TSTP Solution File: LCL753-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL753-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 00:33:59 EDT 2024

% Result   : Unsatisfiable 31.69s 4.99s
% Output   : Refutation 31.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      : 1566
% Syntax   : Number of formulae    : 3927 ( 524 unt;   0 def)
%            Number of atoms       : 11965 (1477 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives : 14847 (6809   ~;6887   |;   0   &)
%                                         (1151 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  : 1191 (1189 usr;1152 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   4 con; 0-3 aty)
%            Number of variables   : 7396 (7396   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f77984,plain,
    $false,
    inference(avatar_sat_refutation,[],[f865,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f994,f999,f1004,f1009,f1014,f1019,f1024,f1029,f1034,f1039,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1175,f1180,f1184,f1188,f1192,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1254,f1258,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1299,f1303,f1308,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1354,f1358,f1362,f1366,f1370,f1423,f1449,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1530,f1534,f1538,f1542,f1546,f1550,f1554,f1558,f1562,f1566,f1570,f1574,f1580,f1604,f1678,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1887,f2016,f2106,f2110,f2114,f2118,f2122,f2126,f2131,f2135,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2228,f2477,f2481,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2752,f2756,f2760,f2764,f2768,f2772,f2776,f2780,f2784,f2788,f2792,f2796,f2800,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2840,f2844,f2848,f2852,f2856,f2860,f2864,f2868,f2872,f2876,f2880,f2884,f2888,f3318,f3637,f3641,f3645,f3649,f3653,f3657,f3662,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f4341,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4528,f4532,f4536,f4540,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4822,f5180,f5541,f5545,f5549,f5553,f5557,f5561,f5565,f5569,f5573,f5577,f5581,f5585,f5589,f5593,f5597,f5601,f5605,f5609,f5613,f5617,f5621,f5625,f5629,f5670,f5728,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5899,f6141,f6145,f6149,f6153,f6157,f6161,f6165,f6169,f6173,f6303,f6474,f6478,f6482,f6486,f6490,f6494,f6498,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6530,f6566,f6570,f6574,f6578,f6582,f6586,f6590,f6594,f6598,f6602,f6623,f6627,f6631,f6635,f6639,f6643,f6647,f6651,f6655,f6659,f6668,f6672,f6676,f6680,f6684,f6688,f6692,f6696,f6700,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7705,f7709,f7713,f7717,f7721,f7725,f7729,f7733,f7737,f7741,f7786,f7790,f7794,f7974,f8543,f8547,f8631,f8635,f8708,f8712,f8716,f8720,f8724,f8728,f8732,f9028,f9055,f9086,f9090,f9094,f9098,f9198,f9202,f9206,f9210,f9214,f9218,f9872,f9876,f9918,f9922,f9926,f9930,f9934,f9938,f10171,f10175,f10245,f10249,f10337,f10341,f10345,f10349,f10353,f10357,f10361,f10365,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10401,f10405,f10916,f10920,f10924,f10928,f10932,f10936,f10940,f10944,f10948,f10952,f10956,f10960,f10964,f10968,f10972,f10976,f10980,f10984,f10988,f10992,f10996,f11000,f11004,f11008,f11012,f11016,f11020,f12125,f12129,f12133,f12137,f12141,f12145,f12252,f12256,f12260,f12264,f12268,f12272,f12276,f12280,f12284,f12288,f12292,f12296,f12300,f12304,f12308,f12312,f12316,f12320,f12324,f12328,f12332,f12336,f12340,f12344,f12348,f12352,f12356,f12360,f12541,f13303,f13598,f13602,f13606,f13610,f13614,f13618,f13622,f13626,f13630,f13634,f13638,f13642,f13646,f13655,f13659,f13663,f13667,f13671,f13675,f13679,f13683,f13687,f13691,f13695,f13699,f13703,f13707,f13711,f13715,f13719,f13723,f13727,f13731,f13735,f13747,f13751,f13755,f13759,f13763,f13767,f13771,f13775,f13779,f13783,f13787,f13791,f13795,f13799,f14667,f15850,f16101,f16105,f16112,f16116,f16120,f16124,f16128,f16132,f16136,f16140,f16144,f16148,f16152,f16156,f16160,f16164,f16168,f16172,f16176,f16180,f16184,f16188,f16192,f16203,f16207,f16273,f16338,f16385,f16422,f16426,f16479,f16523,f16527,f16531,f16535,f16539,f16543,f16547,f16551,f16555,f16559,f16563,f16567,f16571,f16575,f16579,f16583,f16587,f16591,f17746,f19087,f19091,f19095,f19099,f19103,f19107,f19111,f19115,f19119,f19123,f19127,f19131,f19135,f19139,f19143,f19147,f19151,f19155,f19159,f19163,f19167,f19171,f19187,f19191,f19195,f19199,f19203,f19207,f19211,f19215,f19219,f19223,f19235,f19239,f19280,f19284,f19288,f19292,f19296,f19300,f19304,f19308,f19312,f19316,f19320,f19324,f19328,f19332,f19336,f19340,f19344,f19348,f19352,f19356,f19360,f19465,f19469,f19574,f19578,f19582,f19586,f19601,f19642,f19646,f19650,f19655,f19659,f19663,f19667,f19671,f19679,f19683,f19687,f19691,f19695,f19699,f19703,f19707,f19711,f19715,f19719,f19723,f19727,f19731,f19735,f19739,f19743,f19747,f19792,f19796,f19804,f19808,f19857,f20384,f21165,f22716,f25125,f26396,f26400,f26404,f26408,f26412,f26416,f26420,f26424,f26428,f26432,f26436,f26440,f26444,f26448,f26452,f26456,f26460,f26464,f26468,f26472,f26476,f26480,f26484,f26488,f26492,f26496,f26500,f26520,f26524,f26528,f26532,f26536,f26540,f26544,f26548,f26552,f26556,f26566,f26570,f26574,f26578,f26582,f26586,f26590,f26594,f26598,f26602,f26606,f26610,f26614,f26618,f26622,f26626,f26630,f26635,f26736,f26740,f26744,f26748,f26752,f26756,f26760,f26764,f26768,f26772,f26776,f26780,f26784,f26800,f26804,f26808,f26812,f26816,f26820,f26824,f26828,f26832,f26836,f26854,f26858,f27567,f28750,f31718,f36569,f37444,f37448,f37452,f37456,f37460,f37464,f37468,f37472,f37476,f37480,f37484,f37488,f37492,f37496,f37500,f37504,f37508,f37512,f37516,f37520,f37524,f37528,f37532,f37536,f37540,f37544,f37548,f37552,f37556,f37560,f37564,f37568,f37572,f37576,f37580,f37584,f37588,f37600,f37604,f37608,f37612,f37616,f37620,f37624,f37628,f37632,f37636,f37677,f37681,f37685,f37689,f37693,f37697,f37701,f37705,f37709,f37732,f37736,f37740,f37744,f37748,f37752,f37756,f37760,f37764,f37768,f37802,f37806,f37810,f37814,f37818,f37822,f37826,f37830,f37834,f37838,f37842,f37846,f37850,f37854,f38814,f39753,f40626,f41300,f42337,f43643,f46012,f46016,f46054,f46058,f46062,f46066,f46070,f46074,f46078,f46082,f46086,f46090,f46118,f46122,f46126,f46130,f46134,f46138,f46291,f46295,f46299,f46492,f46672,f46800,f46804,f46808,f46812,f46981,f47114,f47273,f47407,f47411,f47415,f47419,f47464,f47469,f47473,f47477,f47481,f47485,f47489,f47493,f47497,f47501,f47505,f47509,f47513,f47517,f47521,f47525,f47529,f47533,f47537,f47541,f47545,f47571,f47575,f47579,f47583,f47587,f47591,f47595,f47599,f47603,f47607,f47611,f47615,f47619,f47623,f47627,f47631,f47635,f47639,f47643,f47647,f47651,f47690,f47694,f47698,f47702,f47706,f47710,f47714,f47718,f47722,f47726,f47730,f47734,f47738,f47742,f50416,f52097,f53087,f54584,f57212,f58681,f58712,f58716,f58720,f58724,f58728,f58732,f58736,f58740,f58744,f58748,f58882,f58886,f58890,f58894,f59006,f59010,f59014,f59121,f59125,f59190,f59306,f59422,f59493,f59600,f59604,f59711,f59715,f59719,f59723,f59852,f59856,f59860,f59864,f60046,f60050,f60054,f60120,f60124,f60245,f60249,f60287,f60291,f60295,f60299,f60303,f60307,f60311,f60315,f60319,f60323,f60360,f60364,f60368,f60372,f60376,f60380,f60384,f60388,f60392,f60396,f60427,f60431,f60435,f60439,f60443,f60447,f60451,f60455,f60459,f60463,f60467,f60471,f60475,f60479,f60483,f60487,f60491,f60495,f60499,f60503,f60507,f60550,f60554,f60558,f60562,f60566,f60570,f60574,f60578,f60582,f60586,f60623,f60627,f60631,f60635,f60639,f60643,f60647,f60651,f60655,f60659,f60684,f60688,f60692,f60696,f60700,f60705,f60710,f60794,f60798,f60802,f60806,f60810,f60814,f60895,f60899,f60903,f60907,f60911,f60915,f60942,f60946,f60950,f60954,f60958,f60962,f60966,f60970,f60974,f60978,f60982,f60986,f60990,f60994,f60998,f61002,f61006,f61010,f61014,f61018,f61022,f61026,f61030,f61034,f61038,f61179,f61338,f61480,f61484,f61488,f61492,f61496,f61500,f62227,f64533,f72056,f73853,f75411,f76908,f77983]) ).

fof(f77983,plain,
    ( spl0_3
    | ~ spl0_1151 ),
    inference(avatar_contradiction_clause,[],[f77970]) ).

fof(f77970,plain,
    ( $false
    | spl0_3
    | ~ spl0_1151 ),
    inference(resolution,[],[f76907,f873]) ).

fof(f873,plain,
    ( ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja))
    | spl0_3 ),
    inference(avatar_component_clause,[],[f871]) ).

fof(f871,plain,
    ( spl0_3
  <=> c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f76907,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1))
    | ~ spl0_1151 ),
    inference(avatar_component_clause,[],[f76906]) ).

fof(f76906,plain,
    ( spl0_1151
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f76908,plain,
    ( spl0_1151
    | ~ spl0_579
    | ~ spl0_1111 ),
    inference(avatar_split_clause,[],[f75412,f60909,f15848,f76906]) ).

fof(f15848,plain,
    ( spl0_579
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f60909,plain,
    ( spl0_1111
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f75412,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(X0),X1))
    | ~ spl0_579
    | ~ spl0_1111 ),
    inference(resolution,[],[f60910,f15849]) ).

fof(f15849,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f15848]) ).

fof(f60910,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
        | c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2)) )
    | ~ spl0_1111 ),
    inference(avatar_component_clause,[],[f60909]) ).

fof(f75411,plain,
    ( spl0_1150
    | ~ spl0_618
    | ~ spl0_964 ),
    inference(avatar_split_clause,[],[f55929,f47617,f16549,f75409]) ).

fof(f75409,plain,
    ( spl0_1150
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),c_HOL_Oone__class_Oone(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f16549,plain,
    ( spl0_618
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f47617,plain,
    ( spl0_964
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f55929,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
    | ~ spl0_618
    | ~ spl0_964 ),
    inference(superposition,[],[f16550,f47618]) ).

fof(f47618,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat))
    | ~ spl0_964 ),
    inference(avatar_component_clause,[],[f47617]) ).

fof(f16550,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X2))
    | ~ spl0_618 ),
    inference(avatar_component_clause,[],[f16549]) ).

fof(f73853,plain,
    ( spl0_1149
    | ~ spl0_618
    | ~ spl0_944 ),
    inference(avatar_split_clause,[],[f52900,f47515,f16549,f73851]) ).

fof(f73851,plain,
    ( spl0_1149
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1),X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f47515,plain,
    ( spl0_944
  <=> ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f52900,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1),X0),X3))
    | ~ spl0_618
    | ~ spl0_944 ),
    inference(superposition,[],[f16550,f47516]) ).

fof(f47516,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_944 ),
    inference(avatar_component_clause,[],[f47515]) ).

fof(f72056,plain,
    ( spl0_1148
    | ~ spl0_618
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f52634,f47511,f16549,f72054]) ).

fof(f72054,plain,
    ( spl0_1148
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f47511,plain,
    ( spl0_943
  <=> ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f52634,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),X0),X3))
    | ~ spl0_618
    | ~ spl0_943 ),
    inference(superposition,[],[f16550,f47512]) ).

fof(f47512,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_943 ),
    inference(avatar_component_clause,[],[f47511]) ).

fof(f64533,plain,
    ( spl0_1147
    | ~ spl0_461
    | ~ spl0_1123 ),
    inference(avatar_split_clause,[],[f63377,f60980,f10383,f64531]) ).

fof(f64531,plain,
    ( spl0_1147
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f10383,plain,
    ( spl0_461
  <=> ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f60980,plain,
    ( spl0_1123
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f63377,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X0),X2))
    | ~ spl0_461
    | ~ spl0_1123 ),
    inference(superposition,[],[f60981,f10384]) ).

fof(f10384,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
    | ~ spl0_461 ),
    inference(avatar_component_clause,[],[f10383]) ).

fof(f60981,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X3))
    | ~ spl0_1123 ),
    inference(avatar_component_clause,[],[f60980]) ).

fof(f62227,plain,
    ( spl0_1146
    | ~ spl0_525
    | ~ spl0_806
    | ~ spl0_1025 ),
    inference(avatar_split_clause,[],[f60417,f59862,f26856,f12350,f62225]) ).

fof(f62225,plain,
    ( spl0_1146
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f12350,plain,
    ( spl0_525
  <=> ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f26856,plain,
    ( spl0_806
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),X1) = c_Lambda_Olift(c_Lambda_Olift(X0,X1),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f59862,plain,
    ( spl0_1025
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f60417,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
    | ~ spl0_525
    | ~ spl0_806
    | ~ spl0_1025 ),
    inference(forward_demodulation,[],[f60402,f26857]) ).

fof(f26857,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),X1) = c_Lambda_Olift(c_Lambda_Olift(X0,X1),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_806 ),
    inference(avatar_component_clause,[],[f26856]) ).

fof(f60402,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X2))
    | ~ spl0_525
    | ~ spl0_1025 ),
    inference(superposition,[],[f59863,f12351]) ).

fof(f12351,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_525 ),
    inference(avatar_component_clause,[],[f12350]) ).

fof(f59863,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
    | ~ spl0_1025 ),
    inference(avatar_component_clause,[],[f59862]) ).

fof(f61500,plain,
    ( spl0_1145
    | ~ spl0_64
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f8854,f8722,f1150,f61498]) ).

fof(f61498,plain,
    ( spl0_1145
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),X0) = c_Lambda_Olift(c_Lambda_Olift(X1,X0),c_HOL_Oone__class_Oone(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f1150,plain,
    ( spl0_64
  <=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f8722,plain,
    ( spl0_422
  <=> ! [X9,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X9,X10),X19) = c_Lambda_Olift(c_Lambda_Olift(X9,X19),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f8854,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),X0) = c_Lambda_Olift(c_Lambda_Olift(X1,X0),c_HOL_Oone__class_Oone(tc_nat)) )
    | ~ spl0_64
    | ~ spl0_422 ),
    inference(superposition,[],[f8723,f1151]) ).

fof(f1151,plain,
    ( ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f1150]) ).

fof(f8723,plain,
    ( ! [X10,X19,X9] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Olift(X9,X10),X19) = c_Lambda_Olift(c_Lambda_Olift(X9,X19),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_422 ),
    inference(avatar_component_clause,[],[f8722]) ).

fof(f61496,plain,
    ( spl0_1144
    | ~ spl0_58
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8391,f7788,f1126,f61494]) ).

fof(f61494,plain,
    ( spl0_1144
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f1126,plain,
    ( spl0_58
  <=> ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f7788,plain,
    ( spl0_411
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f8391,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_58
    | ~ spl0_411 ),
    inference(superposition,[],[f1127,f7789]) ).

fof(f7789,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
    | ~ spl0_411 ),
    inference(avatar_component_clause,[],[f7788]) ).

fof(f1127,plain,
    ( ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X19,tc_nat)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f1126]) ).

fof(f61492,plain,
    ( spl0_1143
    | ~ spl0_81
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8364,f7788,f1230,f61490]) ).

fof(f61490,plain,
    ( spl0_1143
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f1230,plain,
    ( spl0_81
  <=> ! [X4] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f8364,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_81
    | ~ spl0_411 ),
    inference(superposition,[],[f1231,f7789]) ).

fof(f1231,plain,
    ( ! [X4] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f1230]) ).

fof(f61488,plain,
    ( spl0_1142
    | ~ spl0_254
    | ~ spl0_1016 ),
    inference(avatar_split_clause,[],[f60344,f59598,f3688,f61486]) ).

fof(f61486,plain,
    ( spl0_1142
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X2),X1),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f3688,plain,
    ( spl0_254
  <=> ! [X9,X4,X10] : c_Lambda_Olift(c_Lambda_Oliftn(X4,X9,X10),X10) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X9,X10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f59598,plain,
    ( spl0_1016
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f60344,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X2),X1),X1),X3))
    | ~ spl0_254
    | ~ spl0_1016 ),
    inference(superposition,[],[f59599,f3689]) ).

fof(f3689,plain,
    ( ! [X10,X9,X4] : c_Lambda_Olift(c_Lambda_Oliftn(X4,X9,X10),X10) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X9,X10)
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f3688]) ).

fof(f59599,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X3))
    | ~ spl0_1016 ),
    inference(avatar_component_clause,[],[f59598]) ).

fof(f61484,plain,
    ( spl0_1141
    | ~ spl0_80
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8363,f7788,f1226,f61482]) ).

fof(f61482,plain,
    ( spl0_1141
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f1226,plain,
    ( spl0_80
  <=> ! [X4] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f8363,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_80
    | ~ spl0_411 ),
    inference(superposition,[],[f1227,f7789]) ).

fof(f1227,plain,
    ( ! [X4] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat)
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f1226]) ).

fof(f61480,plain,
    ( spl0_1140
    | ~ spl0_62
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f7657,f6698,f1142,f61478]) ).

fof(f61478,plain,
    ( spl0_1140
  <=> ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f1142,plain,
    ( spl0_62
  <=> ! [X4,X3] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f6698,plain,
    ( spl0_391
  <=> ! [X4,X3] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X3,X4,tc_nat),tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f7657,plain,
    ( ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_62
    | ~ spl0_391 ),
    inference(superposition,[],[f1143,f6699]) ).

fof(f6699,plain,
    ( ! [X3,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X3,X4,tc_nat),tc_nat),X4,tc_nat)
    | ~ spl0_391 ),
    inference(avatar_component_clause,[],[f6698]) ).

fof(f1143,plain,
    ( ! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat)
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1142]) ).

fof(f61338,plain,
    ( ~ spl0_4
    | spl0_1139
    | ~ spl0_189
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f7566,f6686,f2173,f61336,f876]) ).

fof(f876,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f61336,plain,
    ( spl0_1139
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f2173,plain,
    ( spl0_189
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f6686,plain,
    ( spl0_388
  <=> ! [X5,X2,X0,X6,X15] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_lessequals(X6,X15,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f7566,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_189
    | ~ spl0_388 ),
    inference(resolution,[],[f6687,f2174]) ).

fof(f2174,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_189 ),
    inference(avatar_component_clause,[],[f2173]) ).

fof(f6687,plain,
    ( ! [X2,X0,X6,X15,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0)
        | ~ c_lessequals(X6,X15,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f6686]) ).

fof(f61179,plain,
    ( ~ spl0_4
    | spl0_1138
    | ~ spl0_64
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f7552,f6682,f1150,f61177,f876]) ).

fof(f61177,plain,
    ( spl0_1138
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f6682,plain,
    ( spl0_387
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f7552,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) )
    | ~ spl0_64
    | ~ spl0_387 ),
    inference(superposition,[],[f6683,f1151]) ).

fof(f6683,plain,
    ( ! [X2,X0,X6,X15,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f6682]) ).

fof(f61038,plain,
    ( ~ spl0_4
    | spl0_1137
    | ~ spl0_189
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f7520,f6682,f2173,f61036,f876]) ).

fof(f61036,plain,
    ( spl0_1137
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f7520,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_189
    | ~ spl0_387 ),
    inference(resolution,[],[f6683,f2174]) ).

fof(f61034,plain,
    ( spl0_1136
    | ~ spl0_32
    | ~ spl0_386 ),
    inference(avatar_split_clause,[],[f7508,f6678,f1016,f61032]) ).

fof(f61032,plain,
    ( spl0_1136
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f1016,plain,
    ( spl0_32
  <=> class_Divides_Osemiring__div(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f6678,plain,
    ( spl0_386
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f7508,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat)
    | ~ spl0_32
    | ~ spl0_386 ),
    inference(resolution,[],[f6679,f1018]) ).

fof(f1018,plain,
    ( class_Divides_Osemiring__div(tc_nat)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f1016]) ).

fof(f6679,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) )
    | ~ spl0_386 ),
    inference(avatar_component_clause,[],[f6678]) ).

