spl0_483
    | ~ spl0_77
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1459,f1358,f852,f10099]) ).

fof(f10099,plain,
    ( spl0_483
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f1459,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) )
    | ~ spl0_77
    | ~ spl0_128 ),
    inference(resolution,[],[f1359,f853]) ).

fof(f10097,plain,
    ( spl0_482
    | ~ spl0_78
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1458,f1358,f856,f10095]) ).

fof(f10095,plain,
    ( spl0_482
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f1458,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_78
    | ~ spl0_128 ),
    inference(resolution,[],[f1359,f857]) ).

fof(f10093,plain,
    ( spl0_481
    | ~ spl0_235
    | ~ spl0_368 ),
    inference(avatar_split_clause,[],[f6596,f6162,f2974,f10091]) ).

fof(f10091,plain,
    ( spl0_481
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f6596,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)
    | ~ spl0_235
    | ~ spl0_368 ),
    inference(resolution,[],[f6163,f2975]) ).

fof(f10089,plain,
    ( spl0_480
    | ~ spl0_108
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1451,f1354,f1064,f10087]) ).

fof(f10087,plain,
    ( spl0_480
  <=> ! [X0,X1] :
        ( ~ hBOOL(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)))
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0),X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f1451,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)))
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0),X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),X1) )
    | ~ spl0_108
    | ~ spl0_127 ),
    inference(superposition,[],[f1355,f1065]) ).

fof(f10085,plain,
    ( spl0_479
    | ~ spl0_95
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1262,f1144,f938,f10083]) ).

fof(f10083,plain,
    ( spl0_479
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f1262,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) )
    | ~ spl0_95
    | ~ spl0_113 ),
    inference(resolution,[],[f1145,f939]) ).

fof(f10081,plain,
    ( spl0_478
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1245,f1140,f938,f10079]) ).

fof(f10079,plain,
    ( spl0_478
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f1245,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) )
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(resolution,[],[f1141,f939]) ).

fof(f10077,plain,
    ( spl0_477
    | ~ spl0_98
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1103,f1056,f951,f10075]) ).

fof(f10075,plain,
    ( spl0_477
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f1103,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_98
    | ~ spl0_106 ),
    inference(resolution,[],[f1057,f952]) ).

fof(f10073,plain,
    ( spl0_476
    | ~ spl0_95
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f1067,f1027,f938,f10071]) ).

fof(f10071,plain,
    ( spl0_476
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f1067,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)) )
    | ~ spl0_95
    | ~ spl0_99 ),
    inference(resolution,[],[f1028,f939]) ).

fof(f9903,plain,
    ( spl0_475
    | ~ spl0_235
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f6551,f6038,f2974,f9901]) ).

fof(f9901,plain,
    ( spl0_475
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f6551,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)
    | ~ spl0_235
    | ~ spl0_359 ),
    inference(resolution,[],[f6039,f2975]) ).

fof(f9705,plain,
    ( spl0_474
    | ~ spl0_256
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f5994,f5589,f3694,f9703]) ).

fof(f9703,plain,
    ( spl0_474
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f5589,plain,
    ( spl0_340
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f5994,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_340 ),
    inference(resolution,[],[f5590,f3695]) ).

fof(f5590,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2),X3)
    | ~ spl0_340 ),
    inference(avatar_component_clause,[],[f5589]) ).

fof(f9380,plain,
    ( spl0_473
    | ~ spl0_112
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4512,f4289,f1140,f9378]) ).

fof(f9378,plain,
    ( spl0_473
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f4289,plain,
    ( spl0_276
  <=> ! [X41,X40] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f4512,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_276 ),
    inference(superposition,[],[f1141,f4290]) ).

fof(f4290,plain,
    ( ! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f4289]) ).

fof(f9376,plain,
    ( spl0_472
    | ~ spl0_112
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f4404,f4285,f1140,f9374]) ).

fof(f9374,plain,
    ( spl0_472
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f4285,plain,
    ( spl0_275
  <=> ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f4404,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_275 ),
    inference(superposition,[],[f1141,f4286]) ).

fof(f4286,plain,
    ( ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f4285]) ).

fof(f9372,plain,
    ( spl0_471
    | ~ spl0_61
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f4222,f3899,f767,f9370]) ).

fof(f9370,plain,
    ( spl0_471
  <=> ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f4222,plain,
    ( ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_61
    | ~ spl0_268 ),
    inference(resolution,[],[f3900,f768]) ).

fof(f9368,plain,
    ( spl0_470
    | ~ spl0_256
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f5893,f5545,f3694,f9366]) ).

fof(f9366,plain,
    ( spl0_470
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f5545,plain,
    ( spl0_329
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f5893,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_329 ),
    inference(resolution,[],[f5546,f3695]) ).

fof(f5546,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3)
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f5545]) ).

fof(f9364,plain,
    ( spl0_469
    | ~ spl0_81
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f4166,f3883,f868,f9362]) ).

fof(f9362,plain,
    ( spl0_469
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f868,plain,
    ( spl0_81
  <=> ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f4166,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_81
    | ~ spl0_264 ),
    inference(superposition,[],[f869,f3884]) ).

fof(f869,plain,
    ( ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f868]) ).

fof(f9360,plain,
    ( spl0_468
    | ~ spl0_161
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f3932,f3879,f1661,f9358]) ).

fof(f9358,plain,
    ( spl0_468
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f3932,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X1)),tc_nat)
    | ~ spl0_161
    | ~ spl0_263 ),
    inference(superposition,[],[f1662,f3880]) ).

fof(f9356,plain,
    ( spl0_467
    | ~ spl0_72
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3566,f3443,f811,f9354]) ).

fof(f9354,plain,
    ( spl0_467
  <=> ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f811,plain,
    ( spl0_72
  <=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f3566,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OdB__size(X1))
    | ~ spl0_72
    | ~ spl0_248 ),
    inference(superposition,[],[f812,f3444]) ).

fof(f812,plain,
    ( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f811]) ).

fof(f9352,plain,
    ( spl0_466
    | ~ spl0_72
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3470,f3439,f811,f9350]) ).

fof(f9350,plain,
    ( spl0_466
  <=> ! [X0,X1] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f3470,plain,
    ( ! [X0,X1] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X0)),c_Type_Otype_Otype__size(X1))
    | ~ spl0_72
    | ~ spl0_247 ),
    inference(superposition,[],[f812,f3440]) ).

fof(f9348,plain,
    ( spl0_465
    | ~ spl0_29
    | ~ spl0_45
    | ~ spl0_183
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3324,f2961,f2131,f701,f637,f9346]) ).

fof(f9346,plain,
    ( spl0_465
  <=> ! [X0,X1] : c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))),X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f637,plain,
    ( spl0_29
  <=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f2131,plain,
    ( spl0_183
  <=> ! [X13,X11] :
        ( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f3324,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))),X1,X0)
    | ~ spl0_29
    | ~ spl0_45
    | ~ spl0_183
    | ~ spl0_232 ),
    inference(forward_demodulation,[],[f3294,f2249]) ).

fof(f2249,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_29
    | ~ spl0_183 ),
    inference(resolution,[],[f2132,f638]) ).

fof(f638,plain,
    ( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f2132,plain,
    ( ! [X11,X13] :
        ( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat))) )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f2131]) ).

fof(f3294,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Lambda_Osubst(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)))),X1,X0)
    | ~ spl0_45
    | ~ spl0_232 ),
    inference(superposition,[],[f2962,f702]) ).

fof(f9344,plain,
    ( spl0_464
    | ~ spl0_58
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2648,f2410,f755,f9342]) ).

fof(f9342,plain,
    ( spl0_464
  <=> ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xvar__app__typesE__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f755,plain,
    ( spl0_58
  <=> ! [X22,X4,X21,X6] : c_List_Ofoldl(X21,X4,c_List_Olist_ONil(X22),X6,X22) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f2410,plain,
    ( spl0_201
  <=> ! [X18,X11,X17,X26] :
        ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xvar__app__typesE__1__1(X18,X17,X11,X26))
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f2648,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xvar__app__typesE__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) )
    | ~ spl0_58
    | ~ spl0_201 ),
    inference(superposition,[],[f2411,f756]) ).

fof(f756,plain,
    ( ! [X21,X6,X4,X22] : c_List_Ofoldl(X21,X4,c_List_Olist_ONil(X22),X6,X22) = X4
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f755]) ).

fof(f2411,plain,
    ( ! [X11,X18,X26,X17] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xvar__app__typesE__1__1(X18,X17,X11,X26)) )
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f2410]) ).

fof(f9340,plain,
    ( spl0_463
    | ~ spl0_162
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2533,f2371,f1665,f9338]) ).

fof(f9338,plain,
    ( spl0_463
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f1665,plain,
    ( spl0_162
  <=> ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f2533,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)),tc_nat)
    | ~ spl0_162
    | ~ spl0_194 ),
    inference(resolution,[],[f2372,f1666]) ).

fof(f1666,plain,
    ( ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)),tc_nat)
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1665]) ).

fof(f9336,plain,
    ( spl0_462
    | ~ spl0_108
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2319,f2143,f1064,f9334]) ).

fof(f9334,plain,
    ( spl0_462
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat)
        | c_Lambda_OdB_OdB__size(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f2319,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat)
        | c_Lambda_OdB_OdB__size(X0) = X1 )
    | ~ spl0_108
    | ~ spl0_186 ),
    inference(superposition,[],[f2144,f1065]) ).

fof(f9332,plain,
    ( spl0_461
    | ~ spl0_9
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f2284,f2135,f540,f9330]) ).

fof(f9330,plain,
    ( spl0_461
  <=> ! [X0,X1] : c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1,tc_nat,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),X1,X0,tc_nat,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f540,plain,
    ( spl0_9
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f2135,plain,
    ( spl0_184
  <=> ! [X6,X20,X4] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X6)
        | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,X4,X6,X6) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X4,X20,X6,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f2284,plain,
    ( ! [X0,X1] : c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1,tc_nat,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),X1,X0,tc_nat,tc_nat)
    | ~ spl0_9
    | ~ spl0_184 ),
    inference(resolution,[],[f2136,f542]) ).

fof(f542,plain,
    ( class_OrderedGroup_Oab__semigroup__add(tc_nat)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f540]) ).

fof(f2136,plain,
    ( ! [X6,X4,X20] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X6)
        | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,X4,X6,X6) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X4,X20,X6,X6) )
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f2135]) ).

fof(f9328,plain,
    ( spl0_460
    | ~ spl0_108
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2059,f1888,f1064,f9326]) ).

fof(f9326,plain,
    ( spl0_460
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))
        | c_Lambda_OdB_OdB__size(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f2059,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))
        | c_Lambda_OdB_OdB__size(X0) = X1 )
    | ~ spl0_108
    | ~ spl0_172 ),
    inference(superposition,[],[f1889,f1065]) ).

fof(f9324,plain,
    ( spl0_459
    | ~ spl0_256
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5664,f5466,f3694,f9322]) ).

fof(f9322,plain,
    ( spl0_459
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f5466,plain,
    ( spl0_323
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f5664,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_323 ),
    inference(resolution,[],[f5467,f3695]) ).

fof(f5467,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f5466]) ).

fof(f9320,plain,
    ( spl0_458
    | ~ spl0_108
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2046,f1884,f1064,f9318]) ).

fof(f9318,plain,
    ( spl0_458
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1)
        | c_HOL_Oone__class_Oone(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f2046,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),X1)
        | c_HOL_Oone__class_Oone(tc_nat) = X1 )
    | ~ spl0_108
    | ~ spl0_171 ),
    inference(superposition,[],[f1885,f1065]) ).

fof(f9315,plain,
    ( spl0_457
    | ~ spl0_85
    | ~ spl0_98
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2014,f1876,f951,f898,f9313]) ).

fof(f9313,plain,
    ( spl0_457
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f2014,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_85
    | ~ spl0_98
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f2000,f899]) ).

fof(f2000,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_98
    | ~ spl0_169 ),
    inference(resolution,[],[f1877,f952]) ).

fof(f9311,plain,
    ( spl0_456
    | ~ spl0_108
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1977,f1868,f1064,f9309]) ).

fof(f9309,plain,
    ( spl0_456
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f1977,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_108
    | ~ spl0_167 ),
    inference(superposition,[],[f1869,f1065]) ).

fof(f9307,plain,
    ( spl0_455
    | ~ spl0_108
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1948,f1864,f1064,f9305]) ).

fof(f9305,plain,
    ( spl0_455
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f1948,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_108
    | ~ spl0_166 ),
    inference(superposition,[],[f1865,f1065]) ).

fof(f9303,plain,
    ( spl0_454
    | ~ spl0_47
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1911,f1860,f709,f9301]) ).

fof(f9301,plain,
    ( spl0_454
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_fequal(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f709,plain,
    ( spl0_47
  <=> ! [X6,X7] : hBOOL(hAPP(hAPP(c_fequal(X6),X7),X7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f1911,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_fequal(X0),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_47
    | ~ spl0_165 ),
    inference(resolution,[],[f1861,f710]) ).

fof(f710,plain,
    ( ! [X6,X7] : hBOOL(hAPP(hAPP(c_fequal(X6),X7),X7))
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f9299,plain,
    ( spl0_453
    | ~ spl0_116
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1755,f1621,f1156,f9297]) ).

fof(f9297,plain,
    ( spl0_453
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_List_Olist_ONil(tc_Lambda_OdB) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1755,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X3,tc_Lambda_OdB,tc_Lambda_OdB)
        | c_List_Olist_ONil(tc_Lambda_OdB) = X3 )
    | ~ spl0_116
    | ~ spl0_151 ),
    inference(superposition,[],[f1157,f1622]) ).

fof(f9295,plain,
    ( spl0_452
    | ~ spl0_111
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1744,f1621,f1136,f9293]) ).

fof(f9293,plain,
    ( spl0_452
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X0) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1744,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X0) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)))
    | ~ spl0_111
    | ~ spl0_151 ),
    inference(superposition,[],[f1622,f1137]) ).

fof(f9291,plain,
    ( spl0_451
    | ~ spl0_48
    | ~ spl0_101
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1737,f1617,f1035,f713,f9289]) ).

fof(f9289,plain,
    ( spl0_451
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f713,plain,
    ( spl0_48
  <=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f1737,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
    | ~ spl0_48
    | ~ spl0_101
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1710,f714]) ).

fof(f714,plain,
    ( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f713]) ).

fof(f1710,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
    | ~ spl0_101
    | ~ spl0_150 ),
    inference(superposition,[],[f1618,f1036]) ).

fof(f9287,plain,
    ( spl0_450
    | ~ spl0_61
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1577,f1430,f767,f9285]) ).

fof(f9285,plain,
    ( spl0_450
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f1577,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),tc_nat)
    | ~ spl0_61
    | ~ spl0_146 ),
    inference(resolution,[],[f1431,f768]) ).

fof(f9283,plain,
    ( spl0_449
    | ~ spl0_95
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1021,f951,f938,f9281]) ).

fof(f9281,plain,
    ( spl0_449
  <=> ! [X0] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1021,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_95
    | ~ spl0_98 ),
    inference(resolution,[],[f952,f939]) ).

fof(f8026,plain,
    ( spl0_448
    | ~ spl0_61
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f4809,f4661,f767,f8024]) ).

fof(f8024,plain,
    ( spl0_448
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f4809,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_61
    | ~ spl0_289 ),
    inference(superposition,[],[f768,f4662]) ).

fof(f8018,plain,
    ( spl0_447
    | ~ spl0_98
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f4794,f4661,f951,f8016]) ).

fof(f8016,plain,
    ( spl0_447
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f4794,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_98
    | ~ spl0_289 ),
    inference(superposition,[],[f952,f4662]) ).

fof(f8014,plain,
    ( spl0_446
    | ~ spl0_112
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3589,f3443,f1140,f8012]) ).

fof(f8012,plain,
    ( spl0_446
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f3589,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_248 ),
    inference(superposition,[],[f1141,f3444]) ).

fof(f8010,plain,
    ( spl0_445
    | ~ spl0_112
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3493,f3439,f1140,f8008]) ).

fof(f8008,plain,
    ( spl0_445
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f3493,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_247 ),
    inference(superposition,[],[f1141,f3440]) ).

fof(f8006,plain,
    ( spl0_444
    | ~ spl0_145
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f2564,f2375,f1426,f8004]) ).

fof(f8004,plain,
    ( spl0_444
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f2564,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) )
    | ~ spl0_145
    | ~ spl0_195 ),
    inference(resolution,[],[f2376,f1427]) ).

fof(f8002,plain,
    ( spl0_443
    | ~ spl0_146
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2531,f2371,f1430,f8000]) ).

fof(f8000,plain,
    ( spl0_443
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f2531,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) )
    | ~ spl0_146
    | ~ spl0_194 ),
    inference(resolution,[],[f2372,f1431]) ).

fof(f7998,plain,
    ( spl0_442
    | ~ spl0_29
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2249,f2131,f637,f7996]) ).

fof(f7994,plain,
    ( spl0_441
    | ~ spl0_58
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2243,f2127,f755,f7992]) ).

fof(f7992,plain,
    ( spl0_441
  <=> ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,X0,X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xlist__app__typeD__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f2127,plain,
    ( spl0_182
  <=> ! [X18,X17,X27,X26] :
        ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26))
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f2243,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,X0,X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xlist__app__typeD__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) )
    | ~ spl0_58
    | ~ spl0_182 ),
    inference(superposition,[],[f2128,f756]) ).

fof(f2128,plain,
    ( ! [X18,X26,X27,X17] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26)) )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f2127]) ).

fof(f7990,plain,
    ( spl0_440
    | ~ spl0_58
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2242,f2112,f755,f7988]) ).

fof(f7988,plain,
    ( spl0_440
  <=> ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,X0,X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xlist__app__typeE__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f2112,plain,
    ( spl0_181
  <=> ! [X18,X17,X27,X26] :
        ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeE__1__1(X18,X17,X27,X26))
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f2242,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Type_Otyping(X1,X0,X2)
        | c_Type_Otypings(X1,c_List_Olist_ONil(tc_Lambda_OdB),c_Type_Osko__Type__Xlist__app__typeE__1__1(X2,X1,X0,c_List_Olist_ONil(tc_Lambda_OdB))) )
    | ~ spl0_58
    | ~ spl0_181 ),
    inference(superposition,[],[f2113,f756]) ).

fof(f2113,plain,
    ( ! [X18,X26,X27,X17] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeE__1__1(X18,X17,X27,X26)) )
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f2112]) ).

fof(f7986,plain,
    ( spl0_439
    | ~ spl0_84
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2212,f2108,f894,f7984]) ).

fof(f7984,plain,
    ( spl0_439
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f2212,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_84
    | ~ spl0_180 ),
    inference(superposition,[],[f895,f2109]) ).