fof(f61030,plain,
    ( spl0_1135
    | ~ spl0_32
    | ~ spl0_385 ),
    inference(avatar_split_clause,[],[f7507,f6674,f1016,f61028]) ).

fof(f61028,plain,
    ( spl0_1135
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f6674,plain,
    ( spl0_385
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f7507,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat)
    | ~ spl0_32
    | ~ spl0_385 ),
    inference(resolution,[],[f6675,f1018]) ).

fof(f6675,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) )
    | ~ spl0_385 ),
    inference(avatar_component_clause,[],[f6674]) ).

fof(f61026,plain,
    ( spl0_1134
    | ~ spl0_254
    | ~ spl0_1010 ),
    inference(avatar_split_clause,[],[f60270,f59119,f3688,f61024]) ).

fof(f61024,plain,
    ( spl0_1134
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X2),X2),X2),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f59119,plain,
    ( spl0_1010
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).

fof(f60270,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X2),X2),X2),X2),X3))
    | ~ spl0_254
    | ~ spl0_1010 ),
    inference(superposition,[],[f59120,f3689]) ).

fof(f59120,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X0),X3))
    | ~ spl0_1010 ),
    inference(avatar_component_clause,[],[f59119]) ).

fof(f61022,plain,
    ( spl0_1133
    | ~ spl0_17
    | ~ spl0_384 ),
    inference(avatar_split_clause,[],[f7506,f6670,f941,f61020]) ).

fof(f61020,plain,
    ( spl0_1133
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f941,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f6670,plain,
    ( spl0_384
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X11,X21,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f7506,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_384 ),
    inference(resolution,[],[f6671,f943]) ).

fof(f943,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f941]) ).

fof(f6671,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X11,X21,X0),X0) )
    | ~ spl0_384 ),
    inference(avatar_component_clause,[],[f6670]) ).

fof(f61018,plain,
    ( spl0_1132
    | ~ spl0_17
    | ~ spl0_382 ),
    inference(avatar_split_clause,[],[f7504,f6657,f941,f61016]) ).

fof(f61016,plain,
    ( spl0_1132
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f6657,plain,
    ( spl0_382
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f7504,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_382 ),
    inference(resolution,[],[f6658,f943]) ).

fof(f6658,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) )
    | ~ spl0_382 ),
    inference(avatar_component_clause,[],[f6657]) ).

fof(f61014,plain,
    ( spl0_1131
    | ~ spl0_32
    | ~ spl0_381 ),
    inference(avatar_split_clause,[],[f7503,f6653,f1016,f61012]) ).

fof(f61012,plain,
    ( spl0_1131
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f6653,plain,
    ( spl0_381
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) = c_HOL_Otimes__class_Otimes(X6,c_Divides_Odiv__class_Omod(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f7503,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
    | ~ spl0_32
    | ~ spl0_381 ),
    inference(resolution,[],[f6654,f1018]) ).

fof(f6654,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) = c_HOL_Otimes__class_Otimes(X6,c_Divides_Odiv__class_Omod(X2,X5,X0),X0) )
    | ~ spl0_381 ),
    inference(avatar_component_clause,[],[f6653]) ).

fof(f61010,plain,
    ( spl0_1130
    | ~ spl0_32
    | ~ spl0_380 ),
    inference(avatar_split_clause,[],[f7502,f6649,f1016,f61008]) ).

fof(f61008,plain,
    ( spl0_1130
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f6649,plain,
    ( spl0_380
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f7502,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_380 ),
    inference(resolution,[],[f6650,f1018]) ).

fof(f6650,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X5,X0),X6,X0) )
    | ~ spl0_380 ),
    inference(avatar_component_clause,[],[f6649]) ).

fof(f61006,plain,
    ( spl0_1129
    | ~ spl0_32
    | ~ spl0_378 ),
    inference(avatar_split_clause,[],[f7457,f6641,f1016,f61004]) ).

fof(f61004,plain,
    ( spl0_1129
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f6641,plain,
    ( spl0_378
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f7457,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat)
    | ~ spl0_32
    | ~ spl0_378 ),
    inference(resolution,[],[f6642,f1018]) ).

fof(f6642,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) )
    | ~ spl0_378 ),
    inference(avatar_component_clause,[],[f6641]) ).

fof(f61002,plain,
    ( spl0_1128
    | ~ spl0_32
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f7456,f6637,f1016,f61000]) ).

fof(f61000,plain,
    ( spl0_1128
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f6637,plain,
    ( spl0_377
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f7456,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat)
    | ~ spl0_32
    | ~ spl0_377 ),
    inference(resolution,[],[f6638,f1018]) ).

fof(f6638,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) )
    | ~ spl0_377 ),
    inference(avatar_component_clause,[],[f6637]) ).

fof(f60998,plain,
    ( spl0_1127
    | ~ spl0_19
    | ~ spl0_375 ),
    inference(avatar_split_clause,[],[f7454,f6629,f951,f60996]) ).

fof(f60996,plain,
    ( spl0_1127
  <=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f951,plain,
    ( spl0_19
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f6629,plain,
    ( spl0_375
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X5,X0),X4,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f7454,plain,
    ( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
    | ~ spl0_19
    | ~ spl0_375 ),
    inference(resolution,[],[f6630,f953]) ).

fof(f953,plain,
    ( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f951]) ).

fof(f6630,plain,
    ( ! [X2,X0,X4,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X5,X0),X4,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) )
    | ~ spl0_375 ),
    inference(avatar_component_clause,[],[f6629]) ).

fof(f60994,plain,
    ( spl0_1126
    | ~ spl0_53
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f7200,f6580,f1106,f60992]) ).

fof(f60992,plain,
    ( spl0_1126
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
        | ~ c_lessequals(X0,X0,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f1106,plain,
    ( spl0_53
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f6580,plain,
    ( spl0_367
  <=> ! [X4,X3,X10] :
        ( X3 = X4
        | ~ c_lessequals(X10,X3,tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat)
        | c_HOL_Ominus__class_Ominus(X3,X10,tc_nat) != c_HOL_Ominus__class_Ominus(X4,X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f7200,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)
        | ~ c_lessequals(X0,X0,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1 )
    | ~ spl0_53
    | ~ spl0_367 ),
    inference(superposition,[],[f6581,f1107]) ).

fof(f1107,plain,
    ( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f1106]) ).

fof(f6581,plain,
    ( ! [X3,X10,X4] :
        ( c_HOL_Ominus__class_Ominus(X3,X10,tc_nat) != c_HOL_Ominus__class_Ominus(X4,X10,tc_nat)
        | ~ c_lessequals(X10,X3,tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_367 ),
    inference(avatar_component_clause,[],[f6580]) ).

fof(f60990,plain,
    ( spl0_1125
    | ~ spl0_47
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f7172,f6576,f1082,f60988]) ).

fof(f60988,plain,
    ( spl0_1125
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f1082,plain,
    ( spl0_47
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f6576,plain,
    ( spl0_366
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f7172,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_47
    | ~ spl0_366 ),
    inference(resolution,[],[f6577,f1083]) ).

fof(f1083,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f1082]) ).

fof(f6577,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f6576]) ).

fof(f60986,plain,
    ( spl0_1124
    | ~ spl0_48
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f7171,f6576,f1086,f60984]) ).

fof(f60984,plain,
    ( spl0_1124
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f1086,plain,
    ( spl0_48
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f7171,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_48
    | ~ spl0_366 ),
    inference(resolution,[],[f6577,f1087]) ).

fof(f1087,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f1086]) ).

fof(f60982,plain,
    ( spl0_1123
    | ~ spl0_254
    | ~ spl0_1010 ),
    inference(avatar_split_clause,[],[f60266,f59119,f3688,f60980]) ).

fof(f60266,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X3))
    | ~ spl0_254
    | ~ spl0_1010 ),
    inference(superposition,[],[f59120,f3689]) ).

fof(f60978,plain,
    ( spl0_1122
    | ~ spl0_49
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f7170,f6576,f1090,f60976]) ).

fof(f60976,plain,
    ( spl0_1122
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f1090,plain,
    ( spl0_49
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f7170,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_49
    | ~ spl0_366 ),
    inference(resolution,[],[f6577,f1091]) ).

fof(f1091,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f1090]) ).

fof(f60974,plain,
    ( spl0_1121
    | ~ spl0_47
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f6927,f6508,f1082,f60972]) ).

fof(f60972,plain,
    ( spl0_1121
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f6508,plain,
    ( spl0_357
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f6927,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_47
    | ~ spl0_357 ),
    inference(resolution,[],[f6509,f1083]) ).

fof(f6509,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0) )
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f6508]) ).

fof(f60970,plain,
    ( spl0_1120
    | ~ spl0_48
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f6926,f6508,f1086,f60968]) ).

fof(f60968,plain,
    ( spl0_1120
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f6926,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_48
    | ~ spl0_357 ),
    inference(resolution,[],[f6509,f1087]) ).

fof(f60966,plain,
    ( spl0_1119
    | ~ spl0_49
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f6925,f6508,f1090,f60964]) ).

fof(f60964,plain,
    ( spl0_1119
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f6925,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_49
    | ~ spl0_357 ),
    inference(resolution,[],[f6509,f1091]) ).

fof(f60962,plain,
    ( spl0_1118
    | ~ spl0_17
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f6701,f6472,f941,f60960]) ).

fof(f60960,plain,
    ( spl0_1118
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f6472,plain,
    ( spl0_348
  <=> ! [X0,X8,X1,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X7,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f6701,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),c_Power_Opower__class_Opower(X0,X2,tc_nat),tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_348 ),
    inference(resolution,[],[f6473,f943]) ).

fof(f6473,plain,
    ( ! [X0,X1,X8,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X7,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X0) )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f6472]) ).

fof(f60958,plain,
    ( spl0_1117
    | ~ spl0_70
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f6088,f5774,f1186,f60956]) ).

fof(f60956,plain,
    ( spl0_1117
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f1186,plain,
    ( spl0_70
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_lessequals(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f5774,plain,
    ( spl0_332
  <=> ! [X4,X3,X26] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X26,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f6088,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_332 ),
    inference(resolution,[],[f5775,f1187]) ).

fof(f1187,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f1186]) ).

fof(f5775,plain,
    ( ! [X3,X26,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X26,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f5774]) ).

fof(f60954,plain,
    ( spl0_1116
    | ~ spl0_238
    | ~ spl0_332 ),
    inference(avatar_split_clause,[],[f6086,f5774,f2882,f60952]) ).

fof(f60952,plain,
    ( spl0_1116
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f2882,plain,
    ( spl0_238
  <=> ! [X18,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f6086,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat),X1,tc_nat) )
    | ~ spl0_238
    | ~ spl0_332 ),
    inference(resolution,[],[f5775,f2883]) ).

fof(f2883,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) )
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f2882]) ).

fof(f60950,plain,
    ( spl0_1115
    | ~ spl0_86
    | ~ spl0_238
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f6081,f5766,f2882,f1265,f60948]) ).

fof(f60948,plain,
    ( spl0_1115
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f1265,plain,
    ( spl0_86
  <=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f5766,plain,
    ( spl0_330
  <=> ! [X6,X2,X5] :
        ( ~ c_lessequals(X6,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X5,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X6,tc_nat),c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f6081,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_238
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f6041,f1266]) ).

fof(f1266,plain,
    ( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f1265]) ).

fof(f6041,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X2,tc_nat),X1,tc_nat) )
    | ~ spl0_238
    | ~ spl0_330 ),
    inference(resolution,[],[f5767,f2883]) ).

fof(f5767,plain,
    ( ! [X2,X6,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X6,tc_nat),c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X5,tc_nat)
        | ~ c_lessequals(X6,X2,tc_nat) )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f5766]) ).

fof(f60946,plain,
    ( spl0_1114
    | ~ spl0_107
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f6075,f5766,f1352,f60944]) ).

fof(f60944,plain,
    ( spl0_1114
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f1352,plain,
    ( spl0_107
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f6075,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_107
    | ~ spl0_330 ),
    inference(superposition,[],[f5767,f1353]) ).

fof(f1353,plain,
    ( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1352]) ).

fof(f60942,plain,
    ( spl0_1113
    | ~ spl0_106
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f6074,f5766,f1346,f60940]) ).

fof(f60940,plain,
    ( spl0_1113
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f1346,plain,
    ( spl0_106
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f6074,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_106
    | ~ spl0_330 ),
    inference(superposition,[],[f5767,f1347]) ).

fof(f1347,plain,
    ( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1346]) ).

fof(f60915,plain,
    ( spl0_1112
    | ~ spl0_70
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f6043,f5766,f1186,f60913]) ).

fof(f60913,plain,
    ( spl0_1112
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f6043,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_330 ),
    inference(resolution,[],[f5767,f1187]) ).

fof(f60911,plain,
    ( spl0_1111
    | ~ spl0_44
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6029,f5762,f1070,f60909]) ).

fof(f1070,plain,
    ( spl0_44
  <=> ! [X30] :
        ( ~ c_InductTermi_OIT(X30)
        | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X30)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f5762,plain,
    ( spl0_329
  <=> ! [X9,X27,X10] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X9),X27,X10) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X9,c_Lambda_Olift(X27,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f6029,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Osubst(X0,c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_44
    | ~ spl0_329 ),
    inference(superposition,[],[f1071,f5763]) ).

fof(f5763,plain,
    ( ! [X10,X9,X27] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X9),X27,X10) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X9,c_Lambda_Olift(X27,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
    | ~ spl0_329 ),
    inference(avatar_component_clause,[],[f5762]) ).

fof(f1071,plain,
    ( ! [X30] :
        ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X30))
        | ~ c_InductTermi_OIT(X30) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f1070]) ).

fof(f60907,plain,
    ( spl0_1110
    | ~ spl0_86
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6022,f5762,f1265,f60905]) ).

fof(f60905,plain,
    ( spl0_1110
  <=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X0) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f6022,plain,
    ( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X1),X2,X0) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X1,c_Lambda_Olift(X2,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)))
    | ~ spl0_86
    | ~ spl0_329 ),
    inference(superposition,[],[f5763,f1266]) ).

fof(f60903,plain,
    ( spl0_1109
    | ~ spl0_86
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f5932,f5750,f1265,f60901]) ).

fof(f60901,plain,
    ( spl0_1109
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f5750,plain,
    ( spl0_326
  <=> ! [X18,X10,X19,X26] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f5932,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_326 ),
    inference(superposition,[],[f5751,f1266]) ).

fof(f5751,plain,
    ( ! [X10,X18,X19,X26] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) )
    | ~ spl0_326 ),
    inference(avatar_component_clause,[],[f5750]) ).

fof(f60899,plain,
    ( spl0_1108
    | ~ spl0_70
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f5913,f5750,f1186,f60897]) ).

fof(f60897,plain,
    ( spl0_1108
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f5913,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_326 ),
    inference(resolution,[],[f5751,f1187]) ).

fof(f60895,plain,
    ( spl0_1107
    | ~ spl0_239
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f5903,f5750,f2886,f60893]) ).

fof(f60893,plain,
    ( spl0_1107
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f2886,plain,
    ( spl0_239
  <=> ! [X18,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat)
        | c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f5903,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_239
    | ~ spl0_326 ),
    inference(resolution,[],[f5751,f2887]) ).

fof(f2887,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat)
        | c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) )
    | ~ spl0_239 ),
    inference(avatar_component_clause,[],[f2886]) ).

fof(f60814,plain,
    ( ~ spl0_16
    | spl0_1106
    | ~ spl0_70
    | ~ spl0_325 ),
    inference(avatar_split_clause,[],[f5879,f5746,f1186,f60812,f936]) ).

fof(f936,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f60812,plain,
    ( spl0_1106
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f5746,plain,
    ( spl0_325
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f5879,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_325 ),
    inference(resolution,[],[f5747,f1187]) ).

fof(f5747,plain,
    ( ! [X2,X0,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_325 ),
    inference(avatar_component_clause,[],[f5746]) ).

fof(f60810,plain,
    ( spl0_1105
    | ~ spl0_86
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5864,f5738,f1265,f60808]) ).

fof(f60808,plain,
    ( spl0_1105
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X3,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f5738,plain,
    ( spl0_323
  <=> ! [X18,X10,X19,X26] :
        ( ~ c_lessequals(X19,X18,tc_nat)
        | ~ c_lessequals(X10,X26,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f5864,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X3,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_323 ),
    inference(superposition,[],[f5739,f1266]) ).

fof(f5739,plain,
    ( ! [X10,X18,X19,X26] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat)
        | ~ c_lessequals(X10,X26,tc_nat)
        | ~ c_lessequals(X19,X18,tc_nat) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f5738]) ).

fof(f60806,plain,
    ( spl0_1104
    | ~ spl0_206
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5843,f5738,f2754,f60804]) ).

fof(f60804,plain,
    ( spl0_1104
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f2754,plain,
    ( spl0_206
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f5843,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat),X3,tc_nat) )
    | ~ spl0_206
    | ~ spl0_323 ),
    inference(resolution,[],[f5739,f2755]) ).

fof(f2755,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat) )
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f2754]) ).

fof(f60802,plain,
    ( spl0_1103
    | ~ spl0_758
    | ~ spl0_989 ),
    inference(avatar_split_clause,[],[f56398,f53085,f26534,f60800]) ).

fof(f60800,plain,
    ( spl0_1103
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f26534,plain,
    ( spl0_758
  <=> ! [X0] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).

fof(f53085,plain,
    ( spl0_989
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f56398,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_758
    | ~ spl0_989 ),
    inference(superposition,[],[f53086,f26535]) ).

fof(f26535,plain,
    ( ! [X0] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_758 ),
    inference(avatar_component_clause,[],[f26534]) ).

fof(f53086,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),X3))
    | ~ spl0_989 ),
    inference(avatar_component_clause,[],[f53085]) ).

fof(f60798,plain,
    ( spl0_1102
    | ~ spl0_86
    | ~ spl0_220
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f5821,f5734,f2810,f1265,f60796]) ).

fof(f60796,plain,
    ( spl0_1102
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f2810,plain,
    ( spl0_220
  <=> ! [X4,X3,X26] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X3,X26,tc_nat),c_HOL_Ominus__class_Ominus(X4,X26,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f5734,plain,
    ( spl0_322
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X10,X18,tc_nat)
        | ~ c_lessequals(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).

fof(f5821,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_220
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f5795,f1266]) ).

fof(f5795,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_220
    | ~ spl0_322 ),
    inference(resolution,[],[f5735,f2811]) ).

fof(f2811,plain,
    ( ! [X3,X26,X4] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X3,X26,tc_nat),c_HOL_Ominus__class_Ominus(X4,X26,tc_nat),tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f2810]) ).

fof(f5735,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_lessequals(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
        | ~ c_lessequals(X10,X18,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f5734]) ).

fof(f60794,plain,
    ( spl0_1101
    | ~ spl0_218
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f5794,f5734,f2802,f60792]) ).

fof(f60792,plain,
    ( spl0_1101
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f2802,plain,
    ( spl0_218
  <=> ! [X4,X3,X26] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f5794,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_218
    | ~ spl0_322 ),
    inference(resolution,[],[f5735,f2803]) ).

fof(f2803,plain,
    ( ! [X3,X26,X4] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f2802]) ).

fof(f60710,plain,
    ( ~ spl0_16
    | spl0_1100
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_214
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f5493,f4562,f2786,f1265,f1146,f60708,f936]) ).

fof(f60708,plain,
    ( spl0_1100
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f1146,plain,
    ( spl0_63
  <=> ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f2786,plain,
    ( spl0_214
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f4562,plain,
    ( spl0_292
  <=> ! [X18,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f5493,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_214
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5492,f1147]) ).

fof(f1147,plain,
    ( ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1146]) ).

fof(f5492,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_86
    | ~ spl0_214
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5465,f1266]) ).

fof(f5465,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_214
    | ~ spl0_292 ),
    inference(resolution,[],[f4563,f2787]) ).

fof(f2787,plain,
    ( ! [X0,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_214 ),
    inference(avatar_component_clause,[],[f2786]) ).

fof(f4563,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X10,tc_nat) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f4562]) ).

fof(f60705,plain,
    ( spl0_1099
    | ~ spl0_107
    | ~ spl0_169
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5312,f4538,f1809,f1352,f60703]) ).

fof(f60703,plain,
    ( spl0_1099
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f1809,plain,
    ( spl0_169
  <=> ! [X3,X19] : c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X19,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f4538,plain,
    ( spl0_286
  <=> ! [X29,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f5312,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X1)
    | ~ spl0_107
    | ~ spl0_169
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5274,f1353]) ).

fof(f5274,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X1)
    | ~ spl0_169
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f1810]) ).

fof(f1810,plain,
    ( ! [X3,X19] : c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X19,tc_nat),tc_nat),tc_nat)
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f1809]) ).

fof(f4539,plain,
    ( ! [X29,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f4538]) ).

fof(f60700,plain,
    ( spl0_1098
    | ~ spl0_107
    | ~ spl0_168
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5311,f4538,f1805,f1352,f60698]) ).

fof(f60698,plain,
    ( spl0_1098
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f1805,plain,
    ( spl0_168
  <=> ! [X1,X3] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f5311,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X0)
    | ~ spl0_107
    | ~ spl0_168
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5273,f1353]) ).

fof(f5273,plain,
    ( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),X2,X0) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_168
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f1806]) ).

fof(f1806,plain,
    ( ! [X3,X1] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1805]) ).