fof(f7962,plain,
    ( spl0_438
    | ~ spl0_235
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f5993,f5589,f2974,f7960]) ).

fof(f7960,plain,
    ( spl0_438
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f5993,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2)),X3),X4)
    | ~ spl0_235
    | ~ spl0_340 ),
    inference(resolution,[],[f5590,f2975]) ).

fof(f7958,plain,
    ( spl0_437
    | ~ spl0_29
    | ~ spl0_183
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f7954,f7951,f2131,f637,f7956]) ).

fof(f7956,plain,
    ( spl0_437
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f7951,plain,
    ( spl0_436
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f7954,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X0)
    | ~ spl0_29
    | ~ spl0_183
    | ~ spl0_436 ),
    inference(forward_demodulation,[],[f7952,f2249]) ).

fof(f7952,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,X0)
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f7951]) ).

fof(f7953,plain,
    ( spl0_436
    | ~ spl0_82
    | ~ spl0_85
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2009,f1876,f898,f872,f7951]) ).

fof(f2009,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,X0)
    | ~ spl0_82
    | ~ spl0_85
    | ~ spl0_169 ),
    inference(forward_demodulation,[],[f1985,f899]) ).

fof(f1985,plain,
    ( ! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))),X1,X0) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_82
    | ~ spl0_169 ),
    inference(resolution,[],[f1877,f873]) ).

fof(f7949,plain,
    ( spl0_435
    | ~ spl0_53
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1798,f1653,f733,f7947]) ).

fof(f7947,plain,
    ( spl0_435
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat)))),X1)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f1798,plain,
    ( ! [X0,X1] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat)))),X1)),X0))
    | ~ spl0_53
    | ~ spl0_159 ),
    inference(superposition,[],[f1654,f734]) ).

fof(f7945,plain,
    ( spl0_434
    | ~ spl0_49
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f1764,f1637,f717,f7943]) ).

fof(f7943,plain,
    ( spl0_434
  <=> ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2))
        | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f717,plain,
    ( spl0_49
  <=> ! [X6] : c_fequal(X6) = c_Predicate_Oconversep(c_fequal(X6),X6,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f1637,plain,
    ( spl0_155
  <=> ! [X6,X4,X19,X5,X22] :
        ( ~ hBOOL(hAPP(hAPP(X19,X4),X5))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X19,X6,X22),X5),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1764,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(hAPP(hAPP(c_fequal(X0),X1),X2))
        | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1)) )
    | ~ spl0_49
    | ~ spl0_155 ),
    inference(superposition,[],[f1638,f718]) ).

fof(f718,plain,
    ( ! [X6] : c_fequal(X6) = c_Predicate_Oconversep(c_fequal(X6),X6,X6)
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f717]) ).

fof(f1638,plain,
    ( ! [X19,X6,X4,X22,X5] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X19,X6,X22),X5),X4))
        | ~ hBOOL(hAPP(hAPP(X19,X4),X5)) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1637]) ).

fof(f7941,plain,
    ( spl0_433
    | ~ spl0_147
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1746,f1621,f1434,f7939]) ).

fof(f7939,plain,
    ( spl0_433
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f1746,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)))
    | ~ spl0_147
    | ~ spl0_151 ),
    inference(superposition,[],[f1622,f1435]) ).

fof(f7937,plain,
    ( spl0_432
    | ~ spl0_46
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1610,f1434,f705,f7935]) ).

fof(f7935,plain,
    ( spl0_432
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)),c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f1610,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)),c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB))
    | ~ spl0_46
    | ~ spl0_147 ),
    inference(superposition,[],[f706,f1435]) ).

fof(f7933,plain,
    ( spl0_431
    | ~ spl0_111
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1585,f1434,f1136,f7931]) ).

fof(f7931,plain,
    ( spl0_431
  <=> ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f1585,plain,
    ( ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB))
    | ~ spl0_111
    | ~ spl0_147 ),
    inference(superposition,[],[f1435,f1137]) ).

fof(f7929,plain,
    ( spl0_430
    | ~ spl0_111
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1579,f1430,f1136,f7927]) ).

fof(f7927,plain,
    ( spl0_430
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1579,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_111
    | ~ spl0_146 ),
    inference(superposition,[],[f1431,f1137]) ).

fof(f7925,plain,
    ( spl0_429
    | ~ spl0_111
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1560,f1426,f1136,f7923]) ).

fof(f7923,plain,
    ( spl0_429
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f1560,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_111
    | ~ spl0_145 ),
    inference(superposition,[],[f1427,f1137]) ).

fof(f7921,plain,
    ( spl0_428
    | ~ spl0_51
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1532,f1394,f725,f7919]) ).

fof(f7919,plain,
    ( spl0_428
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f725,plain,
    ( spl0_51
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oone__class_Oone(X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1532,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_51
    | ~ spl0_137 ),
    inference(resolution,[],[f1395,f726]) ).

fof(f726,plain,
    ( ! [X6] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oone__class_Oone(X6),X6)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f725]) ).

fof(f7917,plain,
    ( spl0_427
    | ~ spl0_235
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f5892,f5545,f2974,f7915]) ).

fof(f7915,plain,
    ( spl0_427
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f5892,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)),X3),X4)
    | ~ spl0_235
    | ~ spl0_329 ),
    inference(resolution,[],[f5546,f2975]) ).

fof(f7913,plain,
    ( spl0_426
    | ~ spl0_51
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1514,f1390,f725,f7911]) ).

fof(f7911,plain,
    ( spl0_426
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f1514,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_51
    | ~ spl0_136 ),
    inference(resolution,[],[f1391,f726]) ).

fof(f7909,plain,
    ( spl0_425
    | ~ spl0_60
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1259,f1140,f763,f7907]) ).

fof(f7907,plain,
    ( spl0_425
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f1259,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X1,tc_nat)
    | ~ spl0_60
    | ~ spl0_112 ),
    inference(forward_demodulation,[],[f1252,f192]) ).

fof(f192,axiom,
    ! [X2,X1,X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X13) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

fof(f1252,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)),X2),X1,tc_nat)
    | ~ spl0_60
    | ~ spl0_112 ),
    inference(resolution,[],[f1141,f764]) ).

fof(f7905,plain,
    ( spl0_424
    | ~ spl0_61
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1253,f1140,f767,f7903]) ).

fof(f7903,plain,
    ( spl0_424
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f1253,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2,tc_nat)
    | ~ spl0_61
    | ~ spl0_112 ),
    inference(resolution,[],[f1141,f768]) ).

fof(f7901,plain,
    ( spl0_423
    | ~ spl0_82
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1106,f1056,f872,f7899]) ).

fof(f7899,plain,
    ( spl0_423
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f1106,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_82
    | ~ spl0_106 ),
    inference(resolution,[],[f1057,f873]) ).

fof(f7897,plain,
    ( spl0_422
    | ~ spl0_70
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f1101,f1056,f803,f7895]) ).

fof(f7895,plain,
    ( spl0_422
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f1101,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_70
    | ~ spl0_106 ),
    inference(resolution,[],[f1057,f804]) ).

fof(f7893,plain,
    ( spl0_421
    | ~ spl0_76
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f1093,f1039,f848,f7891]) ).

fof(f7891,plain,
    ( spl0_421
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f1039,plain,
    ( spl0_102
  <=> ! [X6,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Oone__class_Oone(X6)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1093,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0) )
    | ~ spl0_76
    | ~ spl0_102 ),
    inference(resolution,[],[f1040,f849]) ).

fof(f1040,plain,
    ( ! [X6,X4] :
        ( c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Oone__class_Oone(X6)),X6)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f1039]) ).

fof(f7889,plain,
    ( spl0_420
    | ~ spl0_77
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f1092,f1039,f852,f7887]) ).

fof(f7887,plain,
    ( spl0_420
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f1092,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0) )
    | ~ spl0_77
    | ~ spl0_102 ),
    inference(resolution,[],[f1040,f853]) ).

fof(f7885,plain,
    ( spl0_419
    | ~ spl0_78
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f1091,f1039,f856,f7883]) ).

fof(f7883,plain,
    ( spl0_419
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f1091,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_78
    | ~ spl0_102 ),
    inference(resolution,[],[f1040,f857]) ).

fof(f7881,plain,
    ( spl0_418
    | ~ spl0_86
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f1075,f1027,f902,f7879]) ).

fof(f7879,plain,
    ( spl0_418
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f1075,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) )
    | ~ spl0_86
    | ~ spl0_99 ),
    inference(superposition,[],[f1028,f903]) ).

fof(f7877,plain,
    ( spl0_417
    | ~ spl0_85
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f1074,f1027,f898,f7875]) ).

fof(f7875,plain,
    ( spl0_417
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f1074,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat) )
    | ~ spl0_85
    | ~ spl0_99 ),
    inference(superposition,[],[f1028,f899]) ).

fof(f7873,plain,
    ( spl0_416
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5663,f5466,f2974,f7871]) ).

fof(f7871,plain,
    ( spl0_416
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f5663,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3),X4)
    | ~ spl0_235
    | ~ spl0_323 ),
    inference(resolution,[],[f5467,f2975]) ).

fof(f7869,plain,
    ( spl0_415
    | ~ spl0_95
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f993,f947,f938,f7867]) ).

fof(f7867,plain,
    ( spl0_415
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f993,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) )
    | ~ spl0_95
    | ~ spl0_97 ),
    inference(resolution,[],[f948,f939]) ).

fof(f7554,plain,
    ( spl0_414
    | ~ spl0_256
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f5365,f5297,f3694,f7552]) ).

fof(f7552,plain,
    ( spl0_414
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f5297,plain,
    ( spl0_311
  <=> ! [X2,X0,X1,X3] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f5365,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2),X3,tc_Lambda_OdB,tc_Lambda_OdB),X4)
    | ~ spl0_256
    | ~ spl0_311 ),
    inference(resolution,[],[f5298,f3695]) ).

fof(f5298,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2),X3)
    | ~ spl0_311 ),
    inference(avatar_component_clause,[],[f5297]) ).

fof(f7215,plain,
    ( spl0_413
    | ~ spl0_40
    | ~ spl0_67
    | ~ spl0_147
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4576,f4289,f1434,f791,f681,f7213]) ).

fof(f7213,plain,
    ( spl0_413
  <=> ! [X0,X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f681,plain,
    ( spl0_40
  <=> ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X0),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f4576,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB)
    | ~ spl0_40
    | ~ spl0_67
    | ~ spl0_147
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f4575,f1435]) ).

fof(f4575,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_40
    | ~ spl0_67
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f4482,f792]) ).

fof(f4482,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_40
    | ~ spl0_276 ),
    inference(superposition,[],[f4290,f682]) ).

fof(f682,plain,
    ( ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X0),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f681]) ).

fof(f7211,plain,
    ( spl0_412
    | ~ spl0_40
    | ~ spl0_68
    | ~ spl0_147
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4574,f4289,f1434,f795,f681,f7209]) ).

fof(f7209,plain,
    ( spl0_412
  <=> ! [X0,X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1),tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f4574,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X1),tc_Lambda_OdB) = c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1),tc_Lambda_OdB)
    | ~ spl0_40
    | ~ spl0_68
    | ~ spl0_147
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f4573,f1435]) ).

fof(f4573,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_40
    | ~ spl0_68
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f4481,f796]) ).

fof(f4481,plain,
    ( ! [X0,X1] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osize__class_Osize(X1,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_40
    | ~ spl0_276 ),
    inference(superposition,[],[f4290,f682]) ).

fof(f7207,plain,
    ( spl0_411
    | ~ spl0_58
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4216,f3891,f755,f7205]) ).

fof(f7205,plain,
    ( spl0_411
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X2)
        | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X3)
        | X2 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f3891,plain,
    ( spl0_266
  <=> ! [X18,X11,X17,X28,X26] :
        ( X18 = X28
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f4216,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X2)
        | ~ c_Type_Otyping(X1,c_Lambda_OdB_OVar(X0),X3)
        | X2 = X3 )
    | ~ spl0_58
    | ~ spl0_266 ),
    inference(superposition,[],[f3892,f756]) ).

fof(f3892,plain,
    ( ! [X28,X11,X18,X26,X17] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28)
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | X18 = X28 )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f3891]) ).

fof(f7203,plain,
    ( spl0_410
    | ~ spl0_58
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f2671,f2439,f755,f7201]) ).

fof(f7201,plain,
    ( spl0_410
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f2439,plain,
    ( spl0_208
  <=> ! [X34,X46,X2,X1] :
        ( X1 = X2
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X34,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f2671,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
        | X0 = X1 )
    | ~ spl0_58
    | ~ spl0_208 ),
    inference(superposition,[],[f2440,f756]) ).

fof(f2440,plain,
    ( ! [X2,X46,X1,X34] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X34,tc_Lambda_OdB,tc_Lambda_OdB)
        | X1 = X2 )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f2439]) ).

fof(f7199,plain,
    ( spl0_409
    | ~ spl0_58
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2664,f2431,f755,f7197]) ).

fof(f7197,plain,
    ( spl0_409
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f2431,plain,
    ( spl0_206
  <=> ! [X34,X46,X19,X25] :
        ( X19 = X25
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X34,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X46,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f2664,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
        | X0 = X1 )
    | ~ spl0_58
    | ~ spl0_206 ),
    inference(superposition,[],[f2432,f756]) ).

fof(f2432,plain,
    ( ! [X46,X19,X34,X25] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X34,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X46,tc_Lambda_OdB,tc_Lambda_OdB)
        | X19 = X25 )
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f2431]) ).

fof(f7195,plain,
    ( spl0_408
    | ~ spl0_114
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f2562,f2375,f1148,f7193]) ).

fof(f7193,plain,
    ( spl0_408
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f1148,plain,
    ( spl0_114
  <=> ! [X13,X12,X11] :
        ( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f2562,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat) )
    | ~ spl0_114
    | ~ spl0_195 ),
    inference(resolution,[],[f2376,f1149]) ).

fof(f1149,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X13,tc_nat)
        | c_HOL_Oord__class_Oless(X11,X13,tc_nat) )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f1148]) ).

fof(f7191,plain,
    ( spl0_407
    | ~ spl0_124
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2310,f2143,f1190,f7189]) ).

fof(f7189,plain,
    ( spl0_407
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f2310,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 )
    | ~ spl0_124
    | ~ spl0_186 ),
    inference(resolution,[],[f2144,f1191]) ).

fof(f7187,plain,
    ( spl0_406
    | ~ spl0_235
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f5364,f5297,f2974,f7185]) ).

fof(f7185,plain,
    ( spl0_406
  <=> ! [X4,X0,X3,X2,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2)),X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f5364,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2)),X3),X4)
    | ~ spl0_235
    | ~ spl0_311 ),
    inference(resolution,[],[f5298,f2975]) ).

fof(f7183,plain,
    ( spl0_405
    | ~ spl0_24
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2244,f2131,f614,f7181]) ).

fof(f7181,plain,
    ( spl0_405
  <=> ! [X0] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f614,plain,
    ( spl0_24
  <=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f2244,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_24
    | ~ spl0_183 ),
    inference(resolution,[],[f2132,f615]) ).

fof(f615,plain,
    ( ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f614]) ).

fof(f7179,plain,
    ( spl0_404
    | ~ spl0_41
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f2094,f1908,f685,f7177]) ).

fof(f7177,plain,
    ( spl0_404
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f685,plain,
    ( spl0_41
  <=> ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f2094,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_41
    | ~ spl0_177 ),
    inference(superposition,[],[f1909,f686]) ).

fof(f686,plain,
    ( ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f685]) ).

fof(f7175,plain,
    ( spl0_403
    | ~ spl0_45
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1797,f1653,f701,f7173]) ).

fof(f7173,plain,
    ( spl0_403
  <=> ! [X0] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f1797,plain,
    ( ! [X0] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)))),X0)),X0))
    | ~ spl0_45
    | ~ spl0_159 ),
    inference(superposition,[],[f1654,f702]) ).

fof(f7171,plain,
    ( spl0_402
    | ~ spl0_114
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1607,f1434,f1148,f7169]) ).

fof(f7169,plain,
    ( spl0_402
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1607,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) )
    | ~ spl0_114
    | ~ spl0_147 ),
    inference(superposition,[],[f1149,f1435]) ).

fof(f7167,plain,
    ( spl0_401
    | ~ spl0_113
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1606,f1434,f1144,f7165]) ).

fof(f7165,plain,
    ( spl0_401
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f1606,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat) )
    | ~ spl0_113
    | ~ spl0_147 ),
    inference(superposition,[],[f1145,f1435]) ).

fof(f7163,plain,
    ( spl0_400
    | ~ spl0_146
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1593,f1434,f1430,f7161]) ).

fof(f7161,plain,
    ( spl0_400
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f1593,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) )
    | ~ spl0_146
    | ~ spl0_147 ),
    inference(superposition,[],[f1431,f1435]) ).

fof(f7159,plain,
    ( spl0_399
    | ~ spl0_145
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1592,f1434,f1426,f7157]) ).

fof(f7157,plain,
    ( spl0_399
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f1592,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat) )
    | ~ spl0_145
    | ~ spl0_147 ),
    inference(superposition,[],[f1427,f1435]) ).

fof(f7119,plain,
    ( ~ spl0_7
    | spl0_398
    | ~ spl0_70
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1491,f1374,f803,f7117,f530]) ).

fof(f530,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f7117,plain,
    ( spl0_398
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f1374,plain,
    ( spl0_132
  <=> ! [X6,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1491,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) )
    | ~ spl0_70
    | ~ spl0_132 ),
    inference(resolution,[],[f1375,f804]) ).

fof(f1375,plain,
    ( ! [X2,X6] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X6) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1374]) ).

fof(f7115,plain,
    ( spl0_397
    | ~ spl0_68
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1450,f1354,f795,f7113]) ).

fof(f7113,plain,
    ( spl0_397
  <=> ! [X0,X1] :
        ( ~ hBOOL(X0)
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1450,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(X0)
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1) )
    | ~ spl0_68
    | ~ spl0_127 ),
    inference(superposition,[],[f1355,f796]) ).

fof(f7105,plain,
    ( spl0_396
    | ~ spl0_67
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1447,f1354,f791,f7103]) ).

fof(f7103,plain,
    ( spl0_396
  <=> ! [X0,X1] :
        ( ~ hBOOL(X0)
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1447,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(X0)
        | c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),X0,X1)
        | ~ c_Wellfounded_Oaccp(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),X1) )
    | ~ spl0_67
    | ~ spl0_127 ),
    inference(superposition,[],[f1355,f792]) ).

fof(f7101,plain,
    ( spl0_395
    | ~ spl0_111
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1342,f1190,f1136,f7099]) ).