fof(f60696,plain,
    ( spl0_1097
    | ~ spl0_121
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f5202,f4530,f1486,f60694]) ).

fof(f60694,plain,
    ( spl0_1097
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f1486,plain,
    ( spl0_121
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f4530,plain,
    ( spl0_284
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f5202,plain,
    ( ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_284 ),
    inference(resolution,[],[f4531,f1487]) ).

fof(f1487,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1486]) ).

fof(f4531,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) )
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f4530]) ).

fof(f60692,plain,
    ( spl0_1096
    | ~ spl0_127
    | ~ spl0_282 ),
    inference(avatar_split_clause,[],[f5146,f4522,f1512,f60690]) ).

fof(f60690,plain,
    ( spl0_1096
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f1512,plain,
    ( spl0_127
  <=> ! [X11,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f4522,plain,
    ( spl0_282
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f5146,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_127
    | ~ spl0_282 ),
    inference(resolution,[],[f4523,f1513]) ).

fof(f1513,plain,
    ( ! [X0,X11,X1] :
        ( c_HOL_Oord__class_Oless(X1,X11,X0)
        | c_lessequals(X11,X1,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1512]) ).

fof(f4523,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_282 ),
    inference(avatar_component_clause,[],[f4522]) ).

fof(f60688,plain,
    ( spl0_1095
    | ~ spl0_143
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5110,f4518,f1578,f60686]) ).

fof(f60686,plain,
    ( spl0_1095
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f1578,plain,
    ( spl0_143
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f4518,plain,
    ( spl0_281
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f5110,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_143
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f1579]) ).

fof(f1579,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1578]) ).

fof(f4519,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_281 ),
    inference(avatar_component_clause,[],[f4518]) ).

fof(f60684,plain,
    ( spl0_1094
    | ~ spl0_142
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5109,f4518,f1572,f60682]) ).

fof(f60682,plain,
    ( spl0_1094
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f1572,plain,
    ( spl0_142
  <=> ! [X11,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f5109,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_142
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f1573]) ).

fof(f1573,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1572]) ).

fof(f60659,plain,
    ( spl0_1093
    | ~ spl0_141
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5108,f4518,f1568,f60657]) ).

fof(f60657,plain,
    ( spl0_1093
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f1568,plain,
    ( spl0_141
  <=> ! [X5,X2,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f5108,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_141
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f1569]) ).

fof(f1569,plain,
    ( ! [X2,X0,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X2,X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1568]) ).

fof(f60655,plain,
    ( spl0_1092
    | ~ spl0_123
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5107,f4518,f1496,f60653]) ).

fof(f60653,plain,
    ( spl0_1092
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f1496,plain,
    ( spl0_123
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | c_lessequals(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f5107,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) )
    | ~ spl0_123
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f1497]) ).

fof(f1497,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X11,X0) )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1496]) ).

fof(f60651,plain,
    ( spl0_1091
    | ~ spl0_122
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5106,f4518,f1492,f60649]) ).

fof(f60649,plain,
    ( spl0_1091
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f1492,plain,
    ( spl0_122
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | c_lessequals(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f5106,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) )
    | ~ spl0_122
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f1493]) ).

fof(f1493,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,X11,X0) )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f1492]) ).

fof(f60647,plain,
    ( spl0_1090
    | ~ spl0_143
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f5067,f4514,f1578,f60645]) ).

fof(f60645,plain,
    ( spl0_1090
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f4514,plain,
    ( spl0_280
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f5067,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_143
    | ~ spl0_280 ),
    inference(resolution,[],[f4515,f1579]) ).

fof(f4515,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f4514]) ).

fof(f60643,plain,
    ( spl0_1089
    | ~ spl0_142
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f5066,f4514,f1572,f60641]) ).

fof(f60641,plain,
    ( spl0_1089
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f5066,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_142
    | ~ spl0_280 ),
    inference(resolution,[],[f4515,f1573]) ).

fof(f60639,plain,
    ( spl0_1088
    | ~ spl0_141
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f5065,f4514,f1568,f60637]) ).

fof(f60637,plain,
    ( spl0_1088
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f5065,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_141
    | ~ spl0_280 ),
    inference(resolution,[],[f4515,f1569]) ).

fof(f60635,plain,
    ( spl0_1087
    | ~ spl0_123
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f5064,f4514,f1496,f60633]) ).

fof(f60633,plain,
    ( spl0_1087
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f5064,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) )
    | ~ spl0_123
    | ~ spl0_280 ),
    inference(resolution,[],[f4515,f1497]) ).

fof(f60631,plain,
    ( spl0_1086
    | ~ spl0_122
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f5063,f4514,f1492,f60629]) ).

fof(f60629,plain,
    ( spl0_1086
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f5063,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,X2),c_HOL_Oplus__class_Oplus(X3,X1,X2),X2) )
    | ~ spl0_122
    | ~ spl0_280 ),
    inference(resolution,[],[f4515,f1493]) ).

fof(f60627,plain,
    ( spl0_1085
    | ~ spl0_127
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f5017,f4506,f1512,f60625]) ).

fof(f60625,plain,
    ( spl0_1085
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f4506,plain,
    ( spl0_278
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f5017,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_127
    | ~ spl0_278 ),
    inference(resolution,[],[f4507,f1513]) ).

fof(f4507,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f4506]) ).

fof(f60623,plain,
    ( spl0_1084
    | ~ spl0_143
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4985,f4502,f1578,f60621]) ).

fof(f60621,plain,
    ( spl0_1084
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f4502,plain,
    ( spl0_277
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f4985,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_143
    | ~ spl0_277 ),
    inference(resolution,[],[f4503,f1579]) ).

fof(f4503,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f4502]) ).

fof(f60586,plain,
    ( spl0_1083
    | ~ spl0_142
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4984,f4502,f1572,f60584]) ).

fof(f60584,plain,
    ( spl0_1083
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f4984,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_142
    | ~ spl0_277 ),
    inference(resolution,[],[f4503,f1573]) ).

fof(f60582,plain,
    ( spl0_1082
    | ~ spl0_141
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4983,f4502,f1568,f60580]) ).

fof(f60580,plain,
    ( spl0_1082
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f4983,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_141
    | ~ spl0_277 ),
    inference(resolution,[],[f4503,f1569]) ).

fof(f60578,plain,
    ( spl0_1081
    | ~ spl0_123
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4982,f4502,f1496,f60576]) ).

fof(f60576,plain,
    ( spl0_1081
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f4982,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_123
    | ~ spl0_277 ),
    inference(resolution,[],[f4503,f1497]) ).

fof(f60574,plain,
    ( spl0_1080
    | ~ spl0_122
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f4981,f4502,f1492,f60572]) ).

fof(f60572,plain,
    ( spl0_1080
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f4981,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_122
    | ~ spl0_277 ),
    inference(resolution,[],[f4503,f1493]) ).

fof(f60570,plain,
    ( spl0_1079
    | ~ spl0_143
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4944,f4498,f1578,f60568]) ).

fof(f60568,plain,
    ( spl0_1079
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f4498,plain,
    ( spl0_276
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f4944,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_143
    | ~ spl0_276 ),
    inference(resolution,[],[f4499,f1579]) ).

fof(f4499,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f4498]) ).

fof(f60566,plain,
    ( spl0_1078
    | ~ spl0_142
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4943,f4498,f1572,f60564]) ).

fof(f60564,plain,
    ( spl0_1078
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f4943,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_142
    | ~ spl0_276 ),
    inference(resolution,[],[f4499,f1573]) ).

fof(f60562,plain,
    ( spl0_1077
    | ~ spl0_141
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4942,f4498,f1568,f60560]) ).

fof(f60560,plain,
    ( spl0_1077
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f4942,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_141
    | ~ spl0_276 ),
    inference(resolution,[],[f4499,f1569]) ).

fof(f60558,plain,
    ( spl0_1076
    | ~ spl0_123
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4941,f4498,f1496,f60556]) ).

fof(f60556,plain,
    ( spl0_1076
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f4941,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_123
    | ~ spl0_276 ),
    inference(resolution,[],[f4499,f1497]) ).

fof(f60554,plain,
    ( spl0_1075
    | ~ spl0_122
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f4940,f4498,f1492,f60552]) ).

fof(f60552,plain,
    ( spl0_1075
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f4940,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,X2),c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_122
    | ~ spl0_276 ),
    inference(resolution,[],[f4499,f1493]) ).

fof(f60550,plain,
    ( spl0_1074
    | ~ spl0_129
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f4881,f4486,f1520,f60548]) ).

fof(f60548,plain,
    ( spl0_1074
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f1520,plain,
    ( spl0_129
  <=> ! [X11,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f4486,plain,
    ( spl0_273
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X5,X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f4881,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_129
    | ~ spl0_273 ),
    inference(resolution,[],[f4487,f1521]) ).

fof(f1521,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_lessequals(X11,X1,X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1520]) ).

fof(f4487,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0) )
    | ~ spl0_273 ),
    inference(avatar_component_clause,[],[f4486]) ).

fof(f60507,plain,
    ( spl0_1073
    | ~ spl0_128
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f4880,f4486,f1516,f60505]) ).

fof(f60505,plain,
    ( spl0_1073
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f1516,plain,
    ( spl0_128
  <=> ! [X11,X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f4880,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_128
    | ~ spl0_273 ),
    inference(resolution,[],[f4487,f1517]) ).

fof(f1517,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_lessequals(X11,X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0) )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1516]) ).

fof(f60503,plain,
    ( spl0_1072
    | ~ spl0_129
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f4833,f4482,f1520,f60501]) ).

fof(f60501,plain,
    ( spl0_1072
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f4482,plain,
    ( spl0_272
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X5,X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f4833,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_129
    | ~ spl0_272 ),
    inference(resolution,[],[f4483,f1521]) ).

fof(f4483,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0) )
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f4482]) ).

fof(f60499,plain,
    ( spl0_1071
    | ~ spl0_128
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f4832,f4482,f1516,f60497]) ).

fof(f60497,plain,
    ( spl0_1071
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f4832,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_128
    | ~ spl0_272 ),
    inference(resolution,[],[f4483,f1517]) ).

fof(f60495,plain,
    ( spl0_1070
    | ~ spl0_131
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f4798,f4478,f1528,f60493]) ).

fof(f60493,plain,
    ( spl0_1070
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f1528,plain,
    ( spl0_131
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X1,X11,X0)
        | c_lessequals(X11,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f4478,plain,
    ( spl0_271
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f4798,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_131
    | ~ spl0_271 ),
    inference(resolution,[],[f4479,f1529]) ).

fof(f1529,plain,
    ( ! [X0,X11,X1] :
        ( c_lessequals(X11,X1,X0)
        | c_lessequals(X1,X11,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1528]) ).

fof(f4479,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f4478]) ).

fof(f60491,plain,
    ( spl0_1069
    | ~ spl0_129
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f4742,f4474,f1520,f60489]) ).

fof(f60489,plain,
    ( spl0_1069
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f4474,plain,
    ( spl0_270
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X2,X5,X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f4742,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_129
    | ~ spl0_270 ),
    inference(resolution,[],[f4475,f1521]) ).

fof(f4475,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f4474]) ).

fof(f60487,plain,
    ( spl0_1068
    | ~ spl0_128
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f4741,f4474,f1516,f60485]) ).

fof(f60485,plain,
    ( spl0_1068
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f4741,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
    | ~ spl0_128
    | ~ spl0_270 ),
    inference(resolution,[],[f4475,f1517]) ).

fof(f60483,plain,
    ( spl0_1067
    | ~ spl0_131
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f4716,f4470,f1528,f60481]) ).

fof(f60481,plain,
    ( spl0_1067
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f4470,plain,
    ( spl0_269
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f4716,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_131
    | ~ spl0_269 ),
    inference(resolution,[],[f4471,f1529]) ).

fof(f4471,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f4470]) ).

fof(f60479,plain,
    ( spl0_1066
    | ~ spl0_129
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f4663,f4462,f1520,f60477]) ).

fof(f60477,plain,
    ( spl0_1066
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f4462,plain,
    ( spl0_267
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X2,X5,X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f4663,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Opreorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_129
    | ~ spl0_267 ),
    inference(resolution,[],[f4463,f1521]) ).

fof(f4463,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_267 ),
    inference(avatar_component_clause,[],[f4462]) ).

fof(f60475,plain,
    ( spl0_1065
    | ~ spl0_128
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f4662,f4462,f1516,f60473]) ).

fof(f60473,plain,
    ( spl0_1065
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f4662,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
    | ~ spl0_128
    | ~ spl0_267 ),
    inference(resolution,[],[f4463,f1517]) ).

fof(f60471,plain,
    ( spl0_1064
    | ~ spl0_121
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4630,f4458,f1486,f60469]) ).

fof(f60469,plain,
    ( spl0_1064
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f4458,plain,
    ( spl0_266
  <=> ! [X4,X3,X10] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
        | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f4630,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) = X1 )
    | ~ spl0_121
    | ~ spl0_266 ),
    inference(resolution,[],[f4459,f1487]) ).

fof(f4459,plain,
    ( ! [X3,X10,X4] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f4458]) ).

fof(f60467,plain,
    ( spl0_1063
    | ~ spl0_254
    | ~ spl0_991 ),
    inference(avatar_split_clause,[],[f58695,f57210,f3688,f60465]) ).

fof(f60465,plain,
    ( spl0_1063
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X1),X1),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f57210,plain,
    ( spl0_991
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).

fof(f58695,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X1),X1),X1),X2))
    | ~ spl0_254
    | ~ spl0_991 ),
    inference(superposition,[],[f57211,f3689]) ).

fof(f57211,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X2))
    | ~ spl0_991 ),
    inference(avatar_component_clause,[],[f57210]) ).

fof(f60463,plain,
    ( spl0_1062
    | ~ spl0_246
    | ~ spl0_261 ),
    inference(avatar_split_clause,[],[f4438,f3716,f3655,f60461]) ).

fof(f60461,plain,
    ( spl0_1062
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,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_1062])]) ).

fof(f3655,plain,
    ( spl0_246
  <=> ! [X11,X21,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f3716,plain,
    ( spl0_261
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f4438,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_246
    | ~ spl0_261 ),
    inference(superposition,[],[f3717,f3656]) ).

fof(f3656,plain,
    ( ! [X21,X11,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f3655]) ).

fof(f3717,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
    | ~ spl0_261 ),
    inference(avatar_component_clause,[],[f3716]) ).

fof(f60459,plain,
    ( spl0_1061
    | ~ spl0_247
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f4434,f3712,f3660,f60457]) ).

fof(f60457,plain,
    ( spl0_1061
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f3660,plain,
    ( spl0_247
  <=> ! [X4,X3,X10] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f3712,plain,
    ( spl0_260
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f4434,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X2
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
    | ~ spl0_247
    | ~ spl0_260 ),
    inference(superposition,[],[f3713,f3661]) ).

fof(f3661,plain,
    ( ! [X3,X10,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat)
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f3660]) ).

fof(f3713,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f3712]) ).

fof(f60455,plain,
    ( spl0_1060
    | ~ spl0_184
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4393,f3704,f2153,f60453]) ).

fof(f60453,plain,
    ( spl0_1060
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f2153,plain,
    ( spl0_184
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f3704,plain,
    ( spl0_258
  <=> ! [X18,X19,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X10,X18,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f4393,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_184
    | ~ spl0_258 ),
    inference(superposition,[],[f2154,f3705]) ).

fof(f3705,plain,
    ( ! [X10,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X10,X18,tc_nat),tc_nat)
    | ~ spl0_258 ),
    inference(avatar_component_clause,[],[f3704]) ).

fof(f2154,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f2153]) ).

fof(f60451,plain,
    ( spl0_1059
    | ~ spl0_183
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4392,f3704,f2149,f60449]) ).

fof(f60449,plain,
    ( spl0_1059
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f2149,plain,
    ( spl0_183
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f4392,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_183
    | ~ spl0_258 ),
    inference(superposition,[],[f2150,f3705]) ).

fof(f2150,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f2149]) ).

fof(f60447,plain,
    ( spl0_1058
    | ~ spl0_134
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4298,f3688,f1540,f60445]) ).

fof(f60445,plain,
    ( spl0_1058
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2),c_Lambda_Olift(X3,X2))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f1540,plain,
    ( spl0_134
  <=> ! [X19,X27,X30] :
        ( ~ c_Lambda_Obeta(X30,X27)
        | c_Lambda_Obeta(c_Lambda_Olift(X30,X19),c_Lambda_Olift(X27,X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f4298,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2),c_Lambda_Olift(X3,X2))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,X2),X3) )
    | ~ spl0_134
    | ~ spl0_254 ),
    inference(superposition,[],[f1541,f3689]) ).

fof(f1541,plain,
    ( ! [X19,X27,X30] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X30,X19),c_Lambda_Olift(X27,X19))
        | ~ c_Lambda_Obeta(X30,X27) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1540]) ).

fof(f60443,plain,
    ( spl0_1057
    | ~ spl0_134
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4297,f3688,f1540,f60441]) ).

fof(f60441,plain,
    ( spl0_1057
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f4297,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,X2)) )
    | ~ spl0_134
    | ~ spl0_254 ),
    inference(superposition,[],[f1541,f3689]) ).

fof(f60439,plain,
    ( spl0_1056
    | ~ spl0_111
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f4266,f3684,f1368,f60437]) ).

fof(f60437,plain,
    ( spl0_1056
  <=> ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),X1,X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f1368,plain,
    ( spl0_111
  <=> ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f3684,plain,
    ( spl0_253
  <=> ! [X27,X19,X10] :
        ( X10 = X19
        | c_HOL_Oord__class_Oless(X10,X19,tc_nat)
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X19),X27,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f4266,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oone__class_Oone(tc_nat) = X0
        | c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),X1,X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_111
    | ~ spl0_253 ),
    inference(resolution,[],[f3685,f1369]) ).

fof(f1369,plain,
    ( ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1368]) ).

fof(f3685,plain,
    ( ! [X10,X19,X27] :
        ( c_HOL_Oord__class_Oless(X10,X19,tc_nat)
        | X10 = X19
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X19),X27,X10) )
    | ~ spl0_253 ),
    inference(avatar_component_clause,[],[f3684]) ).

fof(f60435,plain,
    ( spl0_1055
    | ~ spl0_163
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f4258,f3684,f1785,f60433]) ).

fof(f60433,plain,
    ( spl0_1055
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

fof(f1785,plain,
    ( spl0_163
  <=> ! [X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f4258,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) )
    | ~ spl0_163
    | ~ spl0_253 ),
    inference(resolution,[],[f3685,f1786]) ).

fof(f1786,plain,
    ( ! [X10,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1785]) ).

fof(f60431,plain,
    ( spl0_1054
    | ~ spl0_164
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4238,f3680,f1789,f60429]) ).

fof(f60429,plain,
    ( spl0_1054
  <=> ! [X2,X0,X1] :
        ( c_List_Olast(c_List_Oupt(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f1789,plain,
    ( spl0_164
  <=> ! [X18,X4,X10] :
        ( ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X4,tc_nat),X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f3680,plain,
    ( spl0_252
  <=> ! [X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_List_Olast(c_List_Oupt(X19,X18),tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f4238,plain,
    ( ! [X2,X0,X1] :
        ( c_List_Olast(c_List_Oupt(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2),tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_164
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1790]) ).

fof(f1790,plain,
    ( ! [X10,X18,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X4,tc_nat),X10,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat) )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1789]) ).

fof(f3681,plain,
    ( ! [X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_List_Olast(c_List_Oupt(X19,X18),tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_252 ),
    inference(avatar_component_clause,[],[f3680]) ).

fof(f60427,plain,
    ( spl0_1053
    | ~ spl0_165
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4223,f3680,f1793,f60425]) ).

fof(f60425,plain,
    ( spl0_1053
  <=> ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,X1),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f1793,plain,
    ( spl0_165
  <=> ! [X11,X1] :
        ( X1 = X11
        | c_HOL_Oord__class_Oless(X1,X11,tc_nat)
        | c_HOL_Oord__class_Oless(X11,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f4223,plain,
    ( ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,X1),tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 )
    | ~ spl0_165
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1794]) ).

fof(f1794,plain,
    ( ! [X11,X1] :
        ( c_HOL_Oord__class_Oless(X11,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X1,X11,tc_nat)
        | X1 = X11 )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1793]) ).

fof(f60396,plain,
    ( spl0_1052
    | ~ spl0_163
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4168,f3676,f1785,f60394]) ).

fof(f60394,plain,
    ( spl0_1052
  <=> ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f3676,plain,
    ( spl0_251
  <=> ! [X19,X10] :
        ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f4168,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) )
    | ~ spl0_163
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1786]) ).

fof(f3677,plain,
    ( ! [X10,X19] :
        ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_251 ),
    inference(avatar_component_clause,[],[f3676]) ).

fof(f60392,plain,
    ( spl0_1051
    | ~ spl0_184
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4147,f3672,f2153,f60390]) ).

fof(f60390,plain,
    ( spl0_1051
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f3672,plain,
    ( spl0_250
  <=> ! [X4,X3,X10] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f4147,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_184
    | ~ spl0_250 ),
    inference(superposition,[],[f2154,f3673]) ).

fof(f3673,plain,
    ( ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat)
    | ~ spl0_250 ),
    inference(avatar_component_clause,[],[f3672]) ).