fof(f7099,plain,
    ( spl0_395
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f1342,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
    | ~ spl0_111
    | ~ spl0_124 ),
    inference(superposition,[],[f1191,f1137]) ).

fof(f7097,plain,
    ( spl0_394
    | ~ spl0_46
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1225,f1136,f705,f7095]) ).

fof(f7095,plain,
    ( spl0_394
  <=> ! [X0,X1] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1225,plain,
    ( ! [X0,X1] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0))
    | ~ spl0_46
    | ~ spl0_111 ),
    inference(superposition,[],[f706,f1137]) ).

fof(f7093,plain,
    ( spl0_393
    | ~ spl0_73
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f995,f947,f815,f7091]) ).

fof(f7091,plain,
    ( spl0_393
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f995,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_73
    | ~ spl0_97 ),
    inference(resolution,[],[f948,f816]) ).

fof(f7089,plain,
    ( spl0_392
    | ~ spl0_82
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f990,f938,f872,f7087]) ).

fof(f7087,plain,
    ( spl0_392
  <=> ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f990,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_82
    | ~ spl0_95 ),
    inference(resolution,[],[f939,f873]) ).

fof(f7085,plain,
    ( spl0_391
    | ~ spl0_70
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f989,f938,f803,f7083]) ).

fof(f7083,plain,
    ( spl0_391
  <=> ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f989,plain,
    ( ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_70
    | ~ spl0_95 ),
    inference(resolution,[],[f939,f804]) ).

fof(f7081,plain,
    ( spl0_390
    | ~ spl0_84
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f975,f902,f894,f7079]) ).

fof(f7079,plain,
    ( spl0_390
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f975,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),X2,tc_nat) )
    | ~ spl0_84
    | ~ spl0_86 ),
    inference(superposition,[],[f895,f903]) ).

fof(f7027,plain,
    ( spl0_389
    | ~ spl0_256
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5187,f5138,f3694,f7025]) ).

fof(f5138,plain,
    ( spl0_299
  <=> ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f5187,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_256
    | ~ spl0_299 ),
    inference(resolution,[],[f5139,f3695]) ).

fof(f5139,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f5138]) ).

fof(f6624,plain,
    ( spl0_388
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_162
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4579,f4289,f1665,f1434,f1136,f6622]) ).

fof(f6622,plain,
    ( spl0_388
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f4579,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_Lambda_OdB),tc_nat)
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_162
    | ~ spl0_276 ),
    inference(forward_demodulation,[],[f4516,f1585]) ).

fof(f4516,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB)),tc_nat)
    | ~ spl0_162
    | ~ spl0_276 ),
    inference(superposition,[],[f1666,f4290]) ).

fof(f6620,plain,
    ( spl0_387
    | ~ spl0_112
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2298,f2143,f1140,f6618]) ).

fof(f6618,plain,
    ( spl0_387
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f2298,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_186 ),
    inference(resolution,[],[f2144,f1141]) ).

fof(f6616,plain,
    ( spl0_386
    | ~ spl0_48
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f2195,f2104,f713,f6614]) ).

fof(f6614,plain,
    ( spl0_386
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f2104,plain,
    ( spl0_179
  <=> ! [X2,X1] :
        ( X1 = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f2195,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_48
    | ~ spl0_179 ),
    inference(trivial_inequality_removal,[],[f2190]) ).

fof(f2190,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_48
    | ~ spl0_179 ),
    inference(superposition,[],[f2105,f714]) ).

fof(f2105,plain,
    ( ! [X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f2104]) ).

fof(f6612,plain,
    ( spl0_385
    | ~ spl0_58
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2071,f1904,f755,f6610]) ).

fof(f6610,plain,
    ( spl0_385
  <=> ! [X0,X1] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f1904,plain,
    ( spl0_176
  <=> ! [X25,X19,X26] :
        ( X19 = X25
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X26,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f2071,plain,
    ( ! [X0,X1] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != X0
        | X0 = X1 )
    | ~ spl0_58
    | ~ spl0_176 ),
    inference(superposition,[],[f1905,f756]) ).

fof(f1905,plain,
    ( ! [X19,X26,X25] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X26,tc_Lambda_OdB,tc_Lambda_OdB)
        | X19 = X25 )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1904]) ).

fof(f6608,plain,
    ( spl0_384
    | ~ spl0_67
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2054,f1888,f791,f6606]) ).

fof(f6606,plain,
    ( spl0_384
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f2054,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) != X0
        | X0 = X1 )
    | ~ spl0_67
    | ~ spl0_172 ),
    inference(superposition,[],[f1889,f792]) ).

fof(f6604,plain,
    ( spl0_383
    | ~ spl0_68
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2045,f1884,f795,f6602]) ).

fof(f6602,plain,
    ( spl0_383
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f2045,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X1) != X0
        | X0 = X1 )
    | ~ spl0_68
    | ~ spl0_171 ),
    inference(superposition,[],[f1885,f796]) ).

fof(f6595,plain,
    ( spl0_381
    | spl0_382
    | ~ spl0_67
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1929,f1860,f795,f791,f6592,f6589]) ).

fof(f6589,plain,
    ( spl0_381
  <=> ! [X0,X1] :
        ( ~ hBOOL(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f6592,plain,
    ( spl0_382
  <=> hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1929,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_HOL_Ozero__class_Ozero(tc_nat))
        | ~ hBOOL(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_67
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(forward_demodulation,[],[f1925,f792]) ).

fof(f1925,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
        | hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_68
    | ~ spl0_165 ),
    inference(superposition,[],[f1861,f796]) ).

fof(f6587,plain,
    ( spl0_380
    | ~ spl0_108
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1748,f1621,f1064,f6585]) ).

fof(f6585,plain,
    ( spl0_380
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OdB__size(X0)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f1748,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),c_Lambda_OdB_OdB__size(X0)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))))
    | ~ spl0_108
    | ~ spl0_151 ),
    inference(superposition,[],[f1622,f1065]) ).

fof(f6583,plain,
    ( spl0_379
    | ~ spl0_112
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1605,f1434,f1140,f6581]) ).

fof(f6581,plain,
    ( spl0_379
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f1605,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_147 ),
    inference(superposition,[],[f1141,f1435]) ).

fof(f6579,plain,
    ( spl0_378
    | ~ spl0_101
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1599,f1434,f1035,f6577]) ).

fof(f6577,plain,
    ( spl0_378
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1599,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
    | ~ spl0_101
    | ~ spl0_147 ),
    inference(superposition,[],[f1036,f1435]) ).

fof(f6575,plain,
    ( spl0_377
    | ~ spl0_86
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1598,f1434,f902,f6573]) ).

fof(f6573,plain,
    ( spl0_377
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f1598,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat)
    | ~ spl0_86
    | ~ spl0_147 ),
    inference(superposition,[],[f903,f1435]) ).

fof(f6571,plain,
    ( spl0_376
    | ~ spl0_85
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1597,f1434,f898,f6569]) ).

fof(f6569,plain,
    ( spl0_376
  <=> ! [X0] : c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f1597,plain,
    ( ! [X0] : c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_85
    | ~ spl0_147 ),
    inference(superposition,[],[f899,f1435]) ).

fof(f6567,plain,
    ( spl0_375
    | ~ spl0_124
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1591,f1434,f1190,f6565]) ).

fof(f6565,plain,
    ( spl0_375
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f1591,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),X1,tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
    | ~ spl0_124
    | ~ spl0_147 ),
    inference(superposition,[],[f1191,f1435]) ).

fof(f6563,plain,
    ( spl0_374
    | ~ spl0_104
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1215,f1136,f1048,f6561]) ).

fof(f6561,plain,
    ( spl0_374
  <=> ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f1048,plain,
    ( spl0_104
  <=> ! [X4,X7] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X4) != X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f1215,plain,
    ( ! [X0,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_104
    | ~ spl0_111 ),
    inference(superposition,[],[f1049,f1137]) ).

fof(f1049,plain,
    ( ! [X7,X4] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X4) != X7
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f1048]) ).

fof(f6559,plain,
    ( spl0_373
    | ~ spl0_101
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1214,f1136,f1035,f6557]) ).

fof(f6557,plain,
    ( spl0_373
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1214,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat)
    | ~ spl0_101
    | ~ spl0_111 ),
    inference(superposition,[],[f1036,f1137]) ).

fof(f6550,plain,
    ( spl0_372
    | ~ spl0_108
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1205,f1136,f1064,f6548]) ).

fof(f6548,plain,
    ( spl0_372
  <=> ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f6546,plain,
    ( spl0_371
    | ~ spl0_46
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1125,f1064,f705,f6544]) ).

fof(f6544,plain,
    ( spl0_371
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f1125,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X0)),c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)))
    | ~ spl0_46
    | ~ spl0_108 ),
    inference(superposition,[],[f706,f1065]) ).

fof(f6542,plain,
    ( spl0_370
    | ~ spl0_73
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f956,f894,f815,f6540]) ).

fof(f6540,plain,
    ( spl0_370
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f956,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
    | ~ spl0_73
    | ~ spl0_84 ),
    inference(resolution,[],[f895,f816]) ).

fof(f6420,plain,
    ( spl0_369
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5186,f5138,f2974,f6418]) ).

fof(f5186,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3)
    | ~ spl0_235
    | ~ spl0_299 ),
    inference(resolution,[],[f5139,f2975]) ).

fof(f6164,plain,
    ( spl0_368
    | ~ spl0_256
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f5056,f4628,f3694,f6162]) ).

fof(f4628,plain,
    ( spl0_284
  <=> ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f5056,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_256
    | ~ spl0_284 ),
    inference(resolution,[],[f4629,f3695]) ).

fof(f4629,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2)
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f4628]) ).

fof(f6072,plain,
    ( spl0_367
    | ~ spl0_61
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4503,f4289,f767,f6070]) ).

fof(f6070,plain,
    ( spl0_367
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f4503,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_276 ),
    inference(superposition,[],[f768,f4290]) ).

fof(f6068,plain,
    ( spl0_366
    | ~ spl0_98
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4491,f4289,f951,f6066]) ).

fof(f6066,plain,
    ( spl0_366
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f4491,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB),tc_nat)
    | ~ spl0_98
    | ~ spl0_276 ),
    inference(superposition,[],[f952,f4290]) ).

fof(f6064,plain,
    ( spl0_365
    | ~ spl0_61
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f4395,f4285,f767,f6062]) ).

fof(f6062,plain,
    ( spl0_365
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f4395,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_275 ),
    inference(superposition,[],[f768,f4286]) ).

fof(f6060,plain,
    ( spl0_364
    | ~ spl0_98
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f4383,f4285,f951,f6058]) ).

fof(f6058,plain,
    ( spl0_364
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f4383,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype),tc_nat)
    | ~ spl0_98
    | ~ spl0_275 ),
    inference(superposition,[],[f952,f4286]) ).

fof(f6056,plain,
    ( spl0_363
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_162
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3649,f3443,f1665,f1136,f1064,f6054]) ).

fof(f6054,plain,
    ( spl0_363
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f3649,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat)
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_162
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3593,f1205]) ).

fof(f3593,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))),tc_nat)
    | ~ spl0_162
    | ~ spl0_248 ),
    inference(superposition,[],[f1666,f3444]) ).

fof(f6052,plain,
    ( spl0_362
    | ~ spl0_32
    | ~ spl0_67
    | ~ spl0_108
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3645,f3443,f1064,f791,f649,f6050]) ).

fof(f6050,plain,
    ( spl0_362
  <=> ! [X0,X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f649,plain,
    ( spl0_32
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f3645,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0)))
    | ~ spl0_32
    | ~ spl0_67
    | ~ spl0_108
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3644,f1065]) ).

fof(f3644,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_32
    | ~ spl0_67
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3560,f792]) ).

fof(f3560,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X1),c_Lambda_OdB_OVar(X0))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_32
    | ~ spl0_248 ),
    inference(superposition,[],[f3444,f650]) ).

fof(f650,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0))
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f649]) ).

fof(f6048,plain,
    ( spl0_361
    | ~ spl0_32
    | ~ spl0_68
    | ~ spl0_108
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3641,f3443,f1064,f795,f649,f6046]) ).

fof(f6046,plain,
    ( spl0_361
  <=> ! [X0,X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f3641,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X1)) = c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1))
    | ~ spl0_32
    | ~ spl0_68
    | ~ spl0_108
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3640,f1065]) ).

fof(f3640,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X1)),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_32
    | ~ spl0_68
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f3558,f796]) ).

fof(f3558,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0)),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OdB__size(X1))),c_HOL_Oone__class_Oone(tc_nat))
    | ~ spl0_32
    | ~ spl0_248 ),
    inference(superposition,[],[f3444,f650]) ).

fof(f6044,plain,
    ( spl0_360
    | ~ spl0_56
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3368,f2990,f745,f6042]) ).

fof(f6042,plain,
    ( spl0_360
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f745,plain,
    ( spl0_56
  <=> ! [X41,X40,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != c_Lambda_OdB_OAbs(X49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f2990,plain,
    ( spl0_239
  <=> ! [X13,X36,X27,X25] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X25,X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X27,X25,X13)),c_Lambda_Osubst(X36,X25,X13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f3368,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2)
    | ~ spl0_56
    | ~ spl0_239 ),
    inference(superposition,[],[f746,f2991]) ).

fof(f2991,plain,
    ( ! [X36,X27,X25,X13] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X25,X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X27,X25,X13)),c_Lambda_Osubst(X36,X25,X13))
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f2990]) ).

fof(f746,plain,
    ( ! [X40,X41,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != c_Lambda_OdB_OAbs(X49)
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f745]) ).

fof(f6040,plain,
    ( spl0_359
    | ~ spl0_256
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4672,f4596,f3694,f6038]) ).

fof(f4596,plain,
    ( spl0_277
  <=> ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f4672,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_256
    | ~ spl0_277 ),
    inference(resolution,[],[f4597,f3695]) ).

fof(f4597,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f4596]) ).

fof(f6036,plain,
    ( spl0_358
    | ~ spl0_55
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3367,f2990,f741,f6034]) ).

fof(f6034,plain,
    ( spl0_358
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f741,plain,
    ( spl0_55
  <=> ! [X48,X0,X47] : c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f3367,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2)
    | ~ spl0_55
    | ~ spl0_239 ),
    inference(superposition,[],[f742,f2991]) ).

fof(f742,plain,
    ( ! [X48,X0,X47] : c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f6032,plain,
    ( spl0_357
    | ~ spl0_56
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3299,f2961,f745,f6030]) ).

fof(f6030,plain,
    ( spl0_357
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f3299,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != hAPP(hAPP(c_Lambda_OdB_OApp,X3),X4)
    | ~ spl0_56
    | ~ spl0_232 ),
    inference(superposition,[],[f746,f2962]) ).

fof(f6028,plain,
    ( spl0_356
    | ~ spl0_114
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1956,f1868,f1148,f6026]) ).

fof(f6026,plain,
    ( spl0_356
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f1956,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_114
    | ~ spl0_167 ),
    inference(resolution,[],[f1869,f1149]) ).

fof(f6024,plain,
    ( spl0_355
    | ~ spl0_68
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1747,f1621,f795,f6022]) ).

fof(f6022,plain,
    ( spl0_355
  <=> ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f1747,plain,
    ( ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_68
    | ~ spl0_151 ),
    inference(superposition,[],[f1622,f796]) ).

fof(f6020,plain,
    ( spl0_354
    | ~ spl0_108
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1582,f1430,f1064,f6018]) ).

fof(f6018,plain,
    ( spl0_354
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f1582,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_146 ),
    inference(superposition,[],[f1431,f1065]) ).

fof(f6016,plain,
    ( spl0_353
    | ~ spl0_108
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1563,f1426,f1064,f6014]) ).

fof(f6014,plain,
    ( spl0_353
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f1563,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_145 ),
    inference(superposition,[],[f1427,f1065]) ).

fof(f6012,plain,
    ( spl0_352
    | ~ spl0_108
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1287,f1148,f1064,f6010]) ).

fof(f6010,plain,
    ( spl0_352
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f1287,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),X1,tc_nat) )
    | ~ spl0_108
    | ~ spl0_114 ),
    inference(superposition,[],[f1149,f1065]) ).

fof(f6008,plain,
    ( spl0_351
    | ~ spl0_108
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1275,f1144,f1064,f6006]) ).

fof(f6006,plain,
    ( spl0_351
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f1275,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(X0),tc_nat) )
    | ~ spl0_108
    | ~ spl0_113 ),
    inference(superposition,[],[f1145,f1065]) ).

fof(f6004,plain,
    ( spl0_350
    | ~ spl0_108
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1258,f1140,f1064,f6002]) ).

fof(f6002,plain,
    ( spl0_350
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f1258,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_108
    | ~ spl0_112 ),
    inference(superposition,[],[f1141,f1065]) ).

fof(f6000,plain,
    ( spl0_349
    | ~ spl0_98
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1219,f1136,f951,f5998]) ).

fof(f5998,plain,
    ( spl0_349
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f1219,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
    | ~ spl0_98
    | ~ spl0_111 ),
    inference(superposition,[],[f952,f1137]) ).

fof(f5992,plain,
    ( spl0_348
    | ~ spl0_70
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f1077,f1031,f803,f5990]) ).

fof(f5990,plain,
    ( spl0_348
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1031,plain,
    ( spl0_100
  <=> ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1077,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) )
    | ~ spl0_70
    | ~ spl0_100 ),
    inference(resolution,[],[f1032,f804]) ).

fof(f1032,plain,
    ( ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f1031]) ).

fof(f5619,plain,
    ( spl0_347
    | ~ spl0_81
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4489,f4289,f868,f5617]) ).

fof(f5617,plain,
    ( spl0_347
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f4489,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1),tc_Lambda_OdB)
    | ~ spl0_81
    | ~ spl0_276 ),
    inference(superposition,[],[f869,f4290]) ).

fof(f5615,plain,
    ( spl0_346
    | ~ spl0_81
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f4381,f4285,f868,f5613]) ).

fof(f5613,plain,
    ( spl0_346
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f4381,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X0),X1),tc_Type_Otype)
    | ~ spl0_81
    | ~ spl0_275 ),
    inference(superposition,[],[f869,f4286]) ).

fof(f5611,plain,
    ( spl0_345
    | ~ spl0_61
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3580,f3443,f767,f5609]) ).

fof(f5609,plain,
    ( spl0_345
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f3580,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_248 ),
    inference(superposition,[],[f768,f3444]) ).

fof(f5607,plain,
    ( spl0_344
    | ~ spl0_98
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3569,f3443,f951,f5605]) ).