fof(f60388,plain,
    ( spl0_1050
    | ~ spl0_183
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4146,f3672,f2149,f60386]) ).

fof(f60386,plain,
    ( spl0_1050
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f4146,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_183
    | ~ spl0_250 ),
    inference(superposition,[],[f2150,f3673]) ).

fof(f60384,plain,
    ( spl0_1049
    | ~ spl0_184
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4107,f3668,f2153,f60382]) ).

fof(f60382,plain,
    ( spl0_1049
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f3668,plain,
    ( spl0_249
  <=> ! [X4,X3,X10] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f4107,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_184
    | ~ spl0_249 ),
    inference(superposition,[],[f2154,f3669]) ).

fof(f3669,plain,
    ( ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat)
    | ~ spl0_249 ),
    inference(avatar_component_clause,[],[f3668]) ).

fof(f60380,plain,
    ( spl0_1048
    | ~ spl0_183
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4106,f3668,f2149,f60378]) ).

fof(f60378,plain,
    ( spl0_1048
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f4106,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_183
    | ~ spl0_249 ),
    inference(superposition,[],[f2150,f3669]) ).

fof(f60376,plain,
    ( spl0_1047
    | ~ spl0_184
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4062,f3664,f2153,f60374]) ).

fof(f60374,plain,
    ( spl0_1047
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f3664,plain,
    ( spl0_248
  <=> ! [X18,X19,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f4062,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_184
    | ~ spl0_248 ),
    inference(superposition,[],[f2154,f3665]) ).

fof(f3665,plain,
    ( ! [X10,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat)
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f3664]) ).

fof(f60372,plain,
    ( spl0_1046
    | ~ spl0_183
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4061,f3664,f2149,f60370]) ).

fof(f60370,plain,
    ( spl0_1046
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f4061,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_183
    | ~ spl0_248 ),
    inference(superposition,[],[f2150,f3665]) ).

fof(f60368,plain,
    ( spl0_1045
    | ~ spl0_194
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4021,f3660,f2193,f60366]) ).

fof(f60366,plain,
    ( spl0_1045
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f2193,plain,
    ( spl0_194
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f4021,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_194
    | ~ spl0_247 ),
    inference(superposition,[],[f2194,f3661]) ).

fof(f2194,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f2193]) ).

fof(f60364,plain,
    ( spl0_1044
    | ~ spl0_193
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4020,f3660,f2189,f60362]) ).

fof(f60362,plain,
    ( spl0_1044
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f2189,plain,
    ( spl0_193
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f4020,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_193
    | ~ spl0_247 ),
    inference(superposition,[],[f2190,f3661]) ).

fof(f2190,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f2189]) ).

fof(f60360,plain,
    ( spl0_1043
    | ~ spl0_192
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4019,f3660,f2185,f60358]) ).

fof(f60358,plain,
    ( spl0_1043
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f2185,plain,
    ( spl0_192
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f4019,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_192
    | ~ spl0_247 ),
    inference(superposition,[],[f2186,f3661]) ).

fof(f2186,plain,
    ( ! [X3,X4] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_192 ),
    inference(avatar_component_clause,[],[f2185]) ).

fof(f60323,plain,
    ( spl0_1042
    | ~ spl0_191
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4018,f3660,f2181,f60321]) ).

fof(f60321,plain,
    ( spl0_1042
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f2181,plain,
    ( spl0_191
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f4018,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_191
    | ~ spl0_247 ),
    inference(superposition,[],[f2182,f3661]) ).

fof(f2182,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f2181]) ).

fof(f60319,plain,
    ( spl0_1041
    | ~ spl0_190
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4017,f3660,f2177,f60317]) ).

fof(f60317,plain,
    ( spl0_1041
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f2177,plain,
    ( spl0_190
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f4017,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_190
    | ~ spl0_247 ),
    inference(superposition,[],[f2178,f3661]) ).

fof(f2178,plain,
    ( ! [X3,X4] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f2177]) ).

fof(f60315,plain,
    ( spl0_1040
    | ~ spl0_189
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4016,f3660,f2173,f60313]) ).

fof(f60313,plain,
    ( spl0_1040
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f4016,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_189
    | ~ spl0_247 ),
    inference(superposition,[],[f2174,f3661]) ).

fof(f60311,plain,
    ( spl0_1039
    | ~ spl0_188
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4015,f3660,f2169,f60309]) ).

fof(f60309,plain,
    ( spl0_1039
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

fof(f2169,plain,
    ( spl0_188
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f4015,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_188
    | ~ spl0_247 ),
    inference(superposition,[],[f2170,f3661]) ).

fof(f2170,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_188 ),
    inference(avatar_component_clause,[],[f2169]) ).

fof(f60307,plain,
    ( spl0_1038
    | ~ spl0_187
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4014,f3660,f2165,f60305]) ).

fof(f60305,plain,
    ( spl0_1038
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f2165,plain,
    ( spl0_187
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f4014,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X2,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_187
    | ~ spl0_247 ),
    inference(superposition,[],[f2166,f3661]) ).

fof(f2166,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f2165]) ).

fof(f60303,plain,
    ( spl0_1037
    | ~ spl0_180
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3986,f3660,f2137,f60301]) ).

fof(f60301,plain,
    ( spl0_1037
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f2137,plain,
    ( spl0_180
  <=> ! [X4,X3,X10] :
        ( X3 = X4
        | c_HOL_Oplus__class_Oplus(X4,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f3986,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,X2,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X3 )
    | ~ spl0_180
    | ~ spl0_247 ),
    inference(superposition,[],[f2138,f3661]) ).

fof(f2138,plain,
    ( ! [X3,X10,X4] :
        ( c_HOL_Oplus__class_Oplus(X4,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X10,tc_nat)
        | X3 = X4 )
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f2137]) ).

fof(f60299,plain,
    ( spl0_1036
    | ~ spl0_175
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3984,f3660,f2116,f60297]) ).

fof(f60297,plain,
    ( spl0_1036
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat)
        | X2 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f2116,plain,
    ( spl0_175
  <=> ! [X21,X11,X1] :
        ( X11 = X21
        | c_HOL_Oplus__class_Oplus(X1,X21,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X11,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f3984,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat)
        | X2 = X3 )
    | ~ spl0_175
    | ~ spl0_247 ),
    inference(superposition,[],[f2117,f3661]) ).

fof(f2117,plain,
    ( ! [X21,X11,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X21,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X11,tc_nat)
        | X11 = X21 )
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f2116]) ).

fof(f60295,plain,
    ( spl0_1035
    | ~ spl0_180
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3872,f3655,f2137,f60293]) ).

fof(f60293,plain,
    ( spl0_1035
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | X0 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f3872,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | X0 = X3 )
    | ~ spl0_180
    | ~ spl0_246 ),
    inference(superposition,[],[f2138,f3656]) ).

fof(f60291,plain,
    ( spl0_1034
    | ~ spl0_175
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3870,f3655,f2116,f60289]) ).

fof(f60289,plain,
    ( spl0_1034
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f3870,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X3 )
    | ~ spl0_175
    | ~ spl0_246 ),
    inference(superposition,[],[f2117,f3656]) ).

fof(f60287,plain,
    ( spl0_1033
    | ~ spl0_78
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3825,f3651,f1218,f60285]) ).

fof(f60285,plain,
    ( spl0_1033
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2),c_Lambda_OdB_OAbs(X3))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

fof(f1218,plain,
    ( spl0_78
  <=> ! [X9,X27] :
        ( ~ c_Lambda_Obeta(X27,X9)
        | c_Lambda_Obeta(c_Lambda_OdB_OAbs(X27),c_Lambda_OdB_OAbs(X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f3651,plain,
    ( spl0_245
  <=> ! [X4,X27,X10] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f3825,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2),c_Lambda_OdB_OAbs(X3))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X3) )
    | ~ spl0_78
    | ~ spl0_245 ),
    inference(superposition,[],[f1219,f3652]) ).

fof(f3652,plain,
    ( ! [X10,X27,X4] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f3651]) ).

fof(f1219,plain,
    ( ! [X9,X27] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X27),c_Lambda_OdB_OAbs(X9))
        | ~ c_Lambda_Obeta(X27,X9) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f1218]) ).

fof(f60249,plain,
    ( spl0_1032
    | ~ spl0_78
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3824,f3651,f1218,f60247]) ).

fof(f60247,plain,
    ( spl0_1032
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f3824,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X3),c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_78
    | ~ spl0_245 ),
    inference(superposition,[],[f1219,f3652]) ).

fof(f60245,plain,
    ( spl0_1031
    | ~ spl0_76
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3822,f3651,f1210,f60243]) ).

fof(f60243,plain,
    ( spl0_1031
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OAbs(X3)
        | c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f1210,plain,
    ( spl0_76
  <=> ! [X39,X40] :
        ( X39 = X40
        | c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OAbs(X40) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f3822,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OAbs(X3)
        | c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3 )
    | ~ spl0_76
    | ~ spl0_245 ),
    inference(superposition,[],[f1211,f3652]) ).

fof(f1211,plain,
    ( ! [X40,X39] :
        ( c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OAbs(X40)
        | X39 = X40 )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f1210]) ).

fof(f60124,plain,
    ( ~ spl0_16
    | spl0_1030
    | ~ spl0_64
    | ~ spl0_215
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3814,f3647,f2790,f1150,f60122,f936]) ).

fof(f60122,plain,
    ( spl0_1030
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat))
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f2790,plain,
    ( spl0_215
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f3647,plain,
    ( spl0_244
  <=> ! [X4,X19,X10] :
        ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,X4,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f3814,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat))
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_64
    | ~ spl0_215
    | ~ spl0_244 ),
    inference(forward_demodulation,[],[f3804,f1151]) ).

fof(f3804,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat)) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_215
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f2791]) ).

fof(f2791,plain,
    ( ! [X0,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f2790]) ).

fof(f3648,plain,
    ( ! [X10,X19,X4] :
        ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,X4,tc_nat)) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f3647]) ).

fof(f60120,plain,
    ( spl0_1029
    | ~ spl0_163
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3779,f3647,f1785,f60118]) ).

fof(f60118,plain,
    ( spl0_1029
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f3779,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X2) )
    | ~ spl0_163
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1786]) ).

fof(f60054,plain,
    ( ~ spl0_16
    | spl0_1028
    | ~ spl0_153
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f3753,f3639,f1745,f60052,f936]) ).

fof(f60052,plain,
    ( spl0_1028
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f1745,plain,
    ( spl0_153
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f3639,plain,
    ( spl0_242
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f3753,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_242 ),
    inference(resolution,[],[f3640,f1746]) ).

fof(f1746,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1745]) ).

fof(f3640,plain,
    ( ! [X2,X0,X4] :
        ( c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f3639]) ).

fof(f60050,plain,
    ( spl0_1027
    | ~ spl0_188
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3614,f2886,f2169,f60048]) ).

fof(f60048,plain,
    ( spl0_1027
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f3614,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_188
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f2170]) ).

fof(f60046,plain,
    ( spl0_1026
    | ~ spl0_194
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3613,f2886,f2193,f60044]) ).

fof(f60044,plain,
    ( spl0_1026
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f3613,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_194
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f2194]) ).

fof(f59864,plain,
    ( spl0_1025
    | ~ spl0_525
    | ~ spl0_990 ),
    inference(avatar_split_clause,[],[f58780,f54582,f12350,f59862]) ).

fof(f54582,plain,
    ( spl0_990
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f58780,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X2))
    | ~ spl0_525
    | ~ spl0_990 ),
    inference(superposition,[],[f54583,f12351]) ).

fof(f54583,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1),X3))
    | ~ spl0_990 ),
    inference(avatar_component_clause,[],[f54582]) ).

fof(f59860,plain,
    ( ~ spl0_16
    | spl0_1024
    | ~ spl0_121
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3561,f2874,f1486,f59858,f936]) ).

fof(f59858,plain,
    ( spl0_1024
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) = c_Divides_Odiv__class_Omod(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f2874,plain,
    ( spl0_236
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f3561,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) = c_Divides_Odiv__class_Omod(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) )
    | ~ spl0_121
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1487]) ).

fof(f2875,plain,
    ( ! [X3,X0,X4] :
        ( c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2874]) ).

fof(f59856,plain,
    ( spl0_1023
    | ~ spl0_181
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f3533,f2870,f2141,f59854]) ).

fof(f59854,plain,
    ( spl0_1023
  <=> ! [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_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f2141,plain,
    ( spl0_181
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f2870,plain,
    ( spl0_235
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ c_HOL_Oord__class_Oless(X11,X21,X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f3533,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_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_181
    | ~ spl0_235 ),
    inference(resolution,[],[f2871,f2142]) ).

fof(f2142,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f2141]) ).

fof(f2871,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X11,X21,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) )
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2870]) ).

fof(f59852,plain,
    ( spl0_1022
    | ~ spl0_181
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3507,f2866,f2141,f59850]) ).

fof(f59850,plain,
    ( spl0_1022
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),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_1022])]) ).

fof(f2866,plain,
    ( spl0_234
  <=> ! [X21,X11,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X21,X11,X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f3507,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),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_181
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f2142]) ).

fof(f2867,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_HOL_Oord__class_Oless(X21,X11,X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) )
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f2866]) ).

fof(f59723,plain,
    ( ~ spl0_36
    | spl0_1021
    | ~ spl0_194
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3491,f2866,f2193,f59721,f1036]) ).

fof(f1036,plain,
    ( spl0_36
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f59721,plain,
    ( spl0_1021
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
        | 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_1021])]) ).

fof(f3491,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),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) )
    | ~ spl0_194
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f2194]) ).

fof(f59719,plain,
    ( spl0_1020
    | ~ spl0_187
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3469,f2862,f2165,f59717]) ).

fof(f59717,plain,
    ( spl0_1020
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X0,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f2862,plain,
    ( spl0_233
  <=> ! [X4,X3,X10] :
        ( ~ c_lessequals(X10,X4,tc_nat)
        | c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f3469,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X0,tc_nat),X2,tc_nat) )
    | ~ spl0_187
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f2166]) ).

fof(f2863,plain,
    ( ! [X3,X10,X4] :
        ( c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X10,tc_nat),tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat) )
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2862]) ).

fof(f59715,plain,
    ( spl0_1019
    | ~ spl0_193
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3468,f2862,f2189,f59713]) ).

fof(f59713,plain,
    ( spl0_1019
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f3468,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_193
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f2190]) ).

fof(f59711,plain,
    ( spl0_1018
    | ~ spl0_176
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3452,f2862,f2120,f59709]) ).

fof(f59709,plain,
    ( spl0_1018
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat)
        | c_lessequals(X2,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).

fof(f2120,plain,
    ( spl0_176
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X19,X18,tc_nat)
        | ~ c_lessequals(X18,X10,tc_nat)
        | c_lessequals(X19,X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f3452,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat)
        | c_lessequals(X2,X3,tc_nat) )
    | ~ spl0_176
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f2121]) ).

fof(f2121,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_lessequals(X19,X18,tc_nat)
        | ~ c_lessequals(X18,X10,tc_nat)
        | c_lessequals(X19,X10,tc_nat) )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f2120]) ).

fof(f59604,plain,
    ( ~ spl0_34
    | spl0_1017
    | ~ spl0_190
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3358,f2838,f2177,f59602,f1026]) ).

fof(f1026,plain,
    ( spl0_34
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f59602,plain,
    ( spl0_1017
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).

fof(f2838,plain,
    ( spl0_227
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X11,X0)
        | ~ c_lessequals(X11,X21,X0)
        | c_lessequals(X1,X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f3358,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_190
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f2178]) ).

fof(f2839,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X11,X21,X0)
        | ~ c_lessequals(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X21,X0) )
    | ~ spl0_227 ),
    inference(avatar_component_clause,[],[f2838]) ).

fof(f59600,plain,
    ( spl0_1016
    | ~ spl0_522
    | ~ spl0_990 ),
    inference(avatar_split_clause,[],[f58776,f54582,f12338,f59598]) ).

fof(f12338,plain,
    ( spl0_522
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f58776,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X3))
    | ~ spl0_522
    | ~ spl0_990 ),
    inference(superposition,[],[f54583,f12339]) ).

fof(f12339,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1)
    | ~ spl0_522 ),
    inference(avatar_component_clause,[],[f12338]) ).

fof(f59493,plain,
    ( ~ spl0_34
    | spl0_1015
    | ~ spl0_192
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3357,f2838,f2185,f59491,f1026]) ).

fof(f59491,plain,
    ( spl0_1015
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X2,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f3357,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_192
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f2186]) ).

fof(f59422,plain,
    ( ~ spl0_34
    | spl0_1014
    | ~ spl0_173
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3356,f2838,f2108,f59420,f1026]) ).

fof(f59420,plain,
    ( spl0_1014
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f2108,plain,
    ( spl0_173
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f3356,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
    | ~ spl0_173
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f2109]) ).

fof(f2109,plain,
    ( ! [X3,X4] :
        ( c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
    | ~ spl0_173 ),
    inference(avatar_component_clause,[],[f2108]) ).

fof(f59306,plain,
    ( spl0_1013
    | ~ spl0_36
    | ~ spl0_190
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3332,f2834,f2177,f1036,f59304]) ).

fof(f59304,plain,
    ( spl0_1013
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f2834,plain,
    ( spl0_226
  <=> ! [X21,X11,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X11,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X21,X11,X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f3332,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_190
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f2178]) ).

fof(f2835,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X11,X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X21,X11,X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f2834]) ).

fof(f59190,plain,
    ( spl0_1012
    | ~ spl0_36
    | ~ spl0_192
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3331,f2834,f2185,f1036,f59188]) ).

fof(f59188,plain,
    ( spl0_1012
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f3331,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_192
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f2186]) ).

fof(f59125,plain,
    ( spl0_1011
    | ~ spl0_36
    | ~ spl0_173
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3330,f2834,f2108,f1036,f59123]) ).

fof(f59123,plain,
    ( spl0_1011
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).

fof(f3330,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) )
    | ~ spl0_173
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f2109]) ).

fof(f59121,plain,
    ( spl0_1010
    | ~ spl0_522
    | ~ spl0_989 ),
    inference(avatar_split_clause,[],[f56402,f53085,f12338,f59119]) ).

fof(f56402,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X0),X3))
    | ~ spl0_522
    | ~ spl0_989 ),
    inference(superposition,[],[f53086,f12339]) ).

fof(f59014,plain,
    ( spl0_1009
    | ~ spl0_36
    | ~ spl0_173
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3300,f2830,f2108,f1036,f59012]) ).

fof(f59012,plain,
    ( spl0_1009
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f2830,plain,
    ( spl0_225
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X21,X11,X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f3300,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_173
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f2109]) ).

fof(f2831,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X21,X11,X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X21,X1,X0) )
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f2830]) ).

fof(f59010,plain,
    ( spl0_1008
    | ~ spl0_176
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f3155,f2810,f2120,f59008]) ).

fof(f59008,plain,
    ( spl0_1008
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).

fof(f3155,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat) )
    | ~ spl0_176
    | ~ spl0_220 ),
    inference(resolution,[],[f2811,f2121]) ).

fof(f59006,plain,
    ( spl0_1007
    | ~ spl0_176
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3126,f2802,f2120,f59004]) ).

fof(f59004,plain,
    ( spl0_1007
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f3126,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_176
    | ~ spl0_218 ),
    inference(resolution,[],[f2803,f2121]) ).

fof(f58894,plain,
    ( ~ spl0_16
    | spl0_1006
    | ~ spl0_163
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f3090,f2786,f1785,f58892,f936]) ).

fof(f58892,plain,
    ( spl0_1006
  <=> ! [X0] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,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_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f3090,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_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_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat)) )
    | ~ spl0_163
    | ~ spl0_214 ),
    inference(resolution,[],[f2787,f1786]) ).

fof(f58890,plain,
    ( spl0_1005
    | ~ spl0_176
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f3065,f2782,f2120,f58888]) ).

fof(f58888,plain,
    ( spl0_1005
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f2782,plain,
    ( spl0_213
  <=> ! [X4,X3,X10] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f3065,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X3,tc_nat) )
    | ~ spl0_176
    | ~ spl0_213 ),
    inference(resolution,[],[f2783,f2121]) ).

fof(f2783,plain,
    ( ! [X3,X10,X4] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f2782]) ).

fof(f58886,plain,
    ( spl0_1004
    | ~ spl0_176
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f3010,f2774,f2120,f58884]) ).

fof(f58884,plain,
    ( spl0_1004
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f2774,plain,
    ( spl0_211
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X19,X18,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f3010,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X3,tc_nat) )
    | ~ spl0_176
    | ~ spl0_211 ),
    inference(resolution,[],[f2775,f2121]) ).

fof(f2775,plain,
    ( ! [X10,X18,X19] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat)
        | ~ c_lessequals(X19,X18,tc_nat) )
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f2774]) ).

fof(f58882,plain,
    ( spl0_1003
    | ~ spl0_99
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f2995,f2770,f1318,f58880]) ).

fof(f58880,plain,
    ( spl0_1003
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f1318,plain,
    ( spl0_99
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f2770,plain,
    ( spl0_210
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X11,X0)
        | c_lessequals(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f2995,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_210 ),
    inference(resolution,[],[f2771,f1319]) ).