fof(f5605,plain,
    ( spl0_344
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f3569,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)),tc_nat)
    | ~ spl0_98
    | ~ spl0_248 ),
    inference(superposition,[],[f952,f3444]) ).

fof(f5603,plain,
    ( spl0_343
    | ~ spl0_61
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3484,f3439,f767,f5601]) ).

fof(f5601,plain,
    ( spl0_343
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f3484,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_247 ),
    inference(superposition,[],[f768,f3440]) ).

fof(f5599,plain,
    ( spl0_342
    | ~ spl0_98
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3473,f3439,f951,f5597]) ).

fof(f5597,plain,
    ( spl0_342
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f3473,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)),tc_nat)
    | ~ spl0_98
    | ~ spl0_247 ),
    inference(superposition,[],[f952,f3440]) ).

fof(f5595,plain,
    ( spl0_341
    | ~ spl0_224
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3173,f2937,f2929,f5593]) ).

fof(f5593,plain,
    ( spl0_341
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f2929,plain,
    ( spl0_224
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
        | c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f2937,plain,
    ( spl0_226
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f3173,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) )
    | ~ spl0_224
    | ~ spl0_226 ),
    inference(duplicate_literal_removal,[],[f3143]) ).

fof(f3143,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_224
    | ~ spl0_226 ),
    inference(resolution,[],[f2938,f2930]) ).

fof(f2930,plain,
    ( ! [X6,X4,X5,X23] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6)
        | c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6) )
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2929]) ).

fof(f2938,plain,
    ( ! [X6,X4,X5,X23] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2937]) ).

fof(f5591,plain,
    ( spl0_340
    | ~ spl0_235
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f5055,f4628,f2974,f5589]) ).

fof(f5055,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1)),X2),X3)
    | ~ spl0_235
    | ~ spl0_284 ),
    inference(resolution,[],[f4629,f2975]) ).

fof(f5587,plain,
    ( spl0_339
    | ~ spl0_56
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2286,f2139,f745,f5585]) ).

fof(f5585,plain,
    ( spl0_339
  <=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OAbs(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f2286,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_OdB_OAbs(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1)
    | ~ spl0_56
    | ~ spl0_185 ),
    inference(superposition,[],[f746,f2140]) ).

fof(f5583,plain,
    ( spl0_338
    | ~ spl0_55
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2285,f2139,f741,f5581]) ).

fof(f5581,plain,
    ( spl0_338
  <=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OVar(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f2285,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_OdB_OVar(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1)
    | ~ spl0_55
    | ~ spl0_185 ),
    inference(superposition,[],[f742,f2140]) ).

fof(f5579,plain,
    ( spl0_337
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1840,f1661,f1434,f1136,f5577]) ).

fof(f5577,plain,
    ( spl0_337
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f1840,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),tc_Lambda_OdB),tc_nat)
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_161 ),
    inference(forward_demodulation,[],[f1836,f1585]) ).

fof(f1836,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)),tc_nat)
    | ~ spl0_147
    | ~ spl0_161 ),
    inference(superposition,[],[f1662,f1435]) ).

fof(f5575,plain,
    ( spl0_336
    | ~ spl0_58
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1793,f1649,f755,f5573]) ).

fof(f5573,plain,
    ( spl0_336
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f1793,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_58
    | ~ spl0_158 ),
    inference(superposition,[],[f1650,f756]) ).

fof(f5571,plain,
    ( spl0_335
    | ~ spl0_58
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1791,f1649,f755,f5569]) ).

fof(f5569,plain,
    ( spl0_335
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f1791,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_58
    | ~ spl0_158 ),
    inference(superposition,[],[f1650,f756]) ).

fof(f5567,plain,
    ( spl0_334
    | ~ spl0_56
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1752,f1621,f745,f5565]) ).

fof(f5565,plain,
    ( spl0_334
  <=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f1752,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != hAPP(hAPP(c_Lambda_OdB_OApp,X2),X3)
    | ~ spl0_56
    | ~ spl0_151 ),
    inference(superposition,[],[f746,f1622]) ).

fof(f5563,plain,
    ( spl0_333
    | ~ spl0_42
    | ~ spl0_48
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1736,f1617,f713,f689,f5561]) ).

fof(f5561,plain,
    ( spl0_333
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f689,plain,
    ( spl0_42
  <=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1736,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
    | ~ spl0_42
    | ~ spl0_48
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1709,f714]) ).

fof(f1709,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
    | ~ spl0_42
    | ~ spl0_150 ),
    inference(superposition,[],[f1618,f690]) ).

fof(f690,plain,
    ( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f689]) ).

fof(f5559,plain,
    ( spl0_332
    | ~ spl0_68
    | ~ spl0_146 ),
    inference(avatar_split_clause,[],[f1581,f1430,f795,f5557]) ).

fof(f5557,plain,
    ( spl0_332
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1581,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_68
    | ~ spl0_146 ),
    inference(superposition,[],[f1431,f796]) ).

fof(f5555,plain,
    ( spl0_331
    | ~ spl0_108
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1345,f1190,f1064,f5553]) ).

fof(f5553,plain,
    ( spl0_331
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(X0),X1,tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f1345,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(X0),X1,tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
    | ~ spl0_108
    | ~ spl0_124 ),
    inference(superposition,[],[f1191,f1065]) ).

fof(f5551,plain,
    ( spl0_330
    | ~ spl0_81
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1221,f1136,f868,f5549]) ).

fof(f5549,plain,
    ( spl0_330
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f1221,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)
    | ~ spl0_81
    | ~ spl0_111 ),
    inference(superposition,[],[f869,f1137]) ).

fof(f5547,plain,
    ( spl0_329
    | ~ spl0_235
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4671,f4596,f2974,f5545]) ).

fof(f4671,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),X3)
    | ~ spl0_235
    | ~ spl0_277 ),
    inference(resolution,[],[f4597,f2975]) ).

fof(f5543,plain,
    ( spl0_328
    | ~ spl0_82
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1220,f1136,f872,f5541]) ).

fof(f5541,plain,
    ( spl0_328
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f1220,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
    | ~ spl0_82
    | ~ spl0_111 ),
    inference(superposition,[],[f873,f1137]) ).

fof(f5539,plain,
    ( spl0_327
    | ~ spl0_85
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1122,f1064,f898,f5537]) ).

fof(f5537,plain,
    ( spl0_327
  <=> ! [X0] : c_Lambda_OdB_OdB__size(X0) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f1122,plain,
    ( ! [X0] : c_Lambda_OdB_OdB__size(X0) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_85
    | ~ spl0_108 ),
    inference(superposition,[],[f899,f1065]) ).

fof(f5535,plain,
    ( spl0_326
    | ~ spl0_86
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1121,f1064,f902,f5533]) ).

fof(f5533,plain,
    ( spl0_326
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1121,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat)
    | ~ spl0_86
    | ~ spl0_108 ),
    inference(superposition,[],[f903,f1065]) ).

fof(f5531,plain,
    ( spl0_325
    | ~ spl0_101
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1120,f1064,f1035,f5529]) ).

fof(f5529,plain,
    ( spl0_325
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f1120,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
    | ~ spl0_101
    | ~ spl0_108 ),
    inference(superposition,[],[f1036,f1065]) ).

fof(f5527,plain,
    ( spl0_324
    | ~ spl0_53
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f1112,f1060,f733,f5525]) ).

fof(f5525,plain,
    ( spl0_324
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X0))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1060,plain,
    ( spl0_107
  <=> ! [X11,X12,X19] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X19,c_Lambda_OdB_OVar(X11),X12))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1112,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X0))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X0,X1))) )
    | ~ spl0_53
    | ~ spl0_107 ),
    inference(superposition,[],[f1061,f734]) ).

fof(f1061,plain,
    ( ! [X11,X19,X12] :
        ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X19,c_Lambda_OdB_OVar(X11),X12)))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X19)) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1060]) ).

fof(f5468,plain,
    ( spl0_323
    | ~ spl0_256
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f4282,f3751,f3694,f5466]) ).

fof(f3751,plain,
    ( spl0_260
  <=> ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f4282,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB),X3)
    | ~ spl0_256
    | ~ spl0_260 ),
    inference(resolution,[],[f3752,f3695]) ).

fof(f3752,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2)
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f3751]) ).

fof(f5382,plain,
    ( spl0_322
    | ~ spl0_81
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f3567,f3443,f868,f5380]) ).

fof(f5380,plain,
    ( spl0_322
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f3567,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X1))
    | ~ spl0_81
    | ~ spl0_248 ),
    inference(superposition,[],[f869,f3444]) ).

fof(f5378,plain,
    ( spl0_321
    | ~ spl0_81
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3471,f3439,f868,f5376]) ).

fof(f5376,plain,
    ( spl0_321
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f3471,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1))
    | ~ spl0_81
    | ~ spl0_247 ),
    inference(superposition,[],[f869,f3440]) ).

fof(f5374,plain,
    ( spl0_320
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1857,f1665,f1434,f1136,f5372]) ).

fof(f5372,plain,
    ( spl0_320
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f1857,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),tc_Lambda_OdB),tc_nat)
    | ~ spl0_111
    | ~ spl0_147
    | ~ spl0_162 ),
    inference(forward_demodulation,[],[f1854,f1585]) ).

fof(f1854,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)),tc_nat)
    | ~ spl0_147
    | ~ spl0_162 ),
    inference(superposition,[],[f1666,f1435]) ).

fof(f5370,plain,
    ( spl0_319
    | ~ spl0_60
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1595,f1434,f763,f5368]) ).

fof(f5368,plain,
    ( spl0_319
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f1595,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),tc_nat)
    | ~ spl0_60
    | ~ spl0_147 ),
    inference(superposition,[],[f764,f1435]) ).

fof(f5363,plain,
    ( spl0_318
    | ~ spl0_82
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1589,f1434,f872,f5361]) ).

fof(f5361,plain,
    ( spl0_318
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f1589,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
    | ~ spl0_82
    | ~ spl0_147 ),
    inference(superposition,[],[f873,f1435]) ).

fof(f5359,plain,
    ( spl0_317
    | ~ spl0_112
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1549,f1426,f1140,f5357]) ).

fof(f5357,plain,
    ( spl0_317
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f1549,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_112
    | ~ spl0_145 ),
    inference(resolution,[],[f1427,f1141]) ).

fof(f5355,plain,
    ( spl0_316
    | ~ spl0_72
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1222,f1136,f811,f5353]) ).

fof(f5353,plain,
    ( spl0_316
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f1222,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0
    | ~ spl0_72
    | ~ spl0_111 ),
    inference(superposition,[],[f812,f1137]) ).

fof(f5351,plain,
    ( spl0_315
    | ~ spl0_42
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f964,f894,f689,f5349]) ).

fof(f5349,plain,
    ( spl0_315
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f964,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_42
    | ~ spl0_84 ),
    inference(superposition,[],[f895,f690]) ).

fof(f5347,plain,
    ( spl0_314
    | ~ spl0_46
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f834,f807,f705,f5345]) ).

fof(f5345,plain,
    ( spl0_314
  <=> ! [X2,X0,X1,X3] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f807,plain,
    ( spl0_71
  <=> ! [X6,X18,X17,X7] : hAPP(c_Type_Oshift(X17,X7,X18,X6),X7) = X18 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f834,plain,
    ( ! [X2,X3,X0,X1] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2)
    | ~ spl0_46
    | ~ spl0_71 ),
    inference(superposition,[],[f706,f808]) ).

fof(f808,plain,
    ( ! [X18,X6,X7,X17] : hAPP(c_Type_Oshift(X17,X7,X18,X6),X7) = X18
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f807]) ).

fof(f5343,plain,
    ( spl0_313
    | ~ spl0_46
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f828,f795,f705,f5341]) ).

fof(f5341,plain,
    ( spl0_313
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f828,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_46
    | ~ spl0_68 ),
    inference(superposition,[],[f706,f796]) ).

fof(f5339,plain,
    ( spl0_312
    | ~ spl0_46
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f825,f791,f705,f5337]) ).

fof(f5337,plain,
    ( spl0_312
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f825,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
    | ~ spl0_46
    | ~ spl0_67 ),
    inference(superposition,[],[f706,f792]) ).

fof(f5299,plain,
    ( spl0_311
    | ~ spl0_235
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f4281,f3751,f2974,f5297]) ).

fof(f4281,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1)),X2),X3)
    | ~ spl0_235
    | ~ spl0_260 ),
    inference(resolution,[],[f3752,f2975]) ).

fof(f5210,plain,
    ( spl0_310
    | ~ spl0_31
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f3296,f2961,f645,f5208]) ).

fof(f5208,plain,
    ( spl0_310
  <=> ! [X2,X0,X1,X3] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_Lambda_OdB_OVar(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f645,plain,
    ( spl0_31
  <=> ! [X0,X49] : c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X49) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f3296,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_31
    | ~ spl0_232 ),
    inference(superposition,[],[f646,f2962]) ).

fof(f646,plain,
    ( ! [X0,X49] : c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X49)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f645]) ).

fof(f5206,plain,
    ( spl0_309
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1858,f1665,f1136,f1064,f5204]) ).

fof(f5204,plain,
    ( spl0_309
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f1858,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat)
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_162 ),
    inference(forward_demodulation,[],[f1856,f1205]) ).

fof(f1856,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))),tc_nat)
    | ~ spl0_108
    | ~ spl0_162 ),
    inference(superposition,[],[f1666,f1065]) ).

fof(f5202,plain,
    ( spl0_308
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1841,f1661,f1136,f1064,f5200]) ).

fof(f5200,plain,
    ( spl0_308
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f1841,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat)
    | ~ spl0_108
    | ~ spl0_111
    | ~ spl0_161 ),
    inference(forward_demodulation,[],[f1838,f1205]) ).

fof(f1838,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))),tc_nat)
    | ~ spl0_108
    | ~ spl0_161 ),
    inference(superposition,[],[f1662,f1065]) ).

fof(f5198,plain,
    ( spl0_307
    | ~ spl0_40
    | ~ spl0_68
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1611,f1434,f795,f681,f5196]) ).

fof(f5196,plain,
    ( spl0_307
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f1611,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB)
    | ~ spl0_40
    | ~ spl0_68
    | ~ spl0_147 ),
    inference(forward_demodulation,[],[f1584,f796]) ).

fof(f1584,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB)
    | ~ spl0_40
    | ~ spl0_147 ),
    inference(superposition,[],[f1435,f682]) ).

fof(f5194,plain,
    ( spl0_306
    | ~ spl0_61
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1596,f1434,f767,f5192]) ).

fof(f5192,plain,
    ( spl0_306
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f1596,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_147 ),
    inference(superposition,[],[f768,f1435]) ).

fof(f5185,plain,
    ( spl0_305
    | ~ spl0_98
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1590,f1434,f951,f5183]) ).

fof(f5183,plain,
    ( spl0_305
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f1590,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
    | ~ spl0_98
    | ~ spl0_147 ),
    inference(superposition,[],[f952,f1435]) ).

fof(f5181,plain,
    ( spl0_304
    | ~ spl0_72
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1587,f1434,f811,f5179]) ).

fof(f5179,plain,
    ( spl0_304
  <=> ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f1587,plain,
    ( ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)
    | ~ spl0_72
    | ~ spl0_147 ),
    inference(superposition,[],[f812,f1435]) ).

fof(f5167,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f328,f5165]) ).

fof(f5165,plain,
    ( spl0_303
  <=> ! [X17,X51,X11,X36] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
        | ~ c_Type_Otyping(X17,X36,v_T____)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X36,X11)))
        | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X51) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f328,axiom,
    ! [X51,X36,X11,X17] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
      | ~ c_Type_Otyping(X17,X36,v_T____)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X36,X11)))
      | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X51) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SI1_0) ).

fof(f5163,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f102,f5161]) ).

fof(f5161,plain,
    ( spl0_302
  <=> ! [X17,X29,X11,X18,X30,X28,X26] :
        ( ~ c_Type_Otypings(X17,X26,X30)
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28)
        | c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X18,X28,X17,X29),X18,tc_Type_Otype,tc_Type_Otype) = X28
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f102,axiom,
    ! [X28,X29,X11,X18,X26,X17,X30] :
      ( ~ c_Type_Otypings(X17,X26,X30)
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X18,X28,X17,X29),X18,tc_Type_Otype,tc_Type_Otype) = X28
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

fof(f5154,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f260,f5152]) ).

fof(f5152,plain,
    ( spl0_301
  <=> ! [X25,X19,X46] :
        ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X25,tc_Lambda_OdB)
        | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X19,X25,c_HOL_Ozero__class_Ozero(tc_nat)),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
        | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19)),X25),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f260,axiom,
    ! [X46,X19,X25] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X25,tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X19,X25,c_HOL_Ozero__class_Ozero(tc_nat)),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19)),X25),X46,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).

fof(f5144,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f249,f5142]) ).

fof(f5142,plain,
    ( spl0_300
  <=> ! [X28,X17,X11,X18,X29,X26,X30] :
        ( ~ c_Type_Otypings(X17,X26,X30)
        | c_Type_Otypings(X17,X29,c_Type_Osko__Type__Xvar__app__types__1__1(X18,X28,X17,X29))
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28)
        | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f249,axiom,
    ! [X28,X29,X11,X18,X26,X17,X30] :
      ( ~ c_Type_Otypings(X17,X26,X30)
      | c_Type_Otypings(X17,X29,c_Type_Osko__Type__Xvar__app__types__1__1(X18,X28,X17,X29))
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28)
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X29,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

fof(f5140,plain,
    ( spl0_299
    | ~ spl0_256
    | ~ spl0_261 ),
    inference(avatar_split_clause,[],[f4207,f3871,f3694,f5138]) ).

fof(f3871,plain,
    ( spl0_261
  <=> ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f4207,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ spl0_256
    | ~ spl0_261 ),
    inference(resolution,[],[f3872,f3695]) ).

fof(f3872,plain,
    ( ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1)
    | ~ spl0_261 ),
    inference(avatar_component_clause,[],[f3871]) ).

fof(f5090,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f443,f5088]) ).

fof(f5088,plain,
    ( spl0_298
  <=> ! [X35,X11,X12,X36,X27] :
        ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Lambda_Osubst(c_Lambda_Osubst(X27,X36,X11),X35,X12) = c_Lambda_Osubst(c_Lambda_Osubst(X27,c_Lambda_Olift(X35,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Osubst(X36,X35,X12),X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f443,plain,
    ! [X11,X36,X27,X35,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Osubst(c_Lambda_Osubst(X27,X36,X11),X35,X12) = c_Lambda_Osubst(c_Lambda_Osubst(X27,c_Lambda_Olift(X35,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Osubst(X36,X35,X12),X11) ),
    inference(definition_unfolding,[],[f224,f186]) ).

fof(f186,axiom,
    ! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

fof(f224,axiom,
    ! [X11,X36,X27,X35,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Osubst(c_Lambda_Osubst(X27,c_Lambda_Olift(X35,X11),c_Suc(X12)),c_Lambda_Osubst(X36,X35,X12),X11) = c_Lambda_Osubst(c_Lambda_Osubst(X27,X36,X11),X35,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).

fof(f5084,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f227,f5082]) ).

fof(f5082,plain,
    ( spl0_297
  <=> ! [X5,X4,X23,X6,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f227,axiom,
    ! [X6,X4,X15,X5,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f5080,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f355,f5078]) ).

fof(f5078,plain,
    ( spl0_296
  <=> ! [X17,X54,X11,X55,X36,X27,X56] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
        | ~ c_Type_Otyping(X17,X36,X54)
        | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X54),X55)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X27,X36,X11)))
        | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,X54,tc_Type_Otype),X27,X56) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f355,axiom,
    ! [X36,X11,X56,X54,X55,X27,X17] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
      | ~ c_Type_Otyping(X17,X36,X54)
      | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X54),X55)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X27,X36,X11)))
      | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,X54,tc_Type_Otype),X27,X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).

fof(f5076,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f354,f5074]) ).

fof(f5074,plain,
    ( spl0_295
  <=> ! [X55,X11,X54,X17,X56,X36,X27] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
        | ~ c_Type_Otyping(X17,X36,X55)
        | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X54),X55)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X27,X36,X11)))
        | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,X55,tc_Type_Otype),X27,X56) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f354,axiom,
    ! [X36,X11,X56,X54,X55,X27,X17] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
      | ~ c_Type_Otyping(X17,X36,X55)
      | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X54),X55)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X27,X36,X11)))
      | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,X55,tc_Type_Otype),X27,X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).

fof(f5062,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f126,f5060]) ).

fof(f5060,plain,
    ( spl0_294
  <=> ! [X33,X32,X27,X25] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X33))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f126,axiom,
    ! [X27,X25,X32,X33] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X33))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

fof(f4958,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f299,f4956]) ).

fof(f4956,plain,
    ( spl0_293
  <=> ! [X25,X19,X46] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X19,X25,c_HOL_Ozero__class_Ozero(tc_nat)),X46,tc_Lambda_OdB,tc_Lambda_OdB)))
        | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19)),X25),X46,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f299,axiom,
    ! [X46,X19,X25] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X19,X25,c_HOL_Ozero__class_Ozero(tc_nat)),X46,tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19)),X25),X46,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OBeta_0) ).

fof(f4954,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f99,f4952]) ).

fof(f4952,plain,
    ( spl0_292
  <=> ! [X11,X12,X27,X25] :
        ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Lambda_Olift(c_Lambda_Osubst(X27,X25,X12),X11) = c_Lambda_Osubst(c_Lambda_Olift(X27,X11),c_Lambda_Olift(X25,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f99,axiom,
    ! [X11,X27,X12,X25] :
      ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Olift(c_Lambda_Osubst(X27,X25,X12),X11) = c_Lambda_Osubst(c_Lambda_Olift(X27,X11),c_Lambda_Olift(X25,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),c_HOL_Oone__class_Oone(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

fof(f4950,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f98,f4948]) ).

fof(f4948,plain,
    ( spl0_291
  <=> ! [X11,X12,X27,X25] :
        ( ~ c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
        | c_Lambda_Olift(c_Lambda_Osubst(X27,X25,X12),X11) = c_Lambda_Osubst(c_Lambda_Olift(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X25,X11),X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f98,axiom,
    ! [X11,X27,X12,X25] :
      ( ~ c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Olift(c_Lambda_Osubst(X27,X25,X12),X11) = c_Lambda_Osubst(c_Lambda_Olift(X27,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat))),c_Lambda_Olift(X25,X11),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).

fof(f4667,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f442,f4665]) ).

fof(f442,plain,
    ! [X11,X27,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Olift(c_Lambda_Olift(X27,X13),X11) = c_Lambda_Olift(c_Lambda_Olift(X27,X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) ),
    inference(definition_unfolding,[],[f231,f186]) ).

fof(f231,axiom,
    ! [X11,X27,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
      | c_Lambda_Olift(c_Lambda_Olift(X27,X11),c_Suc(X13)) = c_Lambda_Olift(c_Lambda_Olift(X27,X13),X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).

fof(f4663,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f433,f4661]) ).

fof(f433,plain,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition_unfolding,[],[f141,f186]) ).

fof(f141,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

fof(f4659,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f422,f4657]) ).

fof(f4657,plain,
    ( spl0_288
  <=> ! [X18,X11,X6,X17,X28] : c_Type_Oshift(c_Type_Oshift(X17,X11,X28,X6),c_HOL_Ozero__class_Ozero(tc_nat),X18,X6) = c_Type_Oshift(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),X18,X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),X28,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f422,plain,
    ! [X28,X11,X18,X6,X17] : c_Type_Oshift(c_Type_Oshift(X17,X11,X28,X6),c_HOL_Ozero__class_Ozero(tc_nat),X18,X6) = c_Type_Oshift(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),X18,X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),X28,X6),
    inference(definition_unfolding,[],[f256,f186]) ).

fof(f256,axiom,
    ! [X28,X11,X18,X6,X17] : c_Type_Oshift(c_Type_Oshift(X17,X11,X28,X6),c_HOL_Ozero__class_Ozero(tc_nat),X18,X6) = c_Type_Oshift(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),X18,X6),c_Suc(X11),X28,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).

fof(f4655,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f419,f4653]) ).

fof(f4653,plain,
    ( spl0_287
  <=> ! [X13,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f419,plain,
    ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f41,f186,f186]) ).

fof(f41,axiom,
    ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),c_Suc(X13),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X13,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

fof(f4651,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f158,f4649]) ).

fof(f4649,plain,
    ( spl0_286
  <=> ! [X31,X7,X6,X8] :
        ( ~ class_OrderedGroup_Osemigroup__add(X6)
        | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8),X31,X6,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X8,X31,X6,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f158,axiom,
    ! [X31,X8,X6,X7] :
      ( ~ class_OrderedGroup_Osemigroup__add(X6)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8),X31,X6,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X8,X31,X6,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

fof(f4637,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f262,f4635]) ).

fof(f4635,plain,
    ( spl0_285
  <=> ! [X25,X46,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f262,axiom,
    ! [X46,X19,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).

fof(f4630,plain,
    ( spl0_284
    | ~ spl0_235
    | ~ spl0_261 ),
    inference(avatar_split_clause,[],[f4206,f3871,f2974,f4628]) ).

fof(f4206,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1),X2)
    | ~ spl0_235
    | ~ spl0_261 ),
    inference(resolution,[],[f3872,f2975]) ).

fof(f4622,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f198,f4620]) ).

fof(f4620,plain,
    ( spl0_283
  <=> ! [X4,X23,X6,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f198,axiom,
    ! [X6,X4,X15,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f4618,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f197,f4616]) ).

fof(f4616,plain,
    ( spl0_282
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f197,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f4614,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f195,f4612]) ).

fof(f4612,plain,
    ( spl0_281
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f195,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f4610,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f194,f4608]) ).

fof(f4608,plain,
    ( spl0_280
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f194,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f4606,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f193,f4604]) ).

fof(f4604,plain,
    ( spl0_279
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f193,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f4602,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f189,f4600]) ).

fof(f4600,plain,
    ( spl0_278
  <=> ! [X42,X7,X6,X8] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X8),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8)),X42) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f189,axiom,
    ! [X8,X6,X7,X42] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X8),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8)),X42) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f4598,plain,
    ( spl0_277
    | ~ spl0_246
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3839,f3694,f3435,f4596]) ).

fof(f3435,plain,
    ( spl0_246
  <=> ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f3839,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1,tc_Lambda_OdB,tc_Lambda_OdB),X2)
    | ~ spl0_246
    | ~ spl0_256 ),
    inference(resolution,[],[f3695,f3436]) ).

fof(f3436,plain,
    ( ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1)
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f3435]) ).

fof(f4291,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f472,f4289]) ).

fof(f472,plain,
    ! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f471,f236]) ).

fof(f236,axiom,
    ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

fof(f471,plain,
    ! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f424,f161]) ).

fof(f161,axiom,
    ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

fof(f424,plain,
    ! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f146,f186]) ).

fof(f146,axiom,
    ! [X40,X41] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X40,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X41,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).

fof(f4287,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f470,f4285]) ).

fof(f470,plain,
    ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f469,f236]) ).

fof(f469,plain,
    ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f423,f161]) ).

fof(f423,plain,
    ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f140,f186]) ).

fof(f140,axiom,
    ! [X38,X37] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X37),X38),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X37,tc_Type_Otype)),c_Nat_Osize__class_Osize(X38,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).

fof(f4280,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f272,f4278]) ).

fof(f4278,plain,
    ( spl0_274
  <=> ! [X34,X2,X35] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB)),X35))
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X34,X35),tc_Lambda_OdB,tc_Lambda_OdB) = X35 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f272,axiom,
    ! [X2,X34,X35] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB)),X35))
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X34,X35),tc_Lambda_OdB,tc_Lambda_OdB) = X35 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

fof(f4276,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f259,f4274]) ).

fof(f4274,plain,
    ( spl0_273
  <=> ! [X18,X11,X17,X26] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otyping(X17,c_Lambda_OdB_OVar(X11),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X18,X17,X11,X26),X18,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f259,axiom,
    ! [X11,X18,X26,X17] :
      ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
      | c_Type_Otyping(X17,c_Lambda_OdB_OVar(X11),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X18,X17,X11,X26),X18,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

fof(f4272,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f178,f4270]) ).

fof(f4270,plain,
    ( spl0_272
  <=> ! [X42,X7,X8,X6,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X8))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X42))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X42)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f178,axiom,
    ! [X8,X19,X6,X7,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X8))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X42))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X42)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

fof(f4268,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f128,f4266]) ).

fof(f4266,plain,
    ( spl0_271
  <=> ! [X25,X27,X33] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X33))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f128,axiom,
    ! [X27,X25,X33] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X33))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).

fof(f4264,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f127,f4262]) ).

fof(f4262,plain,
    ( spl0_270
  <=> ! [X25,X32,X27] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X27))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f127,axiom,
    ! [X27,X25,X32] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27)),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

fof(f4260,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f62,f4258]) ).

fof(f4258,plain,
    ( spl0_269
  <=> ! [X5,X4,X23,X6,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ c_HOL_Oord__class_Oless(X23,X15,X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X15),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f62,axiom,
    ! [X6,X4,X15,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_HOL_Oord__class_Oless(X23,X15,X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X15),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f3901,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f448,f3899]) ).

fof(f448,plain,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) = X2
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
    inference(definition_unfolding,[],[f216,f186,f186]) ).

fof(f216,axiom,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_Suc(X1) = X2
      | c_HOL_Oord__class_Oless(c_Suc(X1),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f3897,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f349,f3895]) ).

fof(f3895,plain,
    ( spl0_267
  <=> ! [X17,X51,X11,X36] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
        | ~ c_Type_Otyping(X17,X36,v_T____)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X36,X11)))
        | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,v_T____,tc_Type_Otype),v_a____,X51) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f349,axiom,
    ! [X51,X36,X11,X17] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X36))
      | ~ c_Type_Otyping(X17,X36,v_T____)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(v_a____,X36,X11)))
      | ~ c_Type_Otyping(c_Type_Oshift(X17,X11,v_T____,tc_Type_Otype),v_a____,X51) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SI2_0) ).

fof(f3893,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f316,f3891]) ).

fof(f316,axiom,
    ! [X28,X11,X18,X26,X17] :
      ( X18 = X28
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X28) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

fof(f3889,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f215,f3887]) ).

fof(f3887,plain,
    ( spl0_265
  <=> ! [X6,X20,X4] :
        ( ~ class_OrderedGroup_Omonoid__add(X6)
        | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X4,X20,X6,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,c_HOL_Ozero__class_Ozero(X6),X6,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f215,axiom,
    ! [X6,X4,X20] :
      ( ~ class_OrderedGroup_Omonoid__add(X6)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X4,X20,X6,X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,c_HOL_Ozero__class_Ozero(X6),X6,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

fof(f3885,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f192,f3883]) ).

fof(f3881,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f191,f3879]) ).

fof(f191,axiom,
    ! [X8,X7,X42] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X42)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

fof(f3877,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f125,f3875]) ).

fof(f3875,plain,
    ( spl0_262
  <=> ! [X6,X7,X31] :
        ( ~ class_OrderedGroup_Omonoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X31,X6,X6)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X7,X31,X6,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f125,axiom,
    ! [X31,X6,X7] :
      ( ~ class_OrderedGroup_Omonoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X31,X6,X6)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X7,X31,X6,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

fof(f3873,plain,
    ( spl0_261
    | ~ spl0_21
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f3840,f3694,f600,f3871]) ).

fof(f3840,plain,
    ( ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,v_a____,X0,tc_Lambda_OdB,tc_Lambda_OdB),X1)
    | ~ spl0_21
    | ~ spl0_256 ),
    inference(resolution,[],[f3695,f601]) ).

fof(f3753,plain,
    ( spl0_260
    | ~ spl0_235
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3672,f3435,f2974,f3751]) ).

fof(f3672,plain,
    ( ! [X2,X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0)),X1),X2)
    | ~ spl0_235
    | ~ spl0_246 ),
    inference(resolution,[],[f3436,f2975]) ).

fof(f3708,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f305,f3706]) ).

fof(f3706,plain,
    ( spl0_259
  <=> ! [X25,X46,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f305,axiom,
    ! [X46,X19,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

fof(f3704,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f254,f3702]) ).

fof(f3702,plain,
    ( spl0_258
  <=> ! [X18,X17,X27,X26] :
        ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
        | c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X18,X17,X27,X26),X18,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f254,axiom,
    ! [X18,X26,X27,X17] :
      ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
      | c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X18,X17,X27,X26),X18,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

fof(f3700,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f253,f3698]) ).

fof(f3698,plain,
    ( spl0_257
  <=> ! [X18,X17,X30,X27,X26] :
        ( ~ c_Type_Otypings(X17,X26,X30)
        | ~ c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,X30,X18,tc_Type_Otype,tc_Type_Otype))
        | c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f253,axiom,
    ! [X18,X26,X27,X17,X30] :
      ( ~ c_Type_Otypings(X17,X26,X30)
      | ~ c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,X30,X18,tc_Type_Otype,tc_Type_Otype))
      | c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

fof(f3696,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f252,f3694]) ).

fof(f252,axiom,
    ! [X18,X26,X27,X17] :
      ( ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18)
      | c_Type_Otyping(X17,X27,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26),X18,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

fof(f3692,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f134,f3690]) ).

fof(f3690,plain,
    ( spl0_255
  <=> ! [X19,X11,X27,X25] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X27,X19,X11)),c_Lambda_Osubst(X27,X25,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f134,axiom,
    ! [X11,X19,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X27,X19,X11)),c_Lambda_Osubst(X27,X25,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).

fof(f3688,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f133,f3686]) ).

fof(f3686,plain,
    ( spl0_254
  <=> ! [X19,X11,X27,X25] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X19,X27,X11)),c_Lambda_Osubst(X25,X27,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f133,axiom,
    ! [X11,X19,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X19,X27,X11)),c_Lambda_Osubst(X25,X27,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

fof(f3684,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f112,f3682]) ).

fof(f3682,plain,
    ( spl0_253
  <=> ! [X6,X4,X5] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f112,axiom,
    ! [X6,X4,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X5,X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f3680,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f106,f3678]) ).

fof(f3678,plain,
    ( spl0_252
  <=> ! [X6,X4,X5] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
        | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
        | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),c_HOL_Ozero__class_Ozero(X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f106,axiom,
    ! [X6,X4,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X6)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X6),X6)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X6),X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5),c_HOL_Ozero__class_Ozero(X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f3676,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f93,f3674]) ).

fof(f3674,plain,
    ( spl0_251
  <=> ! [X6,X4,X23,X5,X19] :
        ( ~ hBOOL(hAPP(hAPP(X19,X5),X23))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X5))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f93,axiom,
    ! [X19,X6,X4,X5,X23] :
      ( ~ hBOOL(hAPP(hAPP(X19,X5),X23))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X5))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

fof(f3671,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f92,f3669]) ).

fof(f3669,plain,
    ( spl0_250
  <=> ! [X6,X4,X23,X5,X19] :
        ( ~ hBOOL(hAPP(hAPP(X19,X4),X5))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X5),X23))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f92,axiom,
    ! [X19,X6,X4,X5,X23] :
      ( ~ hBOOL(hAPP(hAPP(X19,X4),X5))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X5),X23))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X4),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).

fof(f3667,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f63,f3665]) ).

fof(f3665,plain,
    ( spl0_249
  <=> ! [X11,X14,X13,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X14),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f63,axiom,
    ! [X11,X14,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X14),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

fof(f3445,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f468,f3443]) ).

fof(f468,plain,
    ! [X40,X41] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f467,f236]) ).

fof(f467,plain,
    ! [X40,X41] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f421,f161]) ).

fof(f421,plain,
    ! [X40,X41] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f147,f186]) ).

fof(f147,axiom,
    ! [X40,X41] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X40)),c_Lambda_OdB_OdB__size(X41))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).

fof(f3441,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f466,f3439]) ).

fof(f466,plain,
    ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f465,f236]) ).

fof(f465,plain,
    ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f420,f161]) ).

fof(f420,plain,
    ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f139,f186]) ).

fof(f139,axiom,
    ! [X38,X37] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X37),X38)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X37)),c_Type_Otype_Otype__size(X38))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).

fof(f3437,plain,
    ( spl0_246
    | ~ spl0_21
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f3342,f2974,f600,f3435]) ).

fof(f3342,plain,
    ( ! [X0,X1] : ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,v_a____),X0),X1)
    | ~ spl0_21
    | ~ spl0_235 ),
    inference(resolution,[],[f2975,f601]) ).

fof(f3433,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f425,f3431]) ).

fof(f3431,plain,
    ( spl0_245
  <=> ! [X6,X1] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_Nat_Osemiring__1__class_Oof__nat(X1,X6)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f425,plain,
    ! [X1,X6] :
      ( ~ class_Ring__and__Field_Osemiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_Nat_Osemiring__1__class_Oof__nat(X1,X6)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),X6) ),
    inference(definition_unfolding,[],[f211,f186]) ).

fof(f211,axiom,
    ! [X1,X6] :
      ( ~ class_Ring__and__Field_Osemiring__1(X6)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X1),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_Nat_Osemiring__1__class_Oof__nat(X1,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

fof(f3429,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f261,f3427]) ).