fof(f1319,plain,
    ( ! [X3,X0] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f1318]) ).

fof(f2771,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_lessequals(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) )
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f2770]) ).

fof(f58748,plain,
    ( ~ spl0_16
    | spl0_1002
    | ~ spl0_176
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2969,f2766,f2120,f58746,f936]) ).

fof(f58746,plain,
    ( spl0_1002
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X2,tc_nat)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f2766,plain,
    ( spl0_209
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f2969,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),X2,tc_nat) )
    | ~ spl0_176
    | ~ spl0_209 ),
    inference(resolution,[],[f2767,f2121]) ).

fof(f2767,plain,
    ( ! [X3,X0,X4] :
        ( c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | ~ c_lessequals(X3,X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f2766]) ).

fof(f58744,plain,
    ( spl0_1001
    | ~ spl0_190
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2937,f2754,f2177,f58742]) ).

fof(f58742,plain,
    ( spl0_1001
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f2937,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_190
    | ~ spl0_206 ),
    inference(resolution,[],[f2755,f2178]) ).

fof(f58740,plain,
    ( spl0_1000
    | ~ spl0_192
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2936,f2754,f2185,f58738]) ).

fof(f58738,plain,
    ( spl0_1000
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f2936,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_192
    | ~ spl0_206 ),
    inference(resolution,[],[f2755,f2186]) ).

fof(f58736,plain,
    ( spl0_999
    | ~ spl0_137
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2748,f2510,f1552,f58734]) ).

fof(f58734,plain,
    ( spl0_999
  <=> ! [X2,X0,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X2),c_Lambda_Osubst(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f1552,plain,
    ( spl0_137
  <=> ! [X9,X27] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X27),X9),c_Lambda_Osubst(X27,X9,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f2510,plain,
    ( spl0_204
  <=> ! [X27,X10] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f2748,plain,
    ( ! [X2,X0,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X2),c_Lambda_Osubst(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_137
    | ~ spl0_204 ),
    inference(superposition,[],[f1553,f2511]) ).

fof(f2511,plain,
    ( ! [X10,X27] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
    | ~ spl0_204 ),
    inference(avatar_component_clause,[],[f2510]) ).

fof(f1553,plain,
    ( ! [X9,X27] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X27),X9),c_Lambda_Osubst(X27,X9,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1552]) ).

fof(f58732,plain,
    ( spl0_998
    | ~ spl0_133
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2747,f2510,f1536,f58730]) ).

fof(f58730,plain,
    ( spl0_998
  <=> ! [X2,X0,X1] :
        ( ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X2)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f1536,plain,
    ( spl0_133
  <=> ! [X27,X30] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27)) = X27 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f2747,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X2)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2)) = X2 )
    | ~ spl0_133
    | ~ spl0_204 ),
    inference(superposition,[],[f1537,f2511]) ).

fof(f1537,plain,
    ( ! [X27,X30] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27)) = X27 )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1536]) ).

fof(f58728,plain,
    ( spl0_997
    | ~ spl0_166
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2325,f2157,f1797,f58726]) ).

fof(f58726,plain,
    ( spl0_997
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f1797,plain,
    ( spl0_166
  <=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f2157,plain,
    ( spl0_185
  <=> ! [X29,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X18,X19,tc_nat)
        | c_Lambda_OdB_OVar(X18) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f2325,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_166
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1798]) ).

fof(f1798,plain,
    ( ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1797]) ).

fof(f2158,plain,
    ( ! [X29,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(X18,X19,tc_nat)
        | c_Lambda_OdB_OVar(X18) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f2157]) ).

fof(f58724,plain,
    ( spl0_996
    | ~ spl0_164
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2324,f2157,f1789,f58722]) ).

fof(f58722,plain,
    ( spl0_996
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2,X3)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f2324,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2,X3)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1790]) ).

fof(f58720,plain,
    ( spl0_995
    | ~ spl0_166
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2281,f2145,f1797,f58718]) ).

fof(f58718,plain,
    ( spl0_995
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f2145,plain,
    ( spl0_182
  <=> ! [X4,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f2281,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_166
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1798]) ).

fof(f2146,plain,
    ( ! [X10,X19,X4] :
        ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | c_Lambda_OdB_OVar(X19) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f2145]) ).

fof(f58716,plain,
    ( spl0_994
    | ~ spl0_164
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2280,f2145,f1789,f58714]) ).

fof(f58714,plain,
    ( spl0_994
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X3)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f2280,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X3)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1790]) ).

fof(f58712,plain,
    ( spl0_993
    | ~ spl0_163
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2204,f2112,f1785,f58710]) ).

fof(f58710,plain,
    ( spl0_993
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Lambda_OdB_OVar(c_Divides_Odiv__class_Omod(X1,X0,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Divides_Odiv__class_Omod(X1,X0,tc_nat)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f2112,plain,
    ( spl0_174
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f2204,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_Lambda_OdB_OVar(c_Divides_Odiv__class_Omod(X1,X0,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Divides_Odiv__class_Omod(X1,X0,tc_nat)),X0) )
    | ~ spl0_163
    | ~ spl0_174 ),
    inference(resolution,[],[f2113,f1786]) ).

fof(f2113,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f2112]) ).

fof(f58681,plain,
    ( spl0_992
    | ~ spl0_157
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f2199,f2108,f1761,f58679]) ).

fof(f58679,plain,
    ( spl0_992
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X0,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f1761,plain,
    ( spl0_157
  <=> ! [X4,X3] :
        ( X3 = X4
        | ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f2199,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X0,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X0 )
    | ~ spl0_157
    | ~ spl0_173 ),
    inference(resolution,[],[f2109,f1762]) ).

fof(f1762,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1761]) ).

fof(f57212,plain,
    ( spl0_991
    | ~ spl0_525
    | ~ spl0_989 ),
    inference(avatar_split_clause,[],[f56406,f53085,f12350,f57210]) ).

fof(f56406,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X2))
    | ~ spl0_525
    | ~ spl0_989 ),
    inference(superposition,[],[f53086,f12351]) ).

fof(f54584,plain,
    ( spl0_990
    | ~ spl0_2
    | ~ spl0_944 ),
    inference(avatar_split_clause,[],[f52911,f47515,f867,f54582]) ).

fof(f867,plain,
    ( spl0_2
  <=> ! [X18,X19] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X19),X18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f52911,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1),X3))
    | ~ spl0_2
    | ~ spl0_944 ),
    inference(superposition,[],[f868,f47516]) ).

fof(f868,plain,
    ( ! [X18,X19] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X19),X18))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f867]) ).

fof(f53087,plain,
    ( spl0_989
    | ~ spl0_2
    | ~ spl0_943 ),
    inference(avatar_split_clause,[],[f52644,f47511,f867,f53085]) ).

fof(f52644,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0),X3))
    | ~ spl0_2
    | ~ spl0_943 ),
    inference(superposition,[],[f868,f47512]) ).

fof(f52097,plain,
    ( spl0_988
    | ~ spl0_525
    | ~ spl0_983 ),
    inference(avatar_split_clause,[],[f48581,f47728,f12350,f52095]) ).

fof(f52095,plain,
    ( spl0_988
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f47728,plain,
    ( spl0_983
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).

fof(f48581,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X0),X1))
    | ~ spl0_525
    | ~ spl0_983 ),
    inference(superposition,[],[f47729,f12351]) ).

fof(f47729,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X1),X2))
    | ~ spl0_983 ),
    inference(avatar_component_clause,[],[f47728]) ).

fof(f50416,plain,
    ( spl0_987
    | ~ spl0_522
    | ~ spl0_983 ),
    inference(avatar_split_clause,[],[f48578,f47728,f12338,f50414]) ).

fof(f50414,plain,
    ( spl0_987
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f48578,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X0),X2))
    | ~ spl0_522
    | ~ spl0_983 ),
    inference(superposition,[],[f47729,f12339]) ).

fof(f47742,plain,
    ( spl0_986
    | ~ spl0_42
    | ~ spl0_54
    | ~ spl0_64
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f9782,f9216,f1150,f1110,f1062,f47740]) ).

fof(f47740,plain,
    ( spl0_986
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f1062,plain,
    ( spl0_42
  <=> ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1110,plain,
    ( spl0_54
  <=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f9216,plain,
    ( spl0_436
  <=> ! [X18,X3,X10] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat),X3,tc_nat)
        | ~ c_lessequals(X10,X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f9782,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
    | ~ spl0_42
    | ~ spl0_54
    | ~ spl0_64
    | ~ spl0_436 ),
    inference(forward_demodulation,[],[f9781,f1151]) ).

fof(f9781,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_42
    | ~ spl0_54
    | ~ spl0_436 ),
    inference(forward_demodulation,[],[f9732,f1111]) ).

fof(f1111,plain,
    ( ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f9732,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_42
    | ~ spl0_436 ),
    inference(resolution,[],[f9217,f1063]) ).

fof(f1063,plain,
    ( ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f1062]) ).

fof(f9217,plain,
    ( ! [X3,X10,X18] :
        ( ~ c_lessequals(X10,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat),X3,tc_nat) )
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f9216]) ).

fof(f47738,plain,
    ( spl0_985
    | ~ spl0_63
    | ~ spl0_64
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f8924,f8726,f1150,f1146,f47736]) ).

fof(f47736,plain,
    ( spl0_985
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f8726,plain,
    ( spl0_423
  <=> ! [X4,X3,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f8924,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_63
    | ~ spl0_64
    | ~ spl0_423 ),
    inference(forward_demodulation,[],[f8874,f1147]) ).

fof(f8874,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_64
    | ~ spl0_423 ),
    inference(superposition,[],[f8727,f1151]) ).

fof(f8727,plain,
    ( ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat)
    | ~ spl0_423 ),
    inference(avatar_component_clause,[],[f8726]) ).

fof(f47734,plain,
    ( spl0_984
    | ~ spl0_61
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f8884,f8726,f1138,f47732]) ).

fof(f47732,plain,
    ( spl0_984
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f1138,plain,
    ( spl0_61
  <=> ! [X4,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f8884,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_423 ),
    inference(superposition,[],[f1139,f8727]) ).

fof(f1139,plain,
    ( ! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat)
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f1138]) ).

fof(f47730,plain,
    ( spl0_983
    | ~ spl0_86
    | ~ spl0_962 ),
    inference(avatar_split_clause,[],[f47653,f47609,f1265,f47728]) ).

fof(f47609,plain,
    ( spl0_962
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f47653,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X1),X2))
    | ~ spl0_86
    | ~ spl0_962 ),
    inference(superposition,[],[f47610,f1266]) ).

fof(f47610,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X0),X2))
    | ~ spl0_962 ),
    inference(avatar_component_clause,[],[f47609]) ).

fof(f47726,plain,
    ( spl0_982
    | ~ spl0_130
    | ~ spl0_423 ),
    inference(avatar_split_clause,[],[f8879,f8726,f1524,f47724]) ).

fof(f47724,plain,
    ( spl0_982
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).

fof(f1524,plain,
    ( spl0_130
  <=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f8879,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_130
    | ~ spl0_423 ),
    inference(superposition,[],[f8727,f1525]) ).

fof(f1525,plain,
    ( ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1524]) ).

fof(f47722,plain,
    ( spl0_981
    | ~ spl0_110
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f8841,f8722,f1364,f47720]) ).

fof(f47720,plain,
    ( spl0_981
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f1364,plain,
    ( spl0_110
  <=> ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f8841,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_110
    | ~ spl0_422 ),
    inference(resolution,[],[f8723,f1365]) ).

fof(f1365,plain,
    ( ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f1364]) ).

fof(f47718,plain,
    ( spl0_980
    | ~ spl0_66
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8361,f7788,f1158,f47716]) ).

fof(f47716,plain,
    ( spl0_980
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f1158,plain,
    ( spl0_66
  <=> ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f8361,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_66
    | ~ spl0_411 ),
    inference(superposition,[],[f1159,f7789]) ).

fof(f1159,plain,
    ( ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X4
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1158]) ).

fof(f47714,plain,
    ( spl0_979
    | ~ spl0_95
    | ~ spl0_328 ),
    inference(avatar_split_clause,[],[f5988,f5758,f1301,f47712]) ).

fof(f47712,plain,
    ( spl0_979
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f1301,plain,
    ( spl0_95
  <=> ! [X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f5758,plain,
    ( spl0_328
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f5988,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) )
    | ~ spl0_95
    | ~ spl0_328 ),
    inference(resolution,[],[f5759,f1302]) ).

fof(f1302,plain,
    ( ! [X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f1301]) ).

fof(f5759,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
    | ~ spl0_328 ),
    inference(avatar_component_clause,[],[f5758]) ).

fof(f47710,plain,
    ( spl0_978
    | ~ spl0_62
    | ~ spl0_86
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f5826,f5734,f1265,f1142,f47708]) ).

fof(f47708,plain,
    ( spl0_978
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f5826,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_86
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f5800,f1266]) ).

fof(f5800,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),X0,tc_nat),X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_322 ),
    inference(resolution,[],[f5735,f1143]) ).

fof(f47706,plain,
    ( spl0_977
    | ~ spl0_61
    | ~ spl0_86
    | ~ spl0_248
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f5825,f5734,f3664,f1265,f1138,f47704]) ).

fof(f47704,plain,
    ( spl0_977
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f5825,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_61
    | ~ spl0_86
    | ~ spl0_248
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f5824,f3665]) ).

fof(f5824,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_61
    | ~ spl0_86
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f5799,f1266]) ).

fof(f5799,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),X0,tc_nat),X1,tc_nat) )
    | ~ spl0_61
    | ~ spl0_322 ),
    inference(resolution,[],[f5735,f1139]) ).

fof(f47702,plain,
    ( spl0_976
    | ~ spl0_86
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5641,f5551,f1265,f47700]) ).

fof(f47700,plain,
    ( spl0_976
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f5551,plain,
    ( spl0_299
  <=> ! [X4,X10,X3,X26] :
        ( ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X3,X26,tc_nat) != c_HOL_Oplus__class_Oplus(X10,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f5641,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_86
    | ~ spl0_299 ),
    inference(superposition,[],[f5552,f1266]) ).

fof(f5552,plain,
    ( ! [X3,X10,X26,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X26,tc_nat) != c_HOL_Oplus__class_Oplus(X10,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat) )
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f5551]) ).

fof(f47698,plain,
    ( spl0_975
    | ~ spl0_86
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5634,f5551,f1265,f47696]) ).

fof(f47696,plain,
    ( spl0_975
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f5634,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_299 ),
    inference(superposition,[],[f5552,f1266]) ).

fof(f47694,plain,
    ( spl0_974
    | ~ spl0_95
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5291,f4538,f1301,f47692]) ).

fof(f47692,plain,
    ( spl0_974
  <=> ! [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_974])]) ).

fof(f5291,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_95
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f1302]) ).

fof(f47690,plain,
    ( spl0_973
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4415,f3704,f1797,f1265,f47688]) ).

fof(f47688,plain,
    ( spl0_973
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f4415,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_258 ),
    inference(forward_demodulation,[],[f4391,f1266]) ).

fof(f4391,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_166
    | ~ spl0_258 ),
    inference(superposition,[],[f1798,f3705]) ).

fof(f47651,plain,
    ( spl0_972
    | ~ spl0_164
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4390,f3704,f1789,f47649]) ).

fof(f47649,plain,
    ( spl0_972
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),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_972])]) ).

fof(f4390,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_258 ),
    inference(superposition,[],[f1790,f3705]) ).

fof(f47647,plain,
    ( spl0_971
    | ~ spl0_154
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4389,f3704,f1749,f47645]) ).

fof(f47645,plain,
    ( spl0_971
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).

fof(f1749,plain,
    ( spl0_154
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f4389,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_154
    | ~ spl0_258 ),
    inference(superposition,[],[f1750,f3705]) ).

fof(f1750,plain,
    ( ! [X3,X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_154 ),
    inference(avatar_component_clause,[],[f1749]) ).

fof(f47643,plain,
    ( spl0_970
    | ~ spl0_59
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f4278,f3684,f1130,f47641]) ).

fof(f47641,plain,
    ( spl0_970
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f1130,plain,
    ( spl0_59
  <=> ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f4278,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) )
    | ~ spl0_59
    | ~ spl0_253 ),
    inference(resolution,[],[f3685,f1131]) ).

fof(f1131,plain,
    ( ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X19,tc_nat)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f1130]) ).

fof(f47639,plain,
    ( spl0_969
    | ~ spl0_58
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f4277,f3684,f1126,f47637]) ).

fof(f47637,plain,
    ( spl0_969
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).

fof(f4277,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) )
    | ~ spl0_58
    | ~ spl0_253 ),
    inference(resolution,[],[f3685,f1127]) ).

fof(f47635,plain,
    ( spl0_968
    | ~ spl0_121
    | ~ spl0_253 ),
    inference(avatar_split_clause,[],[f4259,f3684,f1486,f47633]) ).

fof(f47633,plain,
    ( spl0_968
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).

fof(f4259,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_253 ),
    inference(resolution,[],[f3685,f1487]) ).

fof(f47631,plain,
    ( spl0_967
    | ~ spl0_107
    | ~ spl0_169
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4247,f3680,f1809,f1352,f47629]) ).

fof(f47629,plain,
    ( spl0_967
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f4247,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_107
    | ~ spl0_169
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4219,f1353]) ).

fof(f4219,plain,
    ( ! [X0,X1] : c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_169
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1810]) ).

fof(f47627,plain,
    ( spl0_966
    | ~ spl0_107
    | ~ spl0_168
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4246,f3680,f1805,f1352,f47625]) ).

fof(f47625,plain,
    ( spl0_966
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f4246,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_107
    | ~ spl0_168
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4218,f1353]) ).

fof(f4218,plain,
    ( ! [X0,X1] : c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_168
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1806]) ).

fof(f47623,plain,
    ( spl0_965
    | ~ spl0_59
    | ~ spl0_86
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4205,f3676,f1265,f1130,f47621]) ).

fof(f47621,plain,
    ( spl0_965
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f4205,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat))
    | ~ spl0_59
    | ~ spl0_86
    | ~ spl0_251 ),
    inference(forward_demodulation,[],[f4188,f1266]) ).

fof(f4188,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1)
    | ~ spl0_59
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1131]) ).

fof(f47619,plain,
    ( spl0_964
    | ~ spl0_58
    | ~ spl0_86
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4204,f3676,f1265,f1126,f47617]) ).

fof(f4204,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat))
    | ~ spl0_58
    | ~ spl0_86
    | ~ spl0_251 ),
    inference(forward_demodulation,[],[f4187,f1266]) ).

fof(f4187,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_58
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1127]) ).

fof(f47615,plain,
    ( spl0_963
    | ~ spl0_121
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4169,f3676,f1486,f47613]) ).

fof(f47613,plain,
    ( spl0_963
  <=> ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f4169,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1487]) ).

fof(f47611,plain,
    ( spl0_962
    | ~ spl0_522
    | ~ spl0_941 ),
    inference(avatar_split_clause,[],[f47550,f47503,f12338,f47609]) ).

fof(f47503,plain,
    ( spl0_941
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f47550,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X0),X2))
    | ~ spl0_522
    | ~ spl0_941 ),
    inference(superposition,[],[f47504,f12339]) ).

fof(f47504,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X0),X2))
    | ~ spl0_941 ),
    inference(avatar_component_clause,[],[f47503]) ).

fof(f47607,plain,
    ( spl0_961
    | ~ spl0_154
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4143,f3672,f1749,f47605]) ).

fof(f47605,plain,
    ( spl0_961
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f4143,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_154
    | ~ spl0_250 ),
    inference(superposition,[],[f1750,f3673]) ).

fof(f47603,plain,
    ( spl0_960
    | ~ spl0_154
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4103,f3668,f1749,f47601]) ).

fof(f47601,plain,
    ( spl0_960
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f4103,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_154
    | ~ spl0_249 ),
    inference(superposition,[],[f1750,f3669]) ).

fof(f47599,plain,
    ( spl0_959
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4078,f3664,f1797,f1265,f47597]) ).

fof(f47597,plain,
    ( spl0_959
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f4078,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_248 ),
    inference(forward_demodulation,[],[f4060,f1266]) ).

fof(f4060,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_166
    | ~ spl0_248 ),
    inference(superposition,[],[f1798,f3665]) ).

fof(f47595,plain,
    ( spl0_958
    | ~ spl0_164
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4059,f3664,f1789,f47593]) ).

fof(f47593,plain,
    ( spl0_958
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),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_958])]) ).

fof(f4059,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_248 ),
    inference(superposition,[],[f1790,f3665]) ).

fof(f47591,plain,
    ( spl0_957
    | ~ spl0_154
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4058,f3664,f1749,f47589]) ).

fof(f47589,plain,
    ( spl0_957
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f4058,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_154
    | ~ spl0_248 ),
    inference(superposition,[],[f1750,f3665]) ).

fof(f47587,plain,
    ( spl0_956
    | ~ spl0_166
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4013,f3660,f1797,f47585]) ).

fof(f47585,plain,
    ( spl0_956
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f4013,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_166
    | ~ spl0_247 ),
    inference(superposition,[],[f1798,f3661]) ).

fof(f47583,plain,
    ( spl0_955
    | ~ spl0_168
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3982,f3660,f1805,f47581]) ).

fof(f47581,plain,
    ( spl0_955
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f3982,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_168
    | ~ spl0_247 ),
    inference(superposition,[],[f1806,f3661]) ).

fof(f47579,plain,
    ( spl0_954
    | ~ spl0_161
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3981,f3660,f1777,f47577]) ).

fof(f47577,plain,
    ( spl0_954
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f1777,plain,
    ( spl0_161
  <=> ! [X21,X11,X1] :
        ( ~ c_lessequals(X1,X11,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f3981,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_161
    | ~ spl0_247 ),
    inference(superposition,[],[f1778,f3661]) ).

fof(f1778,plain,
    ( ! [X21,X11,X1] :
        ( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X11,tc_nat) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1777]) ).

fof(f47575,plain,
    ( spl0_953
    | ~ spl0_160
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3980,f3660,f1773,f47573]) ).

fof(f47573,plain,
    ( spl0_953
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f1773,plain,
    ( spl0_160
  <=> ! [X4,X3,X10] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f3980,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_160
    | ~ spl0_247 ),
    inference(superposition,[],[f1774,f3661]) ).

fof(f1774,plain,
    ( ! [X3,X10,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1773]) ).

fof(f47571,plain,
    ( spl0_952
    | ~ spl0_152
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3977,f3660,f1741,f47569]) ).

fof(f47569,plain,
    ( spl0_952
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f1741,plain,
    ( spl0_152
  <=> ! [X18,X19,X10] :
        ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X10,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f3977,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_152
    | ~ spl0_247 ),
    inference(superposition,[],[f1742,f3661]) ).

fof(f1742,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X10,tc_nat)
        | c_HOL_Oord__class_Oless(X19,X10,tc_nat) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1741]) ).

fof(f47545,plain,
    ( spl0_951
    | ~ spl0_151
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3976,f3660,f1737,f47543]) ).

fof(f47543,plain,
    ( spl0_951
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f1737,plain,
    ( spl0_151
  <=> ! [X18,X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f3976,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_151
    | ~ spl0_247 ),
    inference(superposition,[],[f1738,f3661]) ).

fof(f1738,plain,
    ( ! [X3,X18,X19] :
        ( c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) )
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1737]) ).

fof(f47541,plain,
    ( spl0_950
    | ~ spl0_146
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3973,f3660,f1717,f47539]) ).

fof(f47539,plain,
    ( spl0_950
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f1717,plain,
    ( spl0_146
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f3973,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) )
    | ~ spl0_146
    | ~ spl0_247 ),
    inference(superposition,[],[f1718,f3661]) ).

fof(f1718,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1717]) ).

fof(f47537,plain,
    ( spl0_949
    | ~ spl0_169
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3869,f3655,f1809,f47535]) ).

fof(f47535,plain,
    ( spl0_949
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f3869,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_169
    | ~ spl0_246 ),
    inference(superposition,[],[f1810,f3656]) ).

fof(f47533,plain,
    ( spl0_948
    | ~ spl0_159
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3865,f3655,f1769,f47531]) ).

fof(f47531,plain,
    ( spl0_948
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f1769,plain,
    ( spl0_159
  <=> ! [X4,X3,X10] :
        ( c_lessequals(X10,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f3865,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat) )
    | ~ spl0_159
    | ~ spl0_246 ),
    inference(superposition,[],[f1770,f3656]) ).

fof(f1770,plain,
    ( ! [X3,X10,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat)
        | c_lessequals(X10,X4,tc_nat) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1769]) ).

fof(f47529,plain,
    ( spl0_947
    | ~ spl0_158
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3864,f3655,f1765,f47527]) ).

fof(f47527,plain,
    ( spl0_947
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f1765,plain,
    ( spl0_158
  <=> ! [X18,X3,X19] :
        ( ~ c_lessequals(X19,X18,tc_nat)
        | c_lessequals(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f3864,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_158
    | ~ spl0_246 ),
    inference(superposition,[],[f1766,f3656]) ).

fof(f1766,plain,
    ( ! [X3,X18,X19] :
        ( c_lessequals(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat)
        | ~ c_lessequals(X19,X18,tc_nat) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1765]) ).

fof(f47525,plain,
    ( spl0_946
    | ~ spl0_150
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3861,f3655,f1733,f47523]) ).

fof(f47523,plain,
    ( spl0_946
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f1733,plain,
    ( spl0_150
  <=> ! [X18,X3,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f3861,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_150
    | ~ spl0_246 ),
    inference(superposition,[],[f1734,f3656]) ).

fof(f1734,plain,
    ( ! [X3,X18,X19] :
        ( c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) )
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1733]) ).

fof(f47521,plain,
    ( spl0_945
    | ~ spl0_147
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3860,f3655,f1721,f47519]) ).

fof(f47519,plain,
    ( spl0_945
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f1721,plain,
    ( spl0_147
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f3860,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) )
    | ~ spl0_147
    | ~ spl0_246 ),
    inference(superposition,[],[f1722,f3656]) ).

fof(f1722,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1721]) ).

fof(f47517,plain,
    ( spl0_944
    | ~ spl0_59
    | ~ spl0_244
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3809,f3660,f3647,f1130,f47515]) ).

fof(f3809,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_59
    | ~ spl0_244
    | ~ spl0_247 ),
    inference(forward_demodulation,[],[f3799,f3661]) ).

fof(f3799,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X2)
    | ~ spl0_59
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1131]) ).

fof(f47513,plain,
    ( spl0_943
    | ~ spl0_58
    | ~ spl0_244
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3808,f3660,f3647,f1126,f47511]) ).

fof(f3808,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_58
    | ~ spl0_244
    | ~ spl0_247 ),
    inference(forward_demodulation,[],[f3798,f3661]) ).

fof(f3798,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat))
    | ~ spl0_58
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1127]) ).

fof(f47509,plain,
    ( spl0_942
    | ~ spl0_121
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3780,f3647,f1486,f47507]) ).

fof(f47507,plain,
    ( spl0_942
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f3780,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_Divides_Odiv__class_Omod(X1,X2,tc_nat) = X1 )
    | ~ spl0_121
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1487]) ).

fof(f47505,plain,
    ( spl0_941
    | ~ spl0_254
    | ~ spl0_895 ),
    inference(avatar_split_clause,[],[f47449,f42335,f3688,f47503]) ).

fof(f42335,plain,
    ( spl0_895
  <=> ! [X0,X3,X2,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Lambda_OdB_OVar(X0),X0),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).

fof(f47449,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X0),X2))
    | ~ spl0_254
    | ~ spl0_895 ),
    inference(superposition,[],[f42336,f3689]) ).

fof(f42336,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Lambda_OdB_OVar(X0),X0),X1),X3))
    | ~ spl0_895 ),
    inference(avatar_component_clause,[],[f42335]) ).

fof(f47501,plain,
    ( spl0_940
    | ~ spl0_129
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3756,f3643,f1520,f47499]) ).

fof(f47499,plain,
    ( spl0_940
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f3643,plain,
    ( spl0_243
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f3756,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_129
    | ~ spl0_243 ),
    inference(resolution,[],[f3644,f1521]) ).

fof(f3644,plain,
    ( ! [X2,X0,X4] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f3643]) ).

fof(f47497,plain,
    ( spl0_939
    | ~ spl0_128
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f3755,f3643,f1516,f47495]) ).

fof(f47495,plain,
    ( spl0_939
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f3755,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_128
    | ~ spl0_243 ),
    inference(resolution,[],[f3644,f1517]) ).

fof(f47493,plain,
    ( spl0_938
    | ~ spl0_129
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f3737,f3639,f1520,f47491]) ).

fof(f47491,plain,
    ( spl0_938
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f3737,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
    | ~ spl0_129
    | ~ spl0_242 ),
    inference(resolution,[],[f3640,f1521]) ).

fof(f47489,plain,
    ( spl0_937
    | ~ spl0_128
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f3736,f3639,f1516,f47487]) ).

fof(f47487,plain,
    ( spl0_937
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f3736,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) )
    | ~ spl0_128
    | ~ spl0_242 ),
    inference(resolution,[],[f3640,f1517]) ).

fof(f47485,plain,
    ( spl0_936
    | ~ spl0_143
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3732,f3635,f1578,f47483]) ).

fof(f47483,plain,
    ( spl0_936
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f3635,plain,
    ( spl0_241
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f3732,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_143
    | ~ spl0_241 ),
    inference(resolution,[],[f3636,f1579]) ).

fof(f3636,plain,
    ( ! [X2,X0,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f3635]) ).

fof(f47481,plain,
    ( spl0_935
    | ~ spl0_142
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3731,f3635,f1572,f47479]) ).

fof(f47479,plain,
    ( spl0_935
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f3731,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_142
    | ~ spl0_241 ),
    inference(resolution,[],[f3636,f1573]) ).

fof(f47477,plain,
    ( spl0_934
    | ~ spl0_141
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3730,f3635,f1568,f47475]) ).

fof(f47475,plain,
    ( spl0_934
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f3730,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_141
    | ~ spl0_241 ),
    inference(resolution,[],[f3636,f1569]) ).

fof(f47473,plain,
    ( spl0_933
    | ~ spl0_123
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3729,f3635,f1496,f47471]) ).

fof(f47471,plain,
    ( spl0_933
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f3729,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
    | ~ spl0_123
    | ~ spl0_241 ),
    inference(resolution,[],[f3636,f1497]) ).

fof(f47469,plain,
    ( spl0_932
    | ~ spl0_122
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f3728,f3635,f1492,f47467]) ).

fof(f47467,plain,
    ( spl0_932
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f3728,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) )
    | ~ spl0_122
    | ~ spl0_241 ),
    inference(resolution,[],[f3636,f1493]) ).

fof(f47464,plain,
    ( spl0_931
    | ~ spl0_168
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3632,f2886,f1805,f47462]) ).

fof(f47462,plain,
    ( spl0_931
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f3632,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_168
    | ~ spl0_239 ),
    inference(forward_demodulation,[],[f3617,f287]) ).

fof(f287,axiom,
    ! [X3,X10,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

fof(f3617,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_168
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f1806]) ).

fof(f47419,plain,
    ( spl0_930
    | ~ spl0_169
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3618,f2886,f1809,f47417]) ).

fof(f47417,plain,
    ( spl0_930
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f3618,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),X2,tc_nat),tc_nat)
    | ~ spl0_169
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f1810]) ).

fof(f47415,plain,
    ( spl0_929
    | ~ spl0_150
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3616,f2886,f1733,f47413]) ).

fof(f47413,plain,
    ( spl0_929
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f3616,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) )
    | ~ spl0_150
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f1734]) ).

fof(f47411,plain,
    ( spl0_928
    | ~ spl0_151
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3615,f2886,f1737,f47409]) ).

fof(f47409,plain,
    ( spl0_928
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f3615,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) )
    | ~ spl0_151
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f1738]) ).

fof(f47407,plain,
    ( spl0_927
    | ~ spl0_164
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f3597,f2882,f1789,f47405]) ).

fof(f47405,plain,
    ( spl0_927
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f3597,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat) )
    | ~ spl0_164
    | ~ spl0_238 ),
    inference(resolution,[],[f2883,f1790]) ).

fof(f47273,plain,
    ( ~ spl0_34
    | spl0_926
    | ~ spl0_165
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f3527,f2870,f1793,f47271,f1026]) ).

fof(f47271,plain,
    ( spl0_926
  <=> ! [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_926])]) ).

fof(f3527,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_165
    | ~ spl0_235 ),
    inference(resolution,[],[f2871,f1794]) ).

fof(f47114,plain,
    ( ~ spl0_36
    | spl0_925
    | ~ spl0_164
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3512,f2866,f1789,f47112,f1036]) ).

fof(f47112,plain,
    ( spl0_925
  <=> ! [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_925])]) ).

fof(f3512,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_164
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f1790]) ).

fof(f46981,plain,
    ( ~ spl0_36
    | spl0_924
    | ~ spl0_165
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3501,f2866,f1793,f46979,f1036]) ).

fof(f46979,plain,
    ( spl0_924
  <=> ! [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_924])]) ).

fof(f3501,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_165
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f1794]) ).

fof(f46812,plain,
    ( ~ spl0_36
    | spl0_923
    | ~ spl0_151
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3493,f2866,f1737,f46810,f1036]) ).

fof(f46810,plain,
    ( spl0_923
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f3493,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(X3,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat) )
    | ~ spl0_151
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f1738]) ).

fof(f46808,plain,
    ( spl0_922
    | ~ spl0_159
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3471,f2862,f1769,f46806]) ).

fof(f46806,plain,
    ( spl0_922
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f3471,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_159
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f1770]) ).

fof(f46804,plain,
    ( spl0_921
    | ~ spl0_160
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3470,f2862,f1773,f46802]) ).

fof(f46802,plain,
    ( spl0_921
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f3470,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_160
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f1774]) ).

fof(f46800,plain,
    ( spl0_920
    | ~ spl0_153
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3455,f2862,f1745,f46798]) ).

fof(f46798,plain,
    ( spl0_920
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f3455,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_233 ),
    inference(resolution,[],[f2863,f1746]) ).

fof(f46672,plain,
    ( spl0_919
    | ~ spl0_36
    | ~ spl0_158
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3336,f2834,f1765,f1036,f46670]) ).

fof(f46670,plain,
    ( spl0_919
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f3336,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X3,tc_nat) )
    | ~ spl0_158
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1766]) ).

fof(f46492,plain,
    ( spl0_918
    | ~ spl0_36
    | ~ spl0_161
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3335,f2834,f1777,f1036,f46490]) ).

fof(f46490,plain,
    ( spl0_918
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f3335,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_161
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1778]) ).

fof(f46299,plain,
    ( spl0_917
    | ~ spl0_36
    | ~ spl0_161
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3305,f2830,f1777,f1036,f46297]) ).

fof(f46297,plain,
    ( spl0_917
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f3305,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X2,tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat) )
    | ~ spl0_161
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1778]) ).

fof(f46295,plain,
    ( spl0_916
    | ~ spl0_153
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f3181,f2810,f1745,f46293]) ).

fof(f46293,plain,
    ( spl0_916
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f3181,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_153
    | ~ spl0_220 ),
    inference(forward_demodulation,[],[f3158,f330]) ).

fof(f330,axiom,
    ! [X10,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

fof(f3158,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_220 ),
    inference(resolution,[],[f2811,f1746]) ).

fof(f46291,plain,
    ( spl0_915
    | ~ spl0_153
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3151,f2802,f1745,f46289]) ).

fof(f46289,plain,
    ( spl0_915
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f3151,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_153
    | ~ spl0_218 ),
    inference(forward_demodulation,[],[f3129,f330]) ).

fof(f3129,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_218 ),
    inference(resolution,[],[f2803,f1746]) ).

fof(f46138,plain,
    ( ~ spl0_16
    | spl0_914
    | ~ spl0_153
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2972,f2766,f1745,f46136,f936]) ).

fof(f46136,plain,
    ( spl0_914
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f2972,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_209 ),
    inference(resolution,[],[f2767,f1746]) ).

fof(f46134,plain,
    ( spl0_913
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2919,f2750,f1765,f46132]) ).

fof(f46132,plain,
    ( spl0_913
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f2750,plain,
    ( spl0_205
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat)
        | c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f2919,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(forward_demodulation,[],[f2905,f287]) ).

fof(f2905,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1766]) ).

fof(f2751,plain,
    ( ! [X10,X18,X19] :
        ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat)
        | c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat) )
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f2750]) ).

fof(f46130,plain,
    ( spl0_912
    | ~ spl0_161
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2918,f2750,f1777,f46128]) ).

fof(f46128,plain,
    ( spl0_912
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f2918,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X1,tc_nat) )
    | ~ spl0_161
    | ~ spl0_205 ),
    inference(forward_demodulation,[],[f2904,f287]) ).

fof(f2904,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X3,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X1,tc_nat) )
    | ~ spl0_161
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1778]) ).

fof(f46126,plain,
    ( spl0_911
    | ~ spl0_182
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2703,f2506,f2145,f46124]) ).

fof(f46124,plain,
    ( spl0_911
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f2506,plain,
    ( spl0_203
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f2703,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X1),X0) )
    | ~ spl0_182
    | ~ spl0_203 ),
    inference(resolution,[],[f2507,f2146]) ).

fof(f2507,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 )
    | ~ spl0_203 ),
    inference(avatar_component_clause,[],[f2506]) ).

fof(f46122,plain,
    ( spl0_910
    | ~ spl0_185
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2702,f2506,f2157,f46120]) ).

fof(f46120,plain,
    ( spl0_910
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f2702,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,X0) )
    | ~ spl0_185
    | ~ spl0_203 ),
    inference(resolution,[],[f2507,f2158]) ).

fof(f46118,plain,
    ( spl0_909
    | ~ spl0_99
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f2607,f2490,f1318,f46116]) ).

fof(f46116,plain,
    ( spl0_909
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f2490,plain,
    ( spl0_199
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | X1 = X11
        | ~ c_lessequals(X1,X11,X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f2607,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(X1,X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_199 ),
    inference(resolution,[],[f2491,f1319]) ).

fof(f2491,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_lessequals(X1,X11,X0)
        | X1 = X11
        | ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f2490]) ).

fof(f46090,plain,
    ( spl0_908
    | ~ spl0_99
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f2583,f2486,f1318,f46088]) ).

fof(f46088,plain,
    ( spl0_908
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X1) = c_Nat_Osemiring__1__class_Oof__nat(X0,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f2486,plain,
    ( spl0_198
  <=> ! [X5,X2,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | X2 = X5
        | ~ c_lessequals(X5,X2,X0)
        | c_HOL_Oord__class_Oless(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f2583,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X1) = c_Nat_Osemiring__1__class_Oof__nat(X0,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_99
    | ~ spl0_198 ),
    inference(resolution,[],[f2487,f1319]) ).

fof(f2487,plain,
    ( ! [X2,X0,X5] :
        ( ~ c_lessequals(X5,X2,X0)
        | X2 = X5
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X5,X2,X0) )
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f2486]) ).

fof(f46086,plain,
    ( spl0_907
    | ~ spl0_99
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f2532,f2475,f1318,f46084]) ).

fof(f46084,plain,
    ( spl0_907
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X1) = c_Nat_Osemiring__1__class_Oof__nat(X0,X1)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).

fof(f2475,plain,
    ( spl0_196
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | X1 = X11
        | ~ c_lessequals(X1,X11,X0)
        | ~ c_lessequals(X11,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f2532,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X1) = c_Nat_Osemiring__1__class_Oof__nat(X0,X1)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Oorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_99
    | ~ spl0_196 ),
    inference(resolution,[],[f2476,f1319]) ).

fof(f2476,plain,
    ( ! [X0,X11,X1] :
        ( ~ c_lessequals(X11,X1,X0)
        | X1 = X11
        | ~ c_lessequals(X1,X11,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f2475]) ).

fof(f46082,plain,
    ( spl0_906
    | ~ spl0_184
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2321,f2157,f2153,f46080]) ).

fof(f46080,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f2321,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_184
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f2154]) ).

fof(f46078,plain,
    ( spl0_905
    | ~ spl0_182
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f2294,f2153,f2145,f46076]) ).

fof(f46076,plain,
    ( spl0_905
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X2,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_905])]) ).

fof(f2294,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)) )
    | ~ spl0_182
    | ~ spl0_184 ),
    inference(resolution,[],[f2154,f2146]) ).

fof(f46074,plain,
    ( spl0_904
    | ~ spl0_163
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2056,f1797,f1785,f46072]) ).

fof(f46072,plain,
    ( spl0_904
  <=> ! [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)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f2056,plain,
    ( ! [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)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_163
    | ~ spl0_166 ),
    inference(resolution,[],[f1798,f1786]) ).

fof(f46070,plain,
    ( spl0_903
    | ~ spl0_152
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2033,f1793,f1741,f46068]) ).

fof(f46068,plain,
    ( spl0_903
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X2
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f2033,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X2
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_152
    | ~ spl0_165 ),
    inference(resolution,[],[f1794,f1742]) ).

fof(f46066,plain,
    ( spl0_902
    | ~ spl0_163
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1994,f1789,f1785,f46064]) ).

fof(f46064,plain,
    ( spl0_902
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).

fof(f1994,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat)),X1) )
    | ~ spl0_163
    | ~ spl0_164 ),
    inference(resolution,[],[f1790,f1786]) ).

fof(f46062,plain,
    ( spl0_901
    | ~ spl0_158
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1981,f1781,f1765,f46060]) ).

fof(f46060,plain,
    ( spl0_901
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).

fof(f1781,plain,
    ( spl0_162
  <=> ! [X4,X3] :
        ( X3 = X4
        | ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f1981,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1766]) ).

fof(f1782,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | X3 = X4
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1781]) ).

fof(f46058,plain,
    ( spl0_900
    | ~ spl0_161
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1980,f1781,f1777,f46056]) ).

fof(f46056,plain,
    ( spl0_900
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).

fof(f1980,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_161
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1778]) ).

fof(f46054,plain,
    ( spl0_899
    | ~ spl0_157
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1958,f1777,f1761,f46052]) ).

fof(f46052,plain,
    ( spl0_899
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f1958,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = X0 )
    | ~ spl0_157
    | ~ spl0_161 ),
    inference(resolution,[],[f1778,f1762]) ).

fof(f46016,plain,
    ( spl0_898
    | ~ spl0_157
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1914,f1765,f1761,f46014]) ).