fof(f3427,plain,
    ( spl0_244
  <=> ! [X34,X19,X46] :
        ( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X34,X46,tc_Lambda_OdB)
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X34,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f261,axiom,
    ! [X46,X19,X34] :
      ( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X34,X46,tc_Lambda_OdB)
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X34,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X46,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

fof(f3425,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f160,f3423]) ).

fof(f160,axiom,
    ! [X2,X1,X14,X13] :
      ( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X14) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

fof(f3421,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f88,f3419]) ).

fof(f3419,plain,
    ( spl0_242
  <=> ! [X6,X2,X1] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_Nat_Osemiring__1__class_Oof__nat(X1,X6)),c_Nat_Osemiring__1__class_Oof__nat(X2,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f88,axiom,
    ! [X2,X1,X6] :
      ( ~ class_Ring__and__Field_Osemiring__1(X6)
      | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_Nat_Osemiring__1__class_Oof__nat(X1,X6)),c_Nat_Osemiring__1__class_Oof__nat(X2,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

fof(f3341,plain,
    ( spl0_241
    | ~ spl0_113
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1548,f1426,f1144,f3339]) ).

fof(f3339,plain,
    ( spl0_241
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f1548,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_113
    | ~ spl0_145 ),
    inference(resolution,[],[f1427,f1145]) ).

fof(f2996,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f437,f2994]) ).

fof(f437,plain,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(definition_unfolding,[],[f246,f186,f186]) ).

fof(f246,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f2992,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f343,f2990]) ).

fof(f343,axiom,
    ! [X36,X27,X25,X13] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X25,X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X27,X25,X13)),c_Lambda_Osubst(X36,X25,X13)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

fof(f2988,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f326,f2986]) ).

fof(f326,axiom,
    ! [X50,X28,X18,X27,X25] :
      ( ~ c_Type_Otyping(X50,X27,X18)
      | ~ c_Type_Otyping(X50,X25,hAPP(hAPP(c_Type_Otype_OFun,X18),X28))
      | c_Type_Otyping(X50,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X28) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

fof(f2984,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f284,f2982]) ).

fof(f2982,plain,
    ( spl0_237
  <=> ! [X25,X36,X27] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X36),X27))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f284,axiom,
    ! [X36,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X36),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X36),X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

fof(f2980,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f283,f2978]) ).

fof(f2978,plain,
    ( spl0_236
  <=> ! [X25,X36,X27] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X36)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f283,axiom,
    ! [X36,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X36)),hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

fof(f2976,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f269,f2974]) ).

fof(f269,axiom,
    ! [X36,X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18)
      | c_Type_Otyping(X17,X27,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)),X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

fof(f2972,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f257,f2970]) ).

fof(f2970,plain,
    ( spl0_234
  <=> ! [X18,X27,X17] :
        ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
        | c_Type_Otyping(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X18,X17,X27),tc_Type_Otype),X27,c_Type_Osko__Type__Xtyping__elims__3__2(X18,X17,X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f257,axiom,
    ! [X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
      | c_Type_Otyping(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(X18,X17,X27),tc_Type_Otype),X27,c_Type_Osko__Type__Xtyping__elims__3__2(X18,X17,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).

fof(f2967,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f255,f2965]) ).

fof(f2965,plain,
    ( spl0_233
  <=> ! [X25,X11,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X19,X11)),c_Lambda_Olift(X25,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f255,axiom,
    ! [X11,X19,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X19),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X19,X11)),c_Lambda_Olift(X25,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).

fof(f2963,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f248,f2961]) ).

fof(f248,axiom,
    ! [X27,X25,X13] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X27),X25,X13) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X27,c_Lambda_Olift(X25,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

fof(f2959,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f135,f2957]) ).

fof(f2957,plain,
    ( spl0_231
  <=> ! [X34,X2,X35] :
        ( c_ListOrder_Ostep1(c_Lambda_Obeta,X34,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X34,X35),tc_Lambda_OdB)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f135,axiom,
    ! [X2,X34,X35] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X34,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X2,X34,X35),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB)),X35)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

fof(f2955,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f132,f2953]) ).

fof(f2953,plain,
    ( spl0_230
  <=> ! [X19,X11,X27,X25] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X27,X19,X11)),c_Lambda_Osubst(X27,X25,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f132,axiom,
    ! [X11,X19,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X27,X19,X11)),c_Lambda_Osubst(X27,X25,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

fof(f2951,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f122,f2949]) ).

fof(f2949,plain,
    ( spl0_229
  <=> ! [X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f122,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

fof(f2947,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f114,f2945]) ).

fof(f2945,plain,
    ( spl0_228
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | ~ c_HOL_Oord__class_Oless(X5,X23,X6)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
        | c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f114,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | ~ c_HOL_Oord__class_Oless(X5,X23,X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),X4,X6)
      | c_HOL_Oord__class_Oless(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f2943,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f81,f2941]) ).

fof(f2941,plain,
    ( spl0_227
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
        | c_HOL_Oord__class_Oless(X4,X5,X6)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f81,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
      | c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f2939,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f80,f2937]) ).

fof(f80,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f2935,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f79,f2933]) ).

fof(f2933,plain,
    ( spl0_225
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f79,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X5),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f2931,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f78,f2929]) ).

fof(f78,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
      | c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f2926,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f77,f2924]) ).

fof(f2924,plain,
    ( spl0_223
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f77,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f2922,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f76,f2920]) ).

fof(f2920,plain,
    ( spl0_222
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f76,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X23),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f2785,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f363,f2783]) ).

fof(f363,axiom,
    ! [X58,X28,X36,X11,X18,X27] :
      ( ~ c_Type_Otyping(X58,X36,X28)
      | c_Type_Otyping(X58,c_Lambda_Osubst(X27,X36,X11),X18)
      | ~ c_Type_Otyping(c_Type_Oshift(X58,X11,X28,tc_Type_Otype),X27,X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

fof(f2781,plain,
    ( spl0_220
    | ~ spl0_125
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f2678,f1892,f1197,f2779]) ).

fof(f2779,plain,
    ( spl0_220
  <=> ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0)) != c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1197,plain,
    ( spl0_125
  <=> ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f1892,plain,
    ( spl0_173
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f2678,plain,
    ( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0)) != c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_125
    | ~ spl0_173 ),
    inference(superposition,[],[f1198,f1893]) ).

fof(f1893,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f1892]) ).

fof(f1198,plain,
    ( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0)
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1197]) ).

fof(f2777,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f214,f2775]) ).

fof(f2775,plain,
    ( spl0_219
  <=> ! [X7,X8,X6,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X7))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X19,X6,X6),X6),X7),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f214,axiom,
    ! [X8,X19,X6,X7] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X7))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X19,X6,X6),X6),X7),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).

fof(f2773,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f213,f2771]) ).

fof(f213,axiom,
    ! [X8,X19,X6,X7] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X8),X7))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X19,X6,X6),X6),X7),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).

fof(f2769,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f69,f2767]) ).

fof(f2767,plain,
    ( spl0_217
  <=> ! [X6,X20] :
        ( ~ class_OrderedGroup_Omonoid__add(X6)
        | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X20,X6,X6) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,c_HOL_Ozero__class_Ozero(X6),X6,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f69,axiom,
    ! [X6,X20] :
      ( ~ class_OrderedGroup_Omonoid__add(X6)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6),X20,X6,X6) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,c_HOL_Ozero__class_Ozero(X6),X6,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).

fof(f2765,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f48,f2763]) ).

fof(f48,axiom,
    ! [X11,X18,X6,X17,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).

fof(f2761,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f36,f2759]) ).

fof(f36,axiom,
    ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

fof(f2757,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f35,f2755]) ).

fof(f35,axiom,
    ! [X2,X1,X13] : c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

fof(f2462,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f477,f2460]) ).

fof(f2460,plain,
    ( spl0_213
  <=> ! [X2] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f477,plain,
    ! [X2] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(forward_demodulation,[],[f438,f161]) ).

fof(f438,plain,
    ! [X2] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
    inference(definition_unfolding,[],[f143,f186]) ).

fof(f143,axiom,
    ! [X2] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

fof(f2458,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f447,f2456]) ).

fof(f2456,plain,
    ( spl0_212
  <=> ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f447,plain,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),X13,tc_nat) ),
    inference(definition_unfolding,[],[f68,f186]) ).

fof(f68,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X11),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f2454,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f360,f2451]) ).

fof(f2451,plain,
    ( spl0_211
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f360,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).

fof(f2449,plain,
    ( spl0_210
    | ~ spl0_31
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1749,f1621,f645,f2447]) ).

fof(f2447,plain,
    ( spl0_210
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f1749,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)
    | ~ spl0_31
    | ~ spl0_151 ),
    inference(superposition,[],[f646,f1622]) ).

fof(f2445,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f357,f2443]) ).

fof(f357,axiom,
    ! [X50,X28,X18,X27] :
      ( ~ c_Type_Otyping(c_Type_Oshift(X50,c_HOL_Ozero__class_Ozero(tc_nat),X18,tc_Type_Otype),X27,X28)
      | c_Type_Otyping(X50,c_Lambda_OdB_OAbs(X27),hAPP(hAPP(c_Type_Otype_OFun,X18),X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

fof(f2441,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f337,f2439]) ).

fof(f337,axiom,
    ! [X2,X46,X1,X34] :
      ( X1 = X2
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X34,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

fof(f2437,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f336,f2435]) ).

fof(f2435,plain,
    ( spl0_207
  <=> ! [X2,X34,X1,X46] :
        ( X34 = X46
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X34,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f336,axiom,
    ! [X2,X46,X1,X34] :
      ( X34 = X46
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X34,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

fof(f2433,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f324,f2431]) ).

fof(f324,axiom,
    ! [X46,X19,X34,X25] :
      ( X19 = X25
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X34,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

fof(f2429,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f323,f2427]) ).

fof(f2427,plain,
    ( spl0_205
  <=> ! [X34,X25,X19,X46] :
        ( X34 = X46
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X34,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X46,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f323,axiom,
    ! [X46,X19,X34,X25] :
      ( X34 = X46
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X34,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25),X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

fof(f2425,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f295,f2423]) ).

fof(f295,axiom,
    ! [X11,X19,X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X19,X27,X11)),c_Lambda_Osubst(X25,X27,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

fof(f2421,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f274,f2418]) ).

fof(f2418,plain,
    ( spl0_203
  <=> c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f274,axiom,
    c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I5_J_0) ).

fof(f2416,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f258,f2414]) ).

fof(f2414,plain,
    ( spl0_202
  <=> ! [X18,X27,X17] :
        ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
        | c_Type_Otyping(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X17,X27),tc_Type_Otype),X27,c_Type_Osko__Type__Xabs__typeE__1__2(X17,X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f258,axiom,
    ! [X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
      | c_Type_Otyping(c_Type_Oshift(X17,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(X17,X27),tc_Type_Otype),X27,c_Type_Osko__Type__Xabs__typeE__1__2(X17,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).

fof(f2412,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f250,f2410]) ).

fof(f250,axiom,
    ! [X11,X18,X26,X17] :
      ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xvar__app__typesE__1__1(X18,X17,X11,X26))
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X11),X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

fof(f2408,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f223,f2406]) ).

fof(f2406,plain,
    ( spl0_200
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X6)
        | X5 = X23
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f223,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X6)
      | X5 = X23
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X23),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f2393,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f222,f2391]) ).

fof(f2391,plain,
    ( spl0_199
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X6)
        | X5 = X23
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f222,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X6)
      | X5 = X23
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f2389,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f221,f2387]) ).

fof(f2387,plain,
    ( spl0_198
  <=> ! [X5,X4,X23,X6] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X6)
        | X5 = X23
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f221,axiom,
    ! [X6,X4,X5,X23] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X6)
      | X5 = X23
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f2385,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f129,f2383]) ).

fof(f2383,plain,
    ( spl0_197
  <=> ! [X25,X32] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X25)),c_Lambda_OdB_OAbs(X32))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f129,axiom,
    ! [X25,X32] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X32))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X25)),c_Lambda_OdB_OAbs(X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

fof(f2381,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f101,f2379]) ).

fof(f2379,plain,
    ( spl0_196
  <=> ! [X18,X27,X17] :
        ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
        | hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X18,X17,X27)),c_Type_Osko__Type__Xtyping__elims__3__2(X18,X17,X27)) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f101,axiom,
    ! [X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OAbs(X27),X18)
      | hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X18,X17,X27)),c_Type_Osko__Type__Xtyping__elims__3__2(X18,X17,X27)) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).

fof(f2377,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f84,f2375]) ).

fof(f84,axiom,
    ! [X2,X1,X13] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

fof(f2373,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f83,f2371]) ).

fof(f83,axiom,
    ! [X2,X1,X13] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

fof(f2369,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f82,f2367]) ).

fof(f82,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

fof(f2365,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f24,f2363]) ).

fof(f2363,plain,
    ( spl0_192
  <=> ! [X2,X1,X14] :
        ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X14,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X2,tc_nat),c_HOL_Ominus__class_Ominus(X14,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f24,axiom,
    ! [X2,X1,X14] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,X14,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X2,tc_nat),c_HOL_Ominus__class_Ominus(X14,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

fof(f2186,plain,
    ( spl0_191
    | ~ spl0_81
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1588,f1434,f868,f2184]) ).

fof(f2184,plain,
    ( spl0_191
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1588,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)
    | ~ spl0_81
    | ~ spl0_147 ),
    inference(superposition,[],[f869,f1435]) ).

fof(f2161,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f495,f2159]) ).

fof(f2159,plain,
    ( spl0_190
  <=> ! [X2,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
        | c_HOL_Oone__class_Oone(tc_nat) = X2
        | c_HOL_Oone__class_Oone(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f495,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
      | c_HOL_Oone__class_Oone(tc_nat) = X2
      | c_HOL_Oone__class_Oone(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f494,f237]) ).

fof(f237,axiom,
    ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

fof(f494,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X2
      | c_HOL_Oone__class_Oone(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(forward_demodulation,[],[f493,f237]) ).

fof(f493,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(forward_demodulation,[],[f455,f237]) ).

fof(f455,plain,
    ! [X2,X1] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition_unfolding,[],[f53,f186,f186,f186]) ).

fof(f53,axiom,
    ! [X2,X1] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

fof(f2157,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f488,f2155]) ).

fof(f2155,plain,
    ( spl0_189
  <=> ! [X2,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
        | c_HOL_Oone__class_Oone(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f488,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
      | c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f487,f237]) ).

fof(f487,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(forward_demodulation,[],[f452,f237]) ).

fof(f452,plain,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition_unfolding,[],[f210,f186,f186]) ).

fof(f210,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

fof(f2153,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f486,f2151]) ).

fof(f2151,plain,
    ( spl0_188
  <=> ! [X2,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
        | c_HOL_Oone__class_Oone(tc_nat) = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f486,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
      | c_HOL_Oone__class_Oone(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ),
    inference(forward_demodulation,[],[f485,f237]) ).

fof(f485,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(forward_demodulation,[],[f451,f237]) ).

fof(f451,plain,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition_unfolding,[],[f209,f186,f186]) ).

fof(f209,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

fof(f2149,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f483,f2147]) ).

fof(f2147,plain,
    ( spl0_187
  <=> ! [X2,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f483,plain,
    ! [X2,X1] :
      ( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
    inference(forward_demodulation,[],[f449,f237]) ).

fof(f449,plain,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
    inference(definition_unfolding,[],[f54,f186]) ).

fof(f54,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

fof(f2145,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f444,f2143]) ).

fof(f444,plain,
    ! [X2,X1] :
      ( X1 = X2
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(definition_unfolding,[],[f58,f186]) ).

fof(f58,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

fof(f2141,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f296,f2139]) ).

fof(f296,axiom,
    ! [X27,X25,X13] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X25),X27),X13) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X25,X13)),c_Lambda_Olift(X27,X13)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

fof(f2137,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f148,f2135]) ).

fof(f148,axiom,
    ! [X6,X4,X20] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X6)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X6),X20,X4,X6,X6) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X6),X4,X20,X6,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

fof(f2133,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f100,f2131]) ).

fof(f100,axiom,
    ! [X11,X13] :
      ( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

fof(f2129,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f97,f2127]) ).

fof(f97,axiom,
    ! [X18,X26,X27,X17] :
      ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeD__1__1(X18,X17,X27,X26))
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

fof(f2114,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f96,f2112]) ).

fof(f96,axiom,
    ! [X18,X26,X27,X17] :
      ( c_Type_Otypings(X17,X26,c_Type_Osko__Type__Xlist__app__typeE__1__1(X18,X17,X27,X26))
      | ~ c_Type_Otyping(X17,c_List_Ofoldl(c_Lambda_OdB_OApp,X27,X26,tc_Lambda_OdB,tc_Lambda_OdB),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

fof(f2110,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f31,f2108]) ).

fof(f31,axiom,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X13),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

fof(f2106,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f14,f2104]) ).

fof(f14,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

fof(f2102,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f3,f2100]) ).

fof(f2100,plain,
    ( spl0_178
  <=> ! [X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f3,axiom,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

fof(f1910,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f479,f1908]) ).

fof(f479,plain,
    ! [X2,X11] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,tc_nat),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    inference(forward_demodulation,[],[f440,f414]) ).

fof(f414,plain,
    ! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f42,f186]) ).

fof(f42,axiom,
    ! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

fof(f440,plain,
    ! [X2,X11] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X2,tc_nat) ),
    inference(definition_unfolding,[],[f46,f186]) ).

fof(f46,axiom,
    ! [X2,X11] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X11),tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

fof(f1906,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f286,f1904]) ).

fof(f286,axiom,
    ! [X19,X26,X25] :
      ( X19 = X25
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X19,X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X26,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

fof(f1902,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f279,f1900]) ).

fof(f1900,plain,
    ( spl0_175
  <=> ! [X25,X11,X19] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X19,X11)),c_Lambda_Olift(X25,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f279,axiom,
    ! [X11,X19,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X19),X25))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X19,X11)),c_Lambda_Olift(X25,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

fof(f1898,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f251,f1896]) ).

fof(f1896,plain,
    ( spl0_174
  <=> ! [X18,X33,X17,X27] :
        ( ~ c_Type_Otyping(X17,X27,X18)
        | c_Type_Otyping(X17,X33,X18)
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f251,axiom,
    ! [X18,X27,X17,X33] :
      ( ~ c_Type_Otyping(X17,X27,X18)
      | c_Type_Otyping(X17,X33,X18)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X27),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

fof(f1894,plain,
    ( spl0_173
    | ~ spl0_32
    | ~ spl0_68
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1126,f1064,f795,f649,f1892]) ).

fof(f1126,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
    | ~ spl0_32
    | ~ spl0_68
    | ~ spl0_108 ),
    inference(forward_demodulation,[],[f1113,f796]) ).