fof(f46014,plain,
    ( spl0_898
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f1914,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = X0 )
    | ~ spl0_157
    | ~ spl0_158 ),
    inference(resolution,[],[f1766,f1762]) ).

fof(f46012,plain,
    ( spl0_897
    | ~ spl0_109
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1674,f1536,f1360,f46010]) ).

fof(f46010,plain,
    ( spl0_897
  <=> ! [X0,X1] :
        ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_OdB_OAbs(X0),X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_OdB_OAbs(X0),X1)))
        | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f1360,plain,
    ( spl0_109
  <=> ! [X27,X30] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27)
        | c_Lambda_Obeta(X30,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1674,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_OdB_OAbs(X0),X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(c_Lambda_OdB_OAbs(X0),X1)))
        | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0)),X1) )
    | ~ spl0_109
    | ~ spl0_133 ),
    inference(resolution,[],[f1537,f1361]) ).

fof(f1361,plain,
    ( ! [X27,X30] :
        ( c_Lambda_Obeta(X30,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27))
        | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1360]) ).

fof(f43643,plain,
    ( spl0_896
    | ~ spl0_86
    | ~ spl0_837 ),
    inference(avatar_split_clause,[],[f37770,f37546,f1265,f43641]) ).

fof(f43641,plain,
    ( spl0_896
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).

fof(f37546,plain,
    ( spl0_837
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f37770,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_86
    | ~ spl0_837 ),
    inference(superposition,[],[f37547,f1266]) ).

fof(f37547,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_837 ),
    inference(avatar_component_clause,[],[f37546]) ).

fof(f42337,plain,
    ( spl0_895
    | ~ spl0_522
    | ~ spl0_815 ),
    inference(avatar_split_clause,[],[f37669,f37458,f12338,f42335]) ).

fof(f37458,plain,
    ( spl0_815
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).

fof(f37669,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Lambda_OdB_OVar(X0),X0),X1),X3))
    | ~ spl0_522
    | ~ spl0_815 ),
    inference(superposition,[],[f37459,f12339]) ).

fof(f37459,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X0),X3))
    | ~ spl0_815 ),
    inference(avatar_component_clause,[],[f37458]) ).

fof(f41300,plain,
    ( spl0_894
    | ~ spl0_754
    | ~ spl0_815 ),
    inference(avatar_split_clause,[],[f37654,f37458,f26518,f41298]) ).

fof(f41298,plain,
    ( spl0_894
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).

fof(f26518,plain,
    ( spl0_754
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f37654,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X3))
    | ~ spl0_754
    | ~ spl0_815 ),
    inference(superposition,[],[f37459,f26519]) ).

fof(f26519,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_754 ),
    inference(avatar_component_clause,[],[f26518]) ).

fof(f40626,plain,
    ( spl0_893
    | ~ spl0_753
    | ~ spl0_815 ),
    inference(avatar_split_clause,[],[f37651,f37458,f26498,f40624]) ).

fof(f40624,plain,
    ( spl0_893
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).

fof(f26498,plain,
    ( spl0_753
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f37651,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X3))
    | ~ spl0_753
    | ~ spl0_815 ),
    inference(superposition,[],[f37459,f26499]) ).

fof(f26499,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_753 ),
    inference(avatar_component_clause,[],[f26498]) ).

fof(f39753,plain,
    ( spl0_892
    | ~ spl0_41
    | ~ spl0_251
    | ~ spl0_413
    | ~ spl0_726
    | ~ spl0_754 ),
    inference(avatar_split_clause,[],[f30257,f26518,f25123,f7972,f3676,f1058,f39751]) ).

fof(f39751,plain,
    ( spl0_892
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).

fof(f1058,plain,
    ( spl0_41
  <=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f7972,plain,
    ( spl0_413
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f25123,plain,
    ( spl0_726
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).

fof(f30257,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X2))
    | ~ spl0_41
    | ~ spl0_251
    | ~ spl0_413
    | ~ spl0_726
    | ~ spl0_754 ),
    inference(forward_demodulation,[],[f30157,f8298]) ).

fof(f8298,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Divides_Odiv__class_Omod(X0,X1,tc_nat))
    | ~ spl0_41
    | ~ spl0_251
    | ~ spl0_413 ),
    inference(forward_demodulation,[],[f8284,f4173]) ).

fof(f4173,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_41
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1059]) ).

fof(f1059,plain,
    ( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f1058]) ).

fof(f8284,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Divides_Odiv__class_Omod(X0,X1,tc_nat))
    | ~ spl0_251
    | ~ spl0_413 ),
    inference(resolution,[],[f7973,f3677]) ).

fof(f7973,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
    | ~ spl0_413 ),
    inference(avatar_component_clause,[],[f7972]) ).

fof(f30157,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),X2))
    | ~ spl0_726
    | ~ spl0_754 ),
    inference(superposition,[],[f25124,f26519]) ).

fof(f25124,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X1),X2))
    | ~ spl0_726 ),
    inference(avatar_component_clause,[],[f25123]) ).

fof(f38814,plain,
    ( spl0_891
    | ~ spl0_41
    | ~ spl0_219
    | ~ spl0_251
    | ~ spl0_726
    | ~ spl0_753 ),
    inference(avatar_split_clause,[],[f29954,f26498,f25123,f3676,f2806,f1058,f38812]) ).

fof(f38812,plain,
    ( spl0_891
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).

fof(f2806,plain,
    ( spl0_219
  <=> ! [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_219])]) ).

fof(f29954,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2))
    | ~ spl0_41
    | ~ spl0_219
    | ~ spl0_251
    | ~ spl0_726
    | ~ spl0_753 ),
    inference(forward_demodulation,[],[f29843,f4197]) ).

fof(f4197,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
    | ~ spl0_41
    | ~ spl0_219
    | ~ spl0_251 ),
    inference(forward_demodulation,[],[f4174,f4173]) ).

fof(f4174,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
    | ~ spl0_219
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f2807]) ).

fof(f2807,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2806]) ).

fof(f29843,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X2))
    | ~ spl0_726
    | ~ spl0_753 ),
    inference(superposition,[],[f25124,f26499]) ).

fof(f37854,plain,
    ( spl0_890
    | ~ spl0_159
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8405,f7788,f1769,f37852]) ).

fof(f37852,plain,
    ( spl0_890
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).

fof(f8405,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_159
    | ~ spl0_411 ),
    inference(superposition,[],[f1770,f7789]) ).

fof(f37850,plain,
    ( spl0_889
    | ~ spl0_158
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8404,f7788,f1765,f37848]) ).

fof(f37848,plain,
    ( spl0_889
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f8404,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_158
    | ~ spl0_411 ),
    inference(superposition,[],[f1766,f7789]) ).

fof(f37846,plain,
    ( spl0_888
    | ~ spl0_150
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8401,f7788,f1733,f37844]) ).

fof(f37844,plain,
    ( spl0_888
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).

fof(f8401,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_150
    | ~ spl0_411 ),
    inference(superposition,[],[f1734,f7789]) ).

fof(f37842,plain,
    ( spl0_887
    | ~ spl0_247
    | ~ spl0_629 ),
    inference(avatar_split_clause,[],[f18472,f17744,f3660,f37840]) ).

fof(f37840,plain,
    ( spl0_887
  <=> ! [X2,X0,X1,X3] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X2),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f17744,plain,
    ( spl0_629
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f18472,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X2),X3))
    | ~ spl0_247
    | ~ spl0_629 ),
    inference(superposition,[],[f17745,f3661]) ).

fof(f17745,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X2))
    | ~ spl0_629 ),
    inference(avatar_component_clause,[],[f17744]) ).

fof(f37838,plain,
    ( spl0_886
    | ~ spl0_278
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f7514,f6682,f4506,f37836]) ).

fof(f37836,plain,
    ( spl0_886
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ c_HOL_Oord__class_Oless(X3,X3,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f7514,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ c_HOL_Oord__class_Oless(X3,X3,X2)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
        | c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) )
    | ~ spl0_278
    | ~ spl0_387 ),
    inference(resolution,[],[f6683,f4507]) ).

fof(f37834,plain,
    ( spl0_885
    | ~ spl0_158
    | ~ spl0_346 ),
    inference(avatar_split_clause,[],[f6445,f6171,f1765,f37832]) ).

fof(f37832,plain,
    ( spl0_885
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
        | ~ c_lessequals(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f6171,plain,
    ( spl0_346
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
        | c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f6445,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
        | ~ c_lessequals(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_158
    | ~ spl0_346 ),
    inference(resolution,[],[f6172,f1766]) ).

fof(f6172,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_lessequals(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3 )
    | ~ spl0_346 ),
    inference(avatar_component_clause,[],[f6171]) ).

fof(f37830,plain,
    ( spl0_884
    | ~ spl0_64
    | ~ spl0_344 ),
    inference(avatar_split_clause,[],[f6396,f6163,f1150,f37828]) ).

fof(f37828,plain,
    ( spl0_884
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f6163,plain,
    ( spl0_344
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f6396,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_64
    | ~ spl0_344 ),
    inference(superposition,[],[f6164,f1151]) ).

fof(f6164,plain,
    ( ! [X2,X0,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_344 ),
    inference(avatar_component_clause,[],[f6163]) ).

fof(f37826,plain,
    ( spl0_883
    | ~ spl0_37
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f6135,f5782,f1041,f37824]) ).

fof(f37824,plain,
    ( spl0_883
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).

fof(f1041,plain,
    ( spl0_37
  <=> class_Power_Opower(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f5782,plain,
    ( spl0_334
  <=> ! [X4,X0,X2] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f6135,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_37
    | ~ spl0_334 ),
    inference(resolution,[],[f5783,f1043]) ).

fof(f1043,plain,
    ( class_Power_Opower(tc_nat)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f1041]) ).

fof(f5783,plain,
    ( ! [X2,X0,X4] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f5782]) ).

fof(f37822,plain,
    ( spl0_882
    | ~ spl0_29
    | ~ spl0_333 ),
    inference(avatar_split_clause,[],[f6134,f5778,f1001,f37820]) ).

fof(f37820,plain,
    ( spl0_882
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),X0,tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).

fof(f1001,plain,
    ( spl0_29
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f5778,plain,
    ( spl0_333
  <=> ! [X4,X0,X2] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f6134,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),X0,tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_29
    | ~ spl0_333 ),
    inference(resolution,[],[f5779,f1003]) ).

fof(f1003,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f1001]) ).

fof(f5779,plain,
    ( ! [X2,X0,X4] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) )
    | ~ spl0_333 ),
    inference(avatar_component_clause,[],[f5778]) ).

fof(f37818,plain,
    ( spl0_881
    | ~ spl0_64
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6024,f5762,f1150,f37816]) ).

fof(f37816,plain,
    ( spl0_881
  <=> ! [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_881])]) ).

fof(f6024,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_64
    | ~ spl0_329 ),
    inference(superposition,[],[f5763,f1151]) ).

fof(f37814,plain,
    ( spl0_880
    | ~ spl0_47
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f5961,f5754,f1082,f37812]) ).

fof(f37812,plain,
    ( spl0_880
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Oorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f5754,plain,
    ( spl0_327
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f5961,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Oorder(X2) )
    | ~ spl0_47
    | ~ spl0_327 ),
    inference(resolution,[],[f5755,f1083]) ).

fof(f5755,plain,
    ( ! [X2,X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f5754]) ).

fof(f37810,plain,
    ( spl0_879
    | ~ spl0_48
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f5960,f5754,f1086,f37808]) ).

fof(f37808,plain,
    ( spl0_879
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f5960,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_48
    | ~ spl0_327 ),
    inference(resolution,[],[f5755,f1087]) ).

fof(f37806,plain,
    ( spl0_878
    | ~ spl0_49
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f5959,f5754,f1090,f37804]) ).

fof(f37804,plain,
    ( spl0_878
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f5959,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(X2) )
    | ~ spl0_49
    | ~ spl0_327 ),
    inference(resolution,[],[f5755,f1091]) ).

fof(f37802,plain,
    ( spl0_877
    | ~ spl0_189
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f5911,f5750,f2173,f37800]) ).

fof(f37800,plain,
    ( spl0_877
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f5911,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_189
    | ~ spl0_326 ),
    inference(resolution,[],[f5751,f2174]) ).

fof(f37768,plain,
    ( spl0_876
    | ~ spl0_191
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f5910,f5750,f2181,f37766]) ).

fof(f37766,plain,
    ( spl0_876
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f5910,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat) )
    | ~ spl0_191
    | ~ spl0_326 ),
    inference(resolution,[],[f5751,f2182]) ).

fof(f37764,plain,
    ( spl0_875
    | ~ spl0_17
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f5878,f5742,f941,f37762]) ).

fof(f37762,plain,
    ( spl0_875
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f5742,plain,
    ( spl0_324
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f5878,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_324 ),
    inference(resolution,[],[f5743,f943]) ).

fof(f5743,plain,
    ( ! [X2,X3,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f5742]) ).

fof(f37760,plain,
    ( spl0_874
    | ~ spl0_64
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5875,f5738,f1150,f37758]) ).

fof(f37758,plain,
    ( spl0_874
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).

fof(f5875,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_64
    | ~ spl0_323 ),
    inference(superposition,[],[f5739,f1151]) ).

fof(f37756,plain,
    ( spl0_873
    | ~ spl0_63
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5870,f5738,f1146,f37754]) ).

fof(f37754,plain,
    ( spl0_873
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f5870,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_63
    | ~ spl0_323 ),
    inference(superposition,[],[f5739,f1147]) ).

fof(f37752,plain,
    ( spl0_872
    | ~ spl0_187
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5838,f5738,f2165,f37750]) ).

fof(f37750,plain,
    ( spl0_872
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f5838,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_187
    | ~ spl0_323 ),
    inference(resolution,[],[f5739,f2166]) ).

fof(f37748,plain,
    ( spl0_871
    | ~ spl0_193
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f5837,f5738,f2189,f37746]) ).

fof(f37746,plain,
    ( spl0_871
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).

fof(f5837,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) )
    | ~ spl0_193
    | ~ spl0_323 ),
    inference(resolution,[],[f5739,f2190]) ).

fof(f37744,plain,
    ( spl0_870
    | ~ spl0_17
    | ~ spl0_321 ),
    inference(avatar_split_clause,[],[f5793,f5730,f941,f37742]) ).

fof(f37742,plain,
    ( spl0_870
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f5730,plain,
    ( spl0_321
  <=> ! [X2,X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f5793,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_17
    | ~ spl0_321 ),
    inference(resolution,[],[f5731,f943]) ).

fof(f5731,plain,
    ( ! [X2,X3,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f5730]) ).

fof(f37740,plain,
    ( spl0_869
    | ~ spl0_130
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f5659,f5555,f1524,f37738]) ).

fof(f37738,plain,
    ( spl0_869
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f5555,plain,
    ( spl0_300
  <=> ! [X4,X3] :
        ( X3 = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f5659,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
    | ~ spl0_130
    | ~ spl0_300 ),
    inference(trivial_inequality_removal,[],[f5650]) ).

fof(f5650,plain,
    ( ! [X0,X1] :
        ( 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(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
    | ~ spl0_130
    | ~ spl0_300 ),
    inference(superposition,[],[f5556,f1525]) ).

fof(f5556,plain,
    ( ! [X3,X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f5555]) ).

fof(f37736,plain,
    ( spl0_868
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_184
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f5485,f4562,f2153,f1265,f1146,f37734]) ).

fof(f37734,plain,
    ( spl0_868
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f5485,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_184
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5484,f1147]) ).

fof(f5484,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_184
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5461,f1266]) ).

fof(f5461,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_184
    | ~ spl0_292 ),
    inference(resolution,[],[f4563,f2154]) ).

fof(f37732,plain,
    ( spl0_867
    | ~ spl0_86
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f5409,f4550,f1265,f37730]) ).

fof(f37730,plain,
    ( spl0_867
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f4550,plain,
    ( spl0_289
  <=> ! [X4,X19] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f5409,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_289 ),
    inference(superposition,[],[f4551,f1266]) ).

fof(f4551,plain,
    ( ! [X19,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f4550]) ).

fof(f37709,plain,
    ( ~ spl0_16
    | spl0_866
    | ~ spl0_39
    | ~ spl0_106
    | ~ spl0_181
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5316,f4538,f3676,f2141,f1346,f1050,f37707,f936]) ).

fof(f37707,plain,
    ( spl0_866
  <=> ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f1050,plain,
    ( spl0_39
  <=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f5316,plain,
    ( ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,c_HOL_Ozero__class_Ozero(tc_nat))
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_39
    | ~ spl0_106
    | ~ spl0_181
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5315,f4165]) ).

fof(f4165,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1051]) ).

fof(f1051,plain,
    ( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f1050]) ).

fof(f5315,plain,
    ( ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X0,c_HOL_Ozero__class_Ozero(tc_nat))
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_106
    | ~ spl0_181
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5293,f1347]) ).

fof(f5293,plain,
    ( ! [X0] :
        ( c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X0,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
    | ~ spl0_181
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f2142]) ).

fof(f37705,plain,
    ( spl0_865
    | ~ spl0_139
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5264,f4534,f1560,f37703]) ).

fof(f37703,plain,
    ( spl0_865
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_Lambda_OdB_OApp(X4,X5) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
        | c_Lambda_Osubst(X0,X1,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f1560,plain,
    ( spl0_139
  <=> ! [X38,X36,X35,X37] :
        ( X35 = X37
        | c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f4534,plain,
    ( spl0_285
  <=> ! [X9,X10,X29,X27] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X9,X29),X27,X10) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X9,X27,X10),c_Lambda_Osubst(X29,X27,X10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f5264,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Lambda_OdB_OApp(X4,X5) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
        | c_Lambda_Osubst(X0,X1,X2) = X4 )
    | ~ spl0_139
    | ~ spl0_285 ),
    inference(superposition,[],[f1561,f4535]) ).

fof(f4535,plain,
    ( ! [X10,X29,X9,X27] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X9,X29),X27,X10) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X9,X27,X10),c_Lambda_Osubst(X29,X27,X10))
    | ~ spl0_285 ),
    inference(avatar_component_clause,[],[f4534]) ).

fof(f1561,plain,
    ( ! [X38,X36,X37,X35] :
        ( c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38)
        | X35 = X37 )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1560]) ).

fof(f37701,plain,
    ( spl0_864
    | ~ spl0_138
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5262,f4534,f1556,f37699]) ).

fof(f37699,plain,
    ( spl0_864
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( c_Lambda_OdB_OApp(X4,X5) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
        | c_Lambda_Osubst(X3,X1,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f1556,plain,
    ( spl0_138
  <=> ! [X38,X36,X37,X35] :
        ( X36 = X38
        | c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f5262,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Lambda_OdB_OApp(X4,X5) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
        | c_Lambda_Osubst(X3,X1,X2) = X5 )
    | ~ spl0_138
    | ~ spl0_285 ),
    inference(superposition,[],[f1557,f4535]) ).

fof(f1557,plain,
    ( ! [X38,X36,X37,X35] :
        ( c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38)
        | X36 = X38 )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1556]) ).

fof(f37697,plain,
    ( spl0_863
    | ~ spl0_139
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f5193,f4526,f1560,f37695]) ).

fof(f37695,plain,
    ( spl0_863
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OApp(X4,X5)
        | c_Lambda_Oliftn(X0,X1,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f4526,plain,
    ( spl0_283
  <=> ! [X4,X10,X9,X27] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X27,X10),c_Lambda_Oliftn(X4,X9,X10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f5193,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OApp(X4,X5)
        | c_Lambda_Oliftn(X0,X1,X2) = X4 )
    | ~ spl0_139
    | ~ spl0_283 ),
    inference(superposition,[],[f1561,f4527]) ).

fof(f4527,plain,
    ( ! [X10,X9,X27,X4] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X27,X10),c_Lambda_Oliftn(X4,X9,X10))
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f4526]) ).

fof(f37693,plain,
    ( spl0_862
    | ~ spl0_138
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f5191,f4526,f1556,f37691]) ).

fof(f37691,plain,
    ( spl0_862
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OApp(X4,X5)
        | c_Lambda_Oliftn(X0,X3,X2) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f5191,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OApp(X4,X5)
        | c_Lambda_Oliftn(X0,X3,X2) = X5 )
    | ~ spl0_138
    | ~ spl0_283 ),
    inference(superposition,[],[f1557,f4527]) ).

fof(f37689,plain,
    ( spl0_861
    | ~ spl0_86
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4648,f4458,f1265,f37687]) ).

fof(f37687,plain,
    ( spl0_861
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f4648,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_266 ),
    inference(superposition,[],[f4459,f1266]) ).

fof(f37685,plain,
    ( spl0_860
    | ~ spl0_222
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4642,f4458,f2818,f37683]) ).

fof(f37683,plain,
    ( spl0_860
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f2818,plain,
    ( spl0_222
  <=> ! [X4,X3,X10] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f4642,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_222
    | ~ spl0_266 ),
    inference(resolution,[],[f4459,f2819]) ).

fof(f2819,plain,
    ( ! [X3,X10,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2818]) ).

fof(f37681,plain,
    ( spl0_859
    | ~ spl0_72
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f4577,f4454,f1194,f37679]) ).