fof(f1113,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
    | ~ spl0_32
    | ~ spl0_108 ),
    inference(superposition,[],[f1065,f650]) ).

fof(f1890,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f218,f1888]) ).

fof(f218,axiom,
    ! [X2,X1,X13] :
      ( X1 = X2
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

fof(f1886,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f217,f1884]) ).

fof(f217,axiom,
    ! [X8,X7,X42] :
      ( X8 = X42
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X42) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

fof(f1882,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f179,f1880]) ).

fof(f1880,plain,
    ( spl0_170
  <=> ! [X5,X4,X6,X19] :
        ( ~ c_Wellfounded_Oaccp(X19,X4,X6)
        | c_Wellfounded_Oaccp(X19,X5,X6)
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X5),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f179,axiom,
    ! [X19,X6,X4,X5] :
      ( ~ c_Wellfounded_Oaccp(X19,X4,X6)
      | c_Wellfounded_Oaccp(X19,X5,X6)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).

fof(f1878,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f137,f1876]) ).

fof(f137,axiom,
    ! [X11,X36,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X12,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).

fof(f1874,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f136,f1872]) ).

fof(f136,axiom,
    ! [X36,X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,hAPP(hAPP(c_Lambda_OdB_OApp,X27),X36),X18)
      | c_Type_Otyping(X17,X36,c_Type_Osko__Type__Xtyping__elims__2__1(X18,X17,X27,X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

fof(f1870,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f13,f1868]) ).

fof(f13,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

fof(f1866,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f12,f1864]) ).

fof(f12,axiom,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X12,X13,tc_nat),tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X13),X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

fof(f1862,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f6,f1860]) ).

fof(f6,axiom,
    ! [X3,X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat)
      | hBOOL(hAPP(X3,c_HOL_Ozero__class_Ozero(tc_nat)))
      | ~ hBOOL(hAPP(X3,c_HOL_Ominus__class_Ominus(X4,X5,tc_nat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

fof(f1823,plain,
    ( spl0_164
    | ~ spl0_60
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1124,f1064,f763,f1821]) ).

fof(f1821,plain,
    ( spl0_164
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f1124,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat)
    | ~ spl0_60
    | ~ spl0_108 ),
    inference(superposition,[],[f764,f1065]) ).

fof(f1707,plain,
    ( spl0_163
    | ~ spl0_61
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1123,f1064,f767,f1705]) ).

fof(f1705,plain,
    ( spl0_163
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f1123,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_108 ),
    inference(superposition,[],[f768,f1065]) ).

fof(f1667,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f458,f1665]) ).

fof(f458,plain,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)),tc_nat),
    inference(forward_demodulation,[],[f406,f404]) ).

fof(f404,plain,
    ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),
    inference(definition_unfolding,[],[f185,f186]) ).

fof(f185,axiom,
    ! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

fof(f406,plain,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f170,f186]) ).

fof(f170,axiom,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

fof(f1663,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f457,f1661]) ).

fof(f457,plain,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X1)),tc_nat),
    inference(forward_demodulation,[],[f405,f404]) ).

fof(f405,plain,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X1)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f171,f186]) ).

fof(f171,axiom,
    ! [X11,X1] : c_HOL_Oord__class_Oless(X11,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X1)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

fof(f1659,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f353,f1657]) ).

fof(f353,axiom,
    ! [X11,X18,X6,X17,X12] :
      ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
      | hAPP(c_Type_Oshift(X17,X11,X18,X6),X12) = hAPP(X17,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

fof(f1655,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f311,f1653]) ).

fof(f311,axiom,
    ! [X27,X25] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27)),c_Lambda_Osubst(X25,X27,c_HOL_Ozero__class_Ozero(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

fof(f1651,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f301,f1649]) ).

fof(f301,axiom,
    ! [X2,X46,X19,X26] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X26,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X19),X46,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

fof(f1647,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f294,f1645]) ).

fof(f1645,plain,
    ( spl0_157
  <=> ! [X13,X25,X11] :
        ( X11 = X13
        | c_HOL_Oord__class_Oless(X13,X11,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X25,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f294,axiom,
    ! [X11,X25,X13] :
      ( X11 = X13
      | c_HOL_Oord__class_Oless(X13,X11,tc_nat)
      | c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X25,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

fof(f1643,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f203,f1641]) ).

fof(f1641,plain,
    ( spl0_156
  <=> ! [X6,X4,X19,X5,X22] :
        ( hBOOL(hAPP(hAPP(X19,X5),X4))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X19,X6,X22),X4),X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f203,axiom,
    ! [X19,X6,X4,X5,X22] :
      ( hBOOL(hAPP(hAPP(X19,X5),X4))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X19,X6,X22),X4),X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).

fof(f1639,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f200,f1637]) ).

fof(f200,axiom,
    ! [X19,X6,X4,X5,X22] :
      ( ~ hBOOL(hAPP(hAPP(X19,X4),X5))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X19,X6,X22),X5),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).

fof(f1635,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f162,f1633]) ).

fof(f1633,plain,
    ( spl0_154
  <=> ! [X6,X4,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f162,axiom,
    ! [X6,X4,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X5),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f1631,plain,
    ( spl0_153
    | ~ spl0_82
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1115,f1064,f872,f1629]) ).

fof(f1629,plain,
    ( spl0_153
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1115,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
    | ~ spl0_82
    | ~ spl0_108 ),
    inference(superposition,[],[f873,f1065]) ).

fof(f1627,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f159,f1625]) ).

fof(f1625,plain,
    ( spl0_152
  <=> ! [X6,X7,X8] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X8),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f159,axiom,
    ! [X8,X6,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X7),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X8),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f1623,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f91,f1621]) ).

fof(f91,axiom,
    ! [X25,X13] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X25),X13) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X25,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

fof(f1619,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f40,f1617]) ).

fof(f40,axiom,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

fof(f1615,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f9,f1613]) ).

fof(f9,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

fof(f1544,plain,
    ( spl0_148
    | ~ spl0_98
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1114,f1064,f951,f1542]) ).

fof(f1542,plain,
    ( spl0_148
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1114,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
    | ~ spl0_98
    | ~ spl0_108 ),
    inference(superposition,[],[f952,f1065]) ).

fof(f1436,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f463,f1434]) ).

fof(f463,plain,
    ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f462,f236]) ).

fof(f462,plain,
    ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f415,f161]) ).

fof(f415,plain,
    ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f144,f186]) ).

fof(f144,axiom,
    ! [X39] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X39),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X39,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).

fof(f1432,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f436,f1430]) ).

fof(f436,plain,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(definition_unfolding,[],[f230,f186]) ).

fof(f230,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f1428,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f428,f1426]) ).

fof(f428,plain,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(definition_unfolding,[],[f229,f186]) ).

fof(f229,axiom,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f1424,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f352,f1422]) ).

fof(f352,axiom,
    ! [X18,X27,X17,X33] :
      ( ~ c_Type_Otyping(X17,X27,X18)
      | c_Type_Otyping(X17,X33,X18)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X27),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

fof(f1420,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f348,f1418]) ).

fof(f348,axiom,
    ! [X28,X11,X18,X27,X17] :
      ( ~ c_Type_Otyping(X17,X27,X18)
      | c_Type_Otyping(c_Type_Oshift(X17,X11,X28,tc_Type_Otype),c_Lambda_Olift(X27,X11),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

fof(f1416,plain,
    ( spl0_142
    | ~ spl0_24
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f954,f894,f614,f1414]) ).

fof(f1414,plain,
    ( spl0_142
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f954,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_84 ),
    inference(resolution,[],[f895,f615]) ).

fof(f1412,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f334,f1410]) ).

fof(f1410,plain,
    ( spl0_141
  <=> ! [X38,X53,X52,X37] :
        ( X37 = X52
        | hAPP(hAPP(c_Type_Otype_OFun,X37),X38) != hAPP(hAPP(c_Type_Otype_OFun,X52),X53) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f334,axiom,
    ! [X38,X37,X52,X53] :
      ( X37 = X52
      | hAPP(hAPP(c_Type_Otype_OFun,X37),X38) != hAPP(hAPP(c_Type_Otype_OFun,X52),X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

fof(f1408,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f333,f1406]) ).

fof(f1406,plain,
    ( spl0_140
  <=> ! [X38,X52,X53,X37] :
        ( X38 = X53
        | hAPP(hAPP(c_Type_Otype_OFun,X37),X38) != hAPP(hAPP(c_Type_Otype_OFun,X52),X53) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f333,axiom,
    ! [X38,X37,X52,X53] :
      ( X38 = X53
      | hAPP(hAPP(c_Type_Otype_OFun,X37),X38) != hAPP(hAPP(c_Type_Otype_OFun,X52),X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

fof(f1404,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f322,f1402]) ).

fof(f1402,plain,
    ( spl0_139
  <=> ! [X41,X40,X48,X47] :
        ( X40 = X47
        | hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f322,axiom,
    ! [X40,X41,X48,X47] :
      ( X40 = X47
      | hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

fof(f1400,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f321,f1398]) ).

fof(f1398,plain,
    ( spl0_138
  <=> ! [X41,X48,X40,X47] :
        ( X41 = X48
        | hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f321,axiom,
    ! [X40,X41,X48,X47] :
      ( X41 = X48
      | hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

fof(f1396,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f292,f1394]) ).

fof(f292,axiom,
    ! [X8,X6,X7,X42] :
      ( ~ class_Orderings_Opreorder(X6)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X6)
      | ~ c_HOL_Oord__class_Oless(X8,X42,X6)
      | c_HOL_Oord__class_Oless(X7,X42,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f1392,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f291,f1390]) ).

fof(f291,axiom,
    ! [X8,X6,X7,X42] :
      ( ~ class_Orderings_Oorder(X6)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X6)
      | ~ c_HOL_Oord__class_Oless(X42,X8,X6)
      | c_HOL_Oord__class_Oless(X42,X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f1388,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f277,f1386]) ).

fof(f277,axiom,
    ! [X2,X46,X27,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X25)),X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X46,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

fof(f1384,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f276,f1382]) ).

fof(f276,axiom,
    ! [X27,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X27))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X25)),c_Lambda_OdB_OAbs(X27))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

fof(f1380,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f273,f1378]) ).

fof(f1378,plain,
    ( spl0_133
  <=> ! [X34,X2] :
        ( ~ c_List_Olistsp(c_InductTermi_OIT,X34,tc_Lambda_OdB)
        | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f273,axiom,
    ! [X2,X34] :
      ( ~ c_List_Olistsp(c_InductTermi_OIT,X34,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X34,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

fof(f1376,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f271,f1374]) ).

fof(f271,axiom,
    ! [X2,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

fof(f1372,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f270,f1370]) ).

fof(f1370,plain,
    ( spl0_131
  <=> ! [X6,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f270,axiom,
    ! [X2,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

fof(f1368,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f232,f1366]) ).

fof(f232,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Oone__class_Oone(X6)),c_HOL_Oone__class_Oone(X6)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

fof(f1364,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f117,f1362]) ).

fof(f1362,plain,
    ( spl0_129
  <=> ! [X6,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f117,axiom,
    ! [X2,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

fof(f1360,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f116,f1358]) ).

fof(f116,axiom,
    ! [X2,X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_Nat_Osemiring__1__class_Oof__nat(X2,X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

fof(f1356,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f94,f1354]) ).

fof(f94,axiom,
    ! [X8,X19,X6,X4] :
      ( ~ c_Wellfounded_Oaccp(X19,X4,X6)
      | c_Wellfounded_Oaccp(X19,X8,X6)
      | ~ hBOOL(hAPP(hAPP(X19,X8),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).

fof(f1352,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f50,f1350]) ).

fof(f50,axiom,
    ! [X8,X19,X6,X7] :
      ( ~ hBOOL(hAPP(hAPP(X19,X7),X8))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).

fof(f1199,plain,
    ( spl0_125
    | ~ spl0_72
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1117,f1064,f811,f1197]) ).

fof(f1117,plain,
    ( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0)
    | ~ spl0_72
    | ~ spl0_108 ),
    inference(superposition,[],[f812,f1065]) ).

fof(f1192,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f403,f1190]) ).

fof(f403,plain,
    ! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f29,f186]) ).

fof(f29,axiom,
    ! [X2,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

fof(f1188,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f364,f1185]) ).

fof(f364,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

fof(f1183,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f339,f1180]) ).

fof(f1180,plain,
    ( spl0_122
  <=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f339,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r____,v_a____,c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I1_J_0) ).

fof(f1178,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f320,f1176]) ).

fof(f320,axiom,
    ! [X8,X6,X7] :
      ( ~ class_Orderings_Olinorder(X6)
      | X7 = X8
      | c_HOL_Oord__class_Oless(X8,X7,X6)
      | c_HOL_Oord__class_Oless(X7,X8,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

fof(f1174,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f304,f1172]) ).

fof(f1172,plain,
    ( spl0_120
  <=> ! [X25,X1,X46] :
        ( c_Lambda_OdB_OVar(X1) = X25
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f304,axiom,
    ! [X46,X1,X25] :
      ( c_Lambda_OdB_OVar(X1) = X25
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

fof(f1170,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f287,f1168]) ).

fof(f287,axiom,
    ! [X46,X19,X25] :
      ( c_Lambda_OdB_OAbs(X19) = X25
      | c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

fof(f1166,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f278,f1164]) ).

fof(f1164,plain,
    ( spl0_118
  <=> ! [X11,X27] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
        | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X27),c_Lambda_OdB_OVar(X11)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f278,axiom,
    ! [X11,X27] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
      | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X27),c_Lambda_OdB_OVar(X11)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

fof(f1162,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f267,f1160]) ).

fof(f1160,plain,
    ( spl0_117
  <=> ! [X25,X1,X46] :
        ( c_List_Olist_ONil(tc_Lambda_OdB) = X46
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f267,axiom,
    ! [X46,X1,X25] :
      ( c_List_Olist_ONil(tc_Lambda_OdB) = X46
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

fof(f1158,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f264,f1156]) ).

fof(f264,axiom,
    ! [X46,X19,X25] :
      ( c_List_Olist_ONil(tc_Lambda_OdB) = X46
      | c_Lambda_OdB_OAbs(X19) != c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X46,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

fof(f1154,plain,
    ( spl0_115
    | ~ spl0_81
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1116,f1064,f868,f1152]) ).

fof(f1152,plain,
    ( spl0_115
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1116,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))
    | ~ spl0_81
    | ~ spl0_108 ),
    inference(superposition,[],[f869,f1065]) ).

fof(f1150,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f166,f1148]) ).

fof(f166,axiom,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

fof(f1146,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f165,f1144]) ).

fof(f165,axiom,
    ! [X11,X1,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X1),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

fof(f1142,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f164,f1140]) ).

fof(f164,axiom,
    ! [X11,X1,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X12),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

fof(f1138,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f161,f1136]) ).

fof(f1134,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f153,f1132]) ).

fof(f1132,plain,
    ( spl0_110
  <=> ! [X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f153,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X1
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

fof(f1130,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f152,f1128]) ).

fof(f1128,plain,
    ( spl0_109
  <=> ! [X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f152,axiom,
    ! [X2,X1] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

fof(f1066,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f461,f1064]) ).

fof(f461,plain,
    ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),c_HOL_Oone__class_Oone(tc_nat)),
    inference(forward_demodulation,[],[f460,f236]) ).

fof(f460,plain,
    ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
    inference(forward_demodulation,[],[f413,f404]) ).

fof(f413,plain,
    ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
    inference(definition_unfolding,[],[f145,f186]) ).

fof(f145,axiom,
    ! [X39] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X39)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X39)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).

fof(f1062,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f332,f1060]) ).

fof(f332,axiom,
    ! [X11,X19,X12] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X19,c_Lambda_OdB_OVar(X11),X12))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

fof(f1058,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f331,f1056]) ).

fof(f331,axiom,
    ! [X11,X36,X12] :
      ( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
      | c_Lambda_OdB_OVar(X12) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X36,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

fof(f1054,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f157,f1052]) ).

fof(f1052,plain,
    ( spl0_105
  <=> ! [X6,X2,X1] :
        ( ~ class_Nat_Osemiring__char__0(X6)
        | X1 = X2
        | c_Nat_Osemiring__1__class_Oof__nat(X1,X6) != c_Nat_Osemiring__1__class_Oof__nat(X2,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f157,axiom,
    ! [X2,X1,X6] :
      ( ~ class_Nat_Osemiring__char__0(X6)
      | X1 = X2
      | c_Nat_Osemiring__1__class_Oof__nat(X1,X6) != c_Nat_Osemiring__1__class_Oof__nat(X2,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

fof(f1050,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f154,f1048]) ).

fof(f154,axiom,
    ! [X7,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X4) != X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

fof(f1046,plain,
    ( spl0_103
    | ~ spl0_13
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f820,f783,f560,f1043]) ).

fof(f1043,plain,
    ( spl0_103
  <=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f560,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f783,plain,
    ( spl0_65
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | c_HOL_Oone__class_Oone(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f820,plain,
    ( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_13
    | ~ spl0_65 ),
    inference(resolution,[],[f784,f562]) ).

fof(f562,plain,
    ( class_Ring__and__Field_Osemiring__1(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f560]) ).

fof(f784,plain,
    ( ! [X6] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | c_HOL_Oone__class_Oone(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X6) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f783]) ).

fof(f1041,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f70,f1039]) ).

fof(f70,axiom,
    ! [X6,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Oone__class_Oone(X6)),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f1037,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f30,f1035]) ).

fof(f30,axiom,
    ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

fof(f1033,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f5,f1031]) ).

fof(f5,axiom,
    ! [X2,X1] :
      ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

fof(f1029,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f4,f1027]) ).

fof(f4,axiom,
    ! [X2,X1] :
      ( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

fof(f953,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f399,f951]) ).

fof(f399,plain,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f120,f186]) ).

fof(f120,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X7),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

fof(f949,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f314,f947]) ).

fof(f314,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | c_HOL_Oord__class_Oless(X1,X2,tc_nat)
      | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

fof(f945,plain,
    ( spl0_96
    | ~ spl0_68
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f892,f872,f795,f942]) ).

fof(f942,plain,
    ( spl0_96
  <=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f892,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_68
    | ~ spl0_82 ),
    inference(superposition,[],[f873,f796]) ).

fof(f940,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f280,f938]) ).

fof(f280,axiom,
    ! [X11,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

fof(f936,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f243,f934]) ).

fof(f934,plain,
    ( spl0_94
  <=> ! [X6,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f243,axiom,
    ! [X6,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f932,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f242,f930]) ).

fof(f930,plain,
    ( spl0_93
  <=> ! [X6,X4] :
        ( ~ class_OrderedGroup_Omonoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f242,axiom,
    ! [X6,X4] :
      ( ~ class_OrderedGroup_Omonoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f928,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f241,f926]) ).

fof(f926,plain,
    ( spl0_92
  <=> ! [X6,X4] :
        ( ~ class_OrderedGroup_Omonoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X4) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f241,axiom,
    ! [X6,X4] :
      ( ~ class_OrderedGroup_Omonoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f924,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f240,f922]) ).

fof(f922,plain,
    ( spl0_91
  <=> ! [X6,X4] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f240,axiom,
    ! [X6,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),X4),c_HOL_Ozero__class_Ozero(X6)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f920,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f235,f918]) ).

fof(f918,plain,
    ( spl0_90
  <=> ! [X6,X4] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X4) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f235,axiom,
    ! [X6,X4] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X4) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f916,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f234,f914]) ).

fof(f914,plain,
    ( spl0_89
  <=> ! [X6,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X7) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f234,axiom,
    ! [X6,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X6)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X6),c_HOL_Ozero__class_Ozero(X6)),X7) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f912,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f177,f910]) ).

fof(f910,plain,
    ( spl0_88
  <=> ! [X27] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
        | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f177,axiom,
    ! [X27] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X27,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).

fof(f908,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f176,f906]) ).

fof(f906,plain,
    ( spl0_87
  <=> ! [X19] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X19))
        | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X19,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f176,axiom,
    ! [X19] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X19))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X19,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).

fof(f904,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f44,f902]) ).

fof(f44,axiom,
    ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),X2,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

fof(f900,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f43,f898]) ).

fof(f43,axiom,
    ! [X2,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X2,tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

fof(f896,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f15,f894]) ).

fof(f15,axiom,
    ! [X2,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X2,tc_nat),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

fof(f879,plain,
    ( ~ spl0_83
    | ~ spl0_68
    | ~ spl0_72 ),
    inference(avatar_split_clause,[],[f840,f811,f795,f876]) ).

fof(f876,plain,
    ( spl0_83
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f840,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_68
    | ~ spl0_72 ),
    inference(superposition,[],[f812,f796]) ).

fof(f874,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f396,f872]) ).

fof(f396,plain,
    ! [X7] : c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
    inference(definition_unfolding,[],[f67,f186]) ).

fof(f67,axiom,
    ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f870,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f392,f868]) ).

fof(f392,plain,
    ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat)),
    inference(definition_unfolding,[],[f173,f186]) ).

fof(f173,axiom,
    ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

fof(f866,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f389,f864]) ).

fof(f864,plain,
    ( spl0_80
  <=> ! [X61,X62,X6] :
        ( X61 = X62
        | ~ hBOOL(hAPP(hAPP(c_fequal(X6),X61),X62)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f389,axiom,
    ! [X6,X62,X61] :
      ( X61 = X62
      | ~ hBOOL(hAPP(hAPP(c_fequal(X6),X61),X62)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f862,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f358,f860]) ).

fof(f860,plain,
    ( spl0_79
  <=> ! [X18,X11,X17] :
        ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OVar(X11),X18)
        | hAPP(X17,X11) = X18 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f358,axiom,
    ! [X11,X18,X17] :
      ( ~ c_Type_Otyping(X17,c_Lambda_OdB_OVar(X11),X18)
      | hAPP(X17,X11) = X18 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

fof(f858,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f347,f856]) ).

fof(f347,axiom,
    ! [X6,X4,X5] :
      ( ~ class_Orderings_Opreorder(X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

fof(f854,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f345,f852]) ).

fof(f345,axiom,
    ! [X8,X6,X7] :
      ( ~ class_Orderings_Olinorder(X6)
      | ~ c_HOL_Oord__class_Oless(X8,X7,X6)
      | ~ c_HOL_Oord__class_Oless(X7,X8,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f850,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f344,f848]) ).

fof(f344,axiom,
    ! [X6,X4,X5] :
      ( ~ class_Orderings_Oorder(X6)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X6)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f846,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f300,f844]) ).

fof(f844,plain,
    ( spl0_75
  <=> ! [X11,X27] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X27,X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f300,axiom,
    ! [X11,X27] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X27,X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

fof(f839,plain,
    ( spl0_74
    | ~ spl0_13
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f819,f775,f560,f836]) ).

fof(f836,plain,
    ( spl0_74
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f775,plain,
    ( spl0_63
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | c_HOL_Ozero__class_Ozero(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f819,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_13
    | ~ spl0_63 ),
    inference(resolution,[],[f776,f562]) ).

fof(f776,plain,
    ( ! [X6] :
        ( ~ class_Ring__and__Field_Osemiring__1(X6)
        | c_HOL_Ozero__class_Ozero(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X6) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f775]) ).

fof(f817,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f474,f815]) ).

fof(f474,plain,
    ! [X2] :
      ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ),
    inference(forward_demodulation,[],[f473,f236]) ).

fof(f473,plain,
    ! [X2] :
      ( ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ),
    inference(forward_demodulation,[],[f432,f161]) ).

fof(f432,plain,
    ! [X2] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
    inference(definition_unfolding,[],[f123,f186]) ).

fof(f123,axiom,
    ! [X2] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

fof(f813,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f390,f811]) ).

fof(f390,plain,
    ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2,
    inference(definition_unfolding,[],[f75,f186]) ).

fof(f75,axiom,
    ! [X2] : c_Suc(X2) != X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f809,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f356,f807]) ).

fof(f356,axiom,
    ! [X18,X6,X7,X17] : hAPP(c_Type_Oshift(X17,X7,X18,X6),X7) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

fof(f805,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f329,f803]) ).

fof(f329,axiom,
    ! [X2] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X2
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f801,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f285,f799]) ).

fof(f799,plain,
    ( spl0_69
  <=> ! [X19] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X19))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f285,axiom,
    ! [X19] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X19))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X19))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

fof(f797,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f237,f795]) ).

fof(f793,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f236,f791]) ).

fof(f789,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f233,f787]) ).

fof(f787,plain,
    ( spl0_66
  <=> ! [X6,X19] : c_Transitive__Closure_Ortranclp(X19,X6) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X19,X6),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f233,axiom,
    ! [X19,X6] : c_Transitive__Closure_Ortranclp(X19,X6) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X19,X6),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).

fof(f785,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f207,f783]) ).

fof(f207,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Osemiring__1(X6)
      | c_HOL_Oone__class_Oone(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

fof(f781,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f205,f779]) ).

fof(f779,plain,
    ( spl0_64
  <=> ! [X6,X4,X22,X21] : c_List_Ofoldr(X21,c_List_Olist_ONil(X22),X4,X22,X6) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f205,axiom,
    ! [X21,X6,X4,X22] : c_List_Ofoldr(X21,c_List_Olist_ONil(X22),X4,X22,X6) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

fof(f777,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f115,f775]) ).

fof(f115,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Osemiring__1(X6)
      | c_HOL_Ozero__class_Ozero(X6) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

fof(f773,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f105,f771]) ).

fof(f105,axiom,
    ! [X1,X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

fof(f769,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f73,f767]) ).

fof(f73,axiom,
    ! [X11,X12] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X11),X11,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

fof(f765,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f72,f763]) ).

fof(f72,axiom,
    ! [X11,X12] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12),X11,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

fof(f761,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f71,f759]) ).

fof(f759,plain,
    ( spl0_59
  <=> ! [X6,X22,X19] : c_Predicate_Oconversep(c_Predicate_Oconversep(X19,X6,X22),X22,X6) = X19 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f71,axiom,
    ! [X19,X6,X22] : c_Predicate_Oconversep(c_Predicate_Oconversep(X19,X6,X22),X22,X6) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).

fof(f757,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f55,f755]) ).

fof(f55,axiom,
    ! [X21,X6,X4,X22] : c_List_Ofoldl(X21,X4,c_List_Olist_ONil(X22),X6,X22) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

fof(f751,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f340,f749]) ).

fof(f749,plain,
    ( spl0_57
  <=> ! [X0,X24] :
        ( X0 = X24
        | c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OVar(X24) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f340,axiom,
    ! [X0,X24] :
      ( X0 = X24
      | c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OVar(X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

fof(f747,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f338,f745]) ).

fof(f338,axiom,
    ! [X40,X41,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,X40),X41) != c_Lambda_OdB_OAbs(X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

fof(f743,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f303,f741]) ).

fof(f303,axiom,
    ! [X48,X0,X47] : c_Lambda_OdB_OVar(X0) != hAPP(hAPP(c_Lambda_OdB_OApp,X47),X48),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).

fof(f739,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f302,f737]) ).

fof(f737,plain,
    ( spl0_54
  <=> ! [X39,X49] :
        ( X39 = X49
        | c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OAbs(X49) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f302,axiom,
    ! [X39,X49] :
      ( X39 = X49
      | c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OAbs(X49) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

fof(f735,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f281,f733]) ).

fof(f281,axiom,
    ! [X27,X25,X13] : c_Lambda_Osubst(c_Lambda_Olift(X27,X13),X25,X13) = X27,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

fof(f731,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f181,f729]) ).

fof(f181,axiom,
    ! [X19,X6,X7] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X19,X6),X7),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

fof(f727,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f113,f725]) ).

fof(f113,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X6),c_HOL_Oone__class_Oone(X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

fof(f723,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f111,f721]) ).

fof(f721,plain,
    ( spl0_50
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X6)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X6),c_HOL_Ozero__class_Ozero(X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f111,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X6)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X6),c_HOL_Ozero__class_Ozero(X6),X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

fof(f719,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f57,f717]) ).

fof(f57,axiom,
    ! [X6] : c_fequal(X6) = c_Predicate_Oconversep(c_fequal(X6),X6,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).

fof(f715,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f34,f713]) ).

fof(f34,axiom,
    ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

fof(f711,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f388,f709]) ).

fof(f388,axiom,
    ! [X6,X7] : hBOOL(hAPP(hAPP(c_fequal(X6),X7),X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f707,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f362,f705]) ).

fof(f362,axiom,
    ! [X50,X7] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X7),hAPP(X50,X7)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

fof(f703,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f335,f701]) ).

fof(f335,axiom,
    ! [X36,X13] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X36,X13) = X36,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

fof(f699,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f327,f697]) ).

fof(f697,plain,
    ( spl0_44
  <=> ! [X11,X27] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X11)),X27)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f327,axiom,
    ! [X11,X27] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X11)),X27)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

fof(f695,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f56,f693]) ).

fof(f693,plain,
    ( spl0_43
  <=> ! [X6] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X6)
        | c_HOL_Ozero__class_Ozero(X6) != c_HOL_Oone__class_Oone(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f56,axiom,
    ! [X6] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X6)
      | c_HOL_Ozero__class_Ozero(X6) != c_HOL_Oone__class_Oone(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

fof(f691,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f18,f689]) ).

fof(f18,axiom,
    ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

fof(f687,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f17,f685]) ).

fof(f17,axiom,
    ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

fof(f683,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f1,f681]) ).

fof(f1,axiom,
    ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X0),tc_Lambda_OdB) = c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).

fof(f679,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f368,f677]) ).

fof(f677,plain,
    ( spl0_39
  <=> ! [X60,X59] :
        ( ~ class_Orderings_Oorder(X60)
        | class_Orderings_Oorder(tc_fun(X59,X60)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f368,axiom,
    ! [X59,X60] :
      ( ~ class_Orderings_Oorder(X60)
      | class_Orderings_Oorder(tc_fun(X59,X60)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f675,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f367,f673]) ).

fof(f673,plain,
    ( spl0_38
  <=> ! [X60,X59] :
        ( ~ class_Orderings_Opreorder(X60)
        | class_Orderings_Opreorder(tc_fun(X59,X60)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f367,axiom,
    ! [X59,X60] :
      ( ~ class_Orderings_Opreorder(X60)
      | class_Orderings_Opreorder(tc_fun(X59,X60)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f671,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f310,f669]) ).

fof(f669,plain,
    ( spl0_37
  <=> ! [X6,X7] :
        ( ~ class_Orderings_Opreorder(X6)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f310,axiom,
    ! [X6,X7] :
      ( ~ class_Orderings_Opreorder(X6)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f667,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f309,f665]) ).

fof(f665,plain,
    ( spl0_36
  <=> ! [X6,X7] :
        ( ~ class_Orderings_Olinorder(X6)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f309,axiom,
    ! [X6,X7] :
      ( ~ class_Orderings_Olinorder(X6)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f663,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f308,f661]) ).

fof(f661,plain,
    ( spl0_35
  <=> ! [X6,X7] :
        ( ~ class_Orderings_Oorder(X6)
        | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f308,axiom,
    ! [X6,X7] :
      ( ~ class_Orderings_Oorder(X6)
      | ~ c_HOL_Oord__class_Oless(X7,X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f659,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f52,f657]) ).

fof(f657,plain,
    ( spl0_34
  <=> ! [X6,X20,X19] : ~ c_ListOrder_Ostep1(X19,X20,c_List_Olist_ONil(X6),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f52,axiom,
    ! [X19,X6,X20] : ~ c_ListOrder_Ostep1(X19,X20,c_List_Olist_ONil(X6),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

fof(f655,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f51,f653]) ).

fof(f653,plain,
    ( spl0_33
  <=> ! [X6,X20,X19] : ~ c_ListOrder_Ostep1(X19,c_List_Olist_ONil(X6),X20,X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f51,axiom,
    ! [X19,X6,X20] : ~ c_ListOrder_Ostep1(X19,c_List_Olist_ONil(X6),X20,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

fof(f651,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f2,f649]) ).

fof(f2,axiom,
    ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).

fof(f647,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f298,f645]) ).

fof(f298,axiom,
    ! [X0,X49] : c_Lambda_OdB_OVar(X0) != c_Lambda_OdB_OAbs(X49),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

fof(f643,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f297,f641]) ).

fof(f641,plain,
    ( spl0_30
  <=> ! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f297,axiom,
    ! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

fof(f639,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f289,f637]) ).

fof(f289,axiom,
    ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

fof(f635,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f183,f633]) ).

fof(f633,plain,
    ( spl0_28
  <=> ! [X6,X43] : c_List_Olistsp(X43,c_List_Olist_ONil(X6),X6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f183,axiom,
    ! [X6,X43] : c_List_Olistsp(X43,c_List_Olist_ONil(X6),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

fof(f631,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f359,f628]) ).

fof(f628,plain,
    ( spl0_27
  <=> c_Type_Otyping(v_ea______,v_ua______,v_T____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f359,axiom,
    c_Type_Otyping(v_ea______,v_ua______,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I7_J_0) ).

fof(f626,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f351,f623]) ).

fof(f623,plain,
    ( spl0_26
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_a____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f351,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_a____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I3_J_0) ).

fof(f621,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f350,f618]) ).

fof(f618,plain,
    ( spl0_25
  <=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f350,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).

fof(f616,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f306,f614]) ).

fof(f306,axiom,
    ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f612,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f293,f609]) ).

fof(f609,plain,
    ( spl0_23
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f293,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I6_J_0) ).

fof(f607,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f282,f604]) ).

fof(f604,plain,
    ( spl0_22
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f282,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

fof(f602,plain,
    ( spl0_21
    | spl0_1 ),
    inference(avatar_split_clause,[],[f366,f500,f600]) ).

fof(f500,plain,
    ( spl0_1
  <=> v_thesis____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f366,axiom,
    ! [X7] :
      ( v_thesis____
      | ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f598,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f387,f595]) ).

fof(f595,plain,
    ( spl0_20
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f387,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f593,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f386,f590]) ).

fof(f590,plain,
    ( spl0_19
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f386,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f588,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f385,f585]) ).

fof(f385,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f583,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f384,f580]) ).

fof(f580,plain,
    ( spl0_17
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f384,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f578,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f383,f575]) ).

fof(f383,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f573,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f382,f570]) ).

fof(f570,plain,
    ( spl0_15
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f382,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f568,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f381,f565]) ).

fof(f565,plain,
    ( spl0_14
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f381,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f563,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f380,f560]) ).

fof(f380,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f558,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f379,f555]) ).

fof(f555,plain,
    ( spl0_12
  <=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f379,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

fof(f553,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f378,f550]) ).

fof(f550,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f378,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

fof(f548,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f377,f545]) ).

fof(f545,plain,
    ( spl0_10
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f377,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f543,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f376,f540]) ).

fof(f376,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f538,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f375,f535]) ).

fof(f535,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f375,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f533,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f374,f530]) ).

fof(f374,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f528,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f373,f525]) ).

fof(f525,plain,
    ( spl0_6
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f373,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f523,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f372,f520]) ).

fof(f520,plain,
    ( spl0_5
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f372,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f518,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f371,f515]) ).

fof(f515,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f371,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f513,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f370,f510]) ).

fof(f510,plain,
    ( spl0_3
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f370,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f508,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f369,f505]) ).

fof(f505,plain,
    ( spl0_2
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f369,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f503,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f365,f500]) ).

fof(f365,axiom,
    ~ v_thesis____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.20  % Problem    : LCL839-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.21  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.42  % Computer : n008.cluster.edu
% 0.12/0.42  % Model    : x86_64 x86_64
% 0.12/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42  % Memory   : 8042.1875MB
% 0.12/0.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42  % CPULimit   : 300
% 0.12/0.42  % WCLimit    : 300
% 0.12/0.42  % DateTime   : Fri May  3 13:31:42 EDT 2024
% 0.12/0.42  % CPUTime    : 
% 0.12/0.42  % (11583)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.45  % (11586)WARNING: value z3 for option sas not known
% 0.12/0.45  % (11589)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)
% 0.12/0.45  % (11590)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)
% 0.12/0.45  % (11584)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.45  % (11588)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)
% 0.12/0.45  % (11585)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.45  % (11587)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.45  % (11586)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)
% 0.17/0.53  TRYING [1]
% 0.74/0.55  TRYING [2]
% 1.78/0.69  TRYING [3]
% 1.78/0.70  TRYING [1]
% 1.78/0.73  TRYING [2]
% 4.55/1.11  % (11588)First to succeed.
% 4.96/1.14  % (11588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11583"
% 4.96/1.14  % (11588)Refutation found. Thanks to Tanya!
% 4.96/1.14  % SZS status Unsatisfiable for theBenchmark
% 4.96/1.14  % SZS output start Proof for theBenchmark
% See solution above
% 4.96/1.16  % (11588)------------------------------
% 4.96/1.16  % (11588)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.96/1.16  % (11588)Termination reason: Refutation
% 4.96/1.16  
% 4.96/1.16  % (11588)Memory used [KB]: 8024
% 4.96/1.16  % (11588)Time elapsed: 0.685 s
% 4.96/1.16  % (11588)Instructions burned: 1215 (million)
% 4.96/1.16  % (11583)Success in time 0.718 s
%------------------------------------------------------------------------------