fof(f37679,plain,
    ( spl0_859
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f1194,plain,
    ( spl0_72
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_lessequals(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f4454,plain,
    ( spl0_265
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f4577,plain,
    ( ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_72
    | ~ spl0_265 ),
    inference(resolution,[],[f4455,f1195]) ).

fof(f1195,plain,
    ( ! [X3,X4] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_lessequals(X4,X3,tc_nat) )
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f1194]) ).

fof(f4455,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f4454]) ).

fof(f37677,plain,
    ( spl0_858
    | ~ spl0_77
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4299,f3688,f1214,f37675]) ).

fof(f37675,plain,
    ( spl0_858
  <=> ! [X0,X3,X2,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f1214,plain,
    ( spl0_77
  <=> ! [X9,X27,X10] : c_Lambda_Osubst(c_Lambda_Olift(X9,X10),X27,X10) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f4299,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2),X3,X2)
    | ~ spl0_77
    | ~ spl0_254 ),
    inference(superposition,[],[f1215,f3689]) ).

fof(f1215,plain,
    ( ! [X10,X9,X27] : c_Lambda_Osubst(c_Lambda_Olift(X9,X10),X27,X10) = X9
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1214]) ).

fof(f37636,plain,
    ( spl0_857
    | ~ spl0_95
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4230,f3680,f1301,f37634]) ).

fof(f37634,plain,
    ( spl0_857
  <=> ! [X0] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_List_Olast(c_List_Oupt(c_HOL_Ozero__class_Ozero(tc_nat),X0),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f4230,plain,
    ( ! [X0] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_List_Olast(c_List_Oupt(c_HOL_Ozero__class_Ozero(tc_nat),X0),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_95
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1302]) ).

fof(f37632,plain,
    ( spl0_856
    | ~ spl0_111
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4176,f3676,f1368,f37630]) ).

fof(f37630,plain,
    ( spl0_856
  <=> ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f4176,plain,
    ( ! [X0] :
        ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_111
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1369]) ).

fof(f37628,plain,
    ( spl0_855
    | ~ spl0_130
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4055,f3664,f1524,f37626]) ).

fof(f37626,plain,
    ( spl0_855
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).

fof(f4055,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_130
    | ~ spl0_248 ),
    inference(superposition,[],[f3665,f1525]) ).

fof(f37624,plain,
    ( spl0_854
    | ~ spl0_130
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3972,f3660,f1524,f37622]) ).

fof(f37622,plain,
    ( spl0_854
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f3972,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_130
    | ~ spl0_247 ),
    inference(superposition,[],[f1525,f3661]) ).

fof(f37620,plain,
    ( spl0_853
    | ~ spl0_114
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3971,f3660,f1458,f37618]) ).

fof(f37618,plain,
    ( spl0_853
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f1458,plain,
    ( spl0_114
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f3971,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
    | ~ spl0_114
    | ~ spl0_247 ),
    inference(superposition,[],[f1459,f3661]) ).

fof(f1459,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f1458]) ).

fof(f37616,plain,
    ( spl0_852
    | ~ spl0_114
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3857,f3655,f1458,f37614]) ).

fof(f37614,plain,
    ( spl0_852
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).

fof(f3857,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) )
    | ~ spl0_114
    | ~ spl0_246 ),
    inference(superposition,[],[f1459,f3656]) ).

fof(f37612,plain,
    ( spl0_851
    | ~ spl0_64
    | ~ spl0_183
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3813,f3647,f2149,f1150,f37610]) ).

fof(f37610,plain,
    ( spl0_851
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),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_851])]) ).

fof(f3813,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat))
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_64
    | ~ spl0_183
    | ~ spl0_244 ),
    inference(forward_demodulation,[],[f3803,f1151]) ).

fof(f3803,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat)) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_183
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f2150]) ).

fof(f37608,plain,
    ( spl0_850
    | ~ spl0_111
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3787,f3647,f1368,f37606]) ).

fof(f37606,plain,
    ( spl0_850
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f3787,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Oone__class_Oone(tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_111
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1369]) ).

fof(f37604,plain,
    ( spl0_849
    | ~ spl0_127
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f3580,f2878,f1512,f37602]) ).

fof(f37602,plain,
    ( spl0_849
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f2878,plain,
    ( spl0_237
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f3580,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_127
    | ~ spl0_237 ),
    inference(resolution,[],[f2879,f1513]) ).

fof(f2879,plain,
    ( ! [X3,X0,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_237 ),
    inference(avatar_component_clause,[],[f2878]) ).

fof(f37600,plain,
    ( spl0_848
    | ~ spl0_143
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3570,f2874,f1578,f37598]) ).

fof(f37598,plain,
    ( spl0_848
  <=> ! [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_848])]) ).

fof(f3570,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_143
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1579]) ).

fof(f37588,plain,
    ( spl0_847
    | ~ spl0_142
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3569,f2874,f1572,f37586]) ).

fof(f37586,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f3569,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_142
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1573]) ).

fof(f37584,plain,
    ( spl0_846
    | ~ spl0_141
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3568,f2874,f1568,f37582]) ).

fof(f37582,plain,
    ( spl0_846
  <=> ! [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_846])]) ).

fof(f3568,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_141
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1569]) ).

fof(f37580,plain,
    ( spl0_845
    | ~ spl0_123
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3567,f2874,f1496,f37578]) ).

fof(f37578,plain,
    ( spl0_845
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f3567,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) )
    | ~ spl0_123
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1497]) ).

fof(f37576,plain,
    ( spl0_844
    | ~ spl0_122
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3566,f2874,f1492,f37574]) ).

fof(f37574,plain,
    ( spl0_844
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f3566,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_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X1,X2),X2) )
    | ~ spl0_122
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1493]) ).

fof(f37572,plain,
    ( spl0_843
    | ~ spl0_140
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f3516,f2870,f1564,f37570]) ).

fof(f37570,plain,
    ( spl0_843
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f1564,plain,
    ( spl0_140
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f3516,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
        | ~ class_Ring__and__Field_Oordered__semidom(X2) )
    | ~ spl0_140
    | ~ spl0_235 ),
    inference(resolution,[],[f2871,f1565]) ).

fof(f1565,plain,
    ( ! [X2,X0] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1564]) ).

fof(f37568,plain,
    ( spl0_842
    | ~ spl0_140
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3490,f2866,f1564,f37566]) ).

fof(f37566,plain,
    ( spl0_842
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,X2,X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f3490,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_HOL_Oord__class_Oless(X0,X2,X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_140
    | ~ spl0_234 ),
    inference(resolution,[],[f2867,f1565]) ).

fof(f37564,plain,
    ( spl0_841
    | ~ spl0_131
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f3406,f2846,f1528,f37562]) ).

fof(f37562,plain,
    ( spl0_841
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X3,X0)
        | c_lessequals(X3,X2,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f2846,plain,
    ( spl0_229
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X11,X21,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f3406,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X3,X0)
        | c_lessequals(X3,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_131
    | ~ spl0_229 ),
    inference(resolution,[],[f2847,f1529]) ).

fof(f2847,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X11,X21,X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) )
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f2846]) ).

fof(f37560,plain,
    ( spl0_840
    | ~ spl0_131
    | ~ spl0_228 ),
    inference(avatar_split_clause,[],[f3380,f2842,f1528,f37558]) ).

fof(f37558,plain,
    ( spl0_840
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | c_lessequals(X1,X3,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f2842,plain,
    ( spl0_228
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X1,X11,X0)
        | ~ c_HOL_Oord__class_Oless(X11,X21,X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f3380,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | c_lessequals(X1,X3,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_131
    | ~ spl0_228 ),
    inference(resolution,[],[f2843,f1529]) ).

fof(f2843,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X1,X11,X0)
        | ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X11,X21,X0)
        | c_HOL_Oord__class_Oless(X1,X21,X0) )
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f2842]) ).

fof(f37556,plain,
    ( spl0_839
    | ~ spl0_131
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3354,f2838,f1528,f37554]) ).

fof(f37554,plain,
    ( spl0_839
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(X0,X3,X2)
        | c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f3354,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Opreorder(X2)
        | c_lessequals(X0,X3,X2)
        | c_lessequals(X3,X1,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_131
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f1529]) ).

fof(f37552,plain,
    ( spl0_838
    | ~ spl0_131
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3328,f2834,f1528,f37550]) ).

fof(f37550,plain,
    ( spl0_838
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X3,X0)
        | c_lessequals(X3,X2,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).

fof(f3328,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X1,X3,X0)
        | c_lessequals(X3,X2,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_131
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1529]) ).

fof(f37548,plain,
    ( spl0_837
    | ~ spl0_522
    | ~ spl0_808 ),
    inference(avatar_split_clause,[],[f35555,f28748,f12338,f37546]) ).

fof(f28748,plain,
    ( spl0_808
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f35555,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_522
    | ~ spl0_808 ),
    inference(superposition,[],[f28749,f12339]) ).

fof(f28749,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_808 ),
    inference(avatar_component_clause,[],[f28748]) ).

fof(f37544,plain,
    ( spl0_836
    | ~ spl0_131
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3298,f2830,f1528,f37542]) ).

fof(f37542,plain,
    ( spl0_836
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | c_lessequals(X1,X3,X0)
        | ~ class_Orderings_Olinorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f3298,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(X3,X2,X0)
        | c_lessequals(X1,X3,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_131
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1529]) ).

fof(f37540,plain,
    ( spl0_835
    | ~ spl0_131
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f3272,f2826,f1528,f37538]) ).

fof(f37538,plain,
    ( spl0_835
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(X3,X1,X2)
        | c_lessequals(X0,X3,X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f2826,plain,
    ( spl0_224
  <=> ! [X21,X11,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_lessequals(X11,X1,X0)
        | ~ c_lessequals(X21,X11,X0)
        | c_lessequals(X21,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f3272,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(X0,X1,X2)
        | ~ class_Orderings_Oorder(X2)
        | c_lessequals(X3,X1,X2)
        | c_lessequals(X0,X3,X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_131
    | ~ spl0_224 ),
    inference(resolution,[],[f2827,f1529]) ).

fof(f2827,plain,
    ( ! [X21,X0,X11,X1] :
        ( ~ c_lessequals(X21,X11,X0)
        | ~ c_lessequals(X11,X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X21,X1,X0) )
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f2826]) ).

fof(f37536,plain,
    ( spl0_834
    | ~ spl0_127
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f3112,f2790,f1512,f37534]) ).

fof(f37534,plain,
    ( spl0_834
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f3112,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X1)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_127
    | ~ spl0_215 ),
    inference(resolution,[],[f2791,f1513]) ).

fof(f37532,plain,
    ( spl0_833
    | ~ spl0_128
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2966,f2766,f1516,f37530]) ).

fof(f37530,plain,
    ( spl0_833
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(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_833])]) ).

fof(f2966,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(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_128
    | ~ spl0_209 ),
    inference(resolution,[],[f2767,f1517]) ).

fof(f37528,plain,
    ( spl0_832
    | ~ spl0_129
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f2965,f2766,f1520,f37526]) ).

fof(f37526,plain,
    ( spl0_832
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(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_832])]) ).

fof(f2965,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | ~ class_Orderings_Opreorder(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_129
    | ~ spl0_209 ),
    inference(resolution,[],[f2767,f1521]) ).

fof(f37524,plain,
    ( spl0_831
    | ~ spl0_131
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f2957,f2762,f1528,f37522]) ).

fof(f37522,plain,
    ( spl0_831
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f2762,plain,
    ( spl0_208
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f2957,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X2)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2)
        | ~ class_Orderings_Olinorder(X2) )
    | ~ spl0_131
    | ~ spl0_208 ),
    inference(resolution,[],[f2763,f1529]) ).

fof(f2763,plain,
    ( ! [X3,X0,X4] :
        ( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
        | c_lessequals(X3,X4,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f2762]) ).

fof(f37520,plain,
    ( spl0_830
    | ~ spl0_78
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2746,f2510,f1218,f37518]) ).

fof(f37518,plain,
    ( spl0_830
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),c_Lambda_OdB_OAbs(X2))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f2746,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),c_Lambda_OdB_OAbs(X2))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X2) )
    | ~ spl0_78
    | ~ spl0_204 ),
    inference(superposition,[],[f1219,f2511]) ).

fof(f37516,plain,
    ( spl0_829
    | ~ spl0_78
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2745,f2510,f1218,f37514]) ).

fof(f37514,plain,
    ( spl0_829
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X2),c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1))
        | ~ c_Lambda_Obeta(X2,c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f2745,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X2),c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1))
        | ~ c_Lambda_Obeta(X2,c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_78
    | ~ spl0_204 ),
    inference(superposition,[],[f1219,f2511]) ).

fof(f37512,plain,
    ( spl0_828
    | ~ spl0_76
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2743,f2510,f1210,f37510]) ).

fof(f37510,plain,
    ( spl0_828
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OAbs(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)
        | c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f2743,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OAbs(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)
        | c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2 )
    | ~ spl0_76
    | ~ spl0_204 ),
    inference(superposition,[],[f1211,f2511]) ).

fof(f37508,plain,
    ( spl0_827
    | ~ spl0_163
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2704,f2506,f1785,f37506]) ).

fof(f37506,plain,
    ( spl0_827
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f2704,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0) )
    | ~ spl0_163
    | ~ spl0_203 ),
    inference(resolution,[],[f2507,f1786]) ).

fof(f37504,plain,
    ( spl0_826
    | ~ spl0_618
    | ~ spl0_757 ),
    inference(avatar_split_clause,[],[f30676,f26530,f16549,f37502]) ).

fof(f37502,plain,
    ( spl0_826
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0),X2))
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f26530,plain,
    ( spl0_757
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f30676,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X1),X0),X2))
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 )
    | ~ spl0_618
    | ~ spl0_757 ),
    inference(superposition,[],[f16550,f26531]) ).

fof(f26531,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 )
    | ~ spl0_757 ),
    inference(avatar_component_clause,[],[f26530]) ).

fof(f37500,plain,
    ( spl0_825
    | ~ spl0_136
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2645,f2498,f1548,f37498]) ).

fof(f37498,plain,
    ( spl0_825
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3),c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).

fof(f1548,plain,
    ( spl0_136
  <=> ! [X29,X9,X27] :
        ( ~ c_Lambda_Obeta(X27,X9)
        | c_Lambda_Obeta(c_Lambda_OdB_OApp(X29,X27),c_Lambda_OdB_OApp(X29,X9)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f2498,plain,
    ( spl0_201
  <=> ! [X9,X27,X10] : c_Lambda_Olift(c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Olift(X27,X10),c_Lambda_Olift(X9,X10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f2645,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3),c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X2,X1)) )
    | ~ spl0_136
    | ~ spl0_201 ),
    inference(superposition,[],[f1549,f2499]) ).

fof(f2499,plain,
    ( ! [X10,X9,X27] : c_Lambda_Olift(c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Olift(X27,X10),c_Lambda_Olift(X9,X10))
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f2498]) ).

fof(f1549,plain,
    ( ! [X29,X9,X27] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X29,X27),c_Lambda_OdB_OApp(X29,X9))
        | ~ c_Lambda_Obeta(X27,X9) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1548]) ).

fof(f37496,plain,
    ( spl0_824
    | ~ spl0_136
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2644,f2498,f1548,f37494]) ).

fof(f37494,plain,
    ( spl0_824
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1),c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X2,X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f2644,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1),c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X2,X1),X3) )
    | ~ spl0_136
    | ~ spl0_201 ),
    inference(superposition,[],[f1549,f2499]) ).

fof(f37492,plain,
    ( spl0_823
    | ~ spl0_135
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2643,f2498,f1544,f37490]) ).

fof(f37490,plain,
    ( spl0_823
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1),c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X2,X1)))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).

fof(f1544,plain,
    ( spl0_135
  <=> ! [X29,X9,X27] :
        ( ~ c_Lambda_Obeta(X27,X9)
        | c_Lambda_Obeta(c_Lambda_OdB_OApp(X27,X29),c_Lambda_OdB_OApp(X9,X29)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f2643,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1),c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X2,X1)))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) )
    | ~ spl0_135
    | ~ spl0_201 ),
    inference(superposition,[],[f1545,f2499]) ).

fof(f1545,plain,
    ( ! [X29,X9,X27] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X27,X29),c_Lambda_OdB_OApp(X9,X29))
        | ~ c_Lambda_Obeta(X27,X9) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1544]) ).

fof(f37488,plain,
    ( spl0_822
    | ~ spl0_135
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2642,f2498,f1544,f37486]) ).

fof(f37486,plain,
    ( spl0_822
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X2,X1)),c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f2642,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X2,X1)),c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) )
    | ~ spl0_135
    | ~ spl0_201 ),
    inference(superposition,[],[f1545,f2499]) ).

fof(f37484,plain,
    ( spl0_821
    | ~ spl0_182
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2455,f2193,f2145,f37482]) ).

fof(f37482,plain,
    ( spl0_821
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X1),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f2455,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X1),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_182
    | ~ spl0_194 ),
    inference(resolution,[],[f2194,f2146]) ).

fof(f37480,plain,
    ( spl0_820
    | ~ spl0_185
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2454,f2193,f2157,f37478]) ).

fof(f37478,plain,
    ( spl0_820
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f2454,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X1),X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_185
    | ~ spl0_194 ),
    inference(resolution,[],[f2194,f2158]) ).

fof(f37476,plain,
    ( spl0_819
    | ~ spl0_176
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f2424,f2185,f2120,f37474]) ).

fof(f37474,plain,
    ( spl0_819
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f2424,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) )
    | ~ spl0_176
    | ~ spl0_192 ),
    inference(resolution,[],[f2186,f2121]) ).

fof(f37472,plain,
    ( spl0_818
    | ~ spl0_176
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f2393,f2177,f2120,f37470]) ).

fof(f37470,plain,
    ( spl0_818
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f2393,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) )
    | ~ spl0_176
    | ~ spl0_190 ),
    inference(resolution,[],[f2178,f2121]) ).

fof(f37468,plain,
    ( spl0_817
    | ~ spl0_182
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2352,f2169,f2145,f37466]) ).

fof(f37466,plain,
    ( spl0_817
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f2352,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_182
    | ~ spl0_188 ),
    inference(resolution,[],[f2170,f2146]) ).

fof(f37464,plain,
    ( spl0_816
    | ~ spl0_185
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2351,f2169,f2157,f37462]) ).

fof(f37462,plain,
    ( spl0_816
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f2351,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_185
    | ~ spl0_188 ),
    inference(resolution,[],[f2170,f2158]) ).

fof(f37460,plain,
    ( spl0_815
    | ~ spl0_246
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f17220,f16549,f3655,f37458]) ).

fof(f17220,plain,
    ( ! [X2,X3,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X0),X3))
    | ~ spl0_246
    | ~ spl0_618 ),
    inference(superposition,[],[f16550,f3656]) ).

fof(f37456,plain,
    ( spl0_814
    | ~ spl0_163
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f2295,f2153,f1785,f37454]) ).

fof(f37454,plain,
    ( spl0_814
  <=> ! [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_814])]) ).

fof(f2295,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_163
    | ~ spl0_184 ),
    inference(resolution,[],[f2154,f1786]) ).

fof(f37452,plain,
    ( spl0_813
    | ~ spl0_173
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2240,f2120,f2108,f37450]) ).

fof(f37450,plain,
    ( spl0_813
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X2,X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).

fof(f2240,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X2,X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_173
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f2109]) ).

fof(f37448,plain,
    ( spl0_812
    | ~ spl0_121
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2057,f1797,f1486,f37446]) ).

fof(f37446,plain,
    ( spl0_812
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).

fof(f2057,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_121
    | ~ spl0_166 ),
    inference(resolution,[],[f1798,f1487]) ).

fof(f37444,plain,
    ( spl0_811
    | ~ spl0_121
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1995,f1789,f1486,f37442]) ).

fof(f37442,plain,
    ( spl0_811
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f1995,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_121
    | ~ spl0_164 ),
    inference(resolution,[],[f1790,f1487]) ).

fof(f36569,plain,
    ( spl0_810
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_568
    | ~ spl0_609 ),
    inference(avatar_split_clause,[],[f16595,f16424,f13761,f8722,f1364,f36567]) ).

fof(f36567,plain,
    ( spl0_810
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f13761,plain,
    ( spl0_568
  <=> ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f16424,plain,
    ( spl0_609
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f16595,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_568
    | ~ spl0_609 ),
    inference(forward_demodulation,[],[f16593,f8841]) ).

fof(f16593,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1))
    | ~ spl0_568
    | ~ spl0_609 ),
    inference(superposition,[],[f16425,f13762]) ).

fof(f13762,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f13761]) ).

fof(f16425,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),X1))
    | ~ spl0_609 ),
    inference(avatar_component_clause,[],[f16424]) ).

fof(f31718,plain,
    ( spl0_809
    | ~ spl0_618
    | ~ spl0_758 ),
    inference(avatar_split_clause,[],[f30983,f26534,f16549,f31716]) ).

fof(f31716,plain,
    ( spl0_809
  <=> ! [X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat)),X1))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f30983,plain,
    ( ! [X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oone__class_Oone(tc_nat)),X1))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_618
    | ~ spl0_758 ),
    inference(superposition,[],[f16550,f26535]) ).

fof(f28750,plain,
    ( spl0_808
    | ~ spl0_254
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f19592,f19306,f3688,f28748]) ).

fof(f19306,plain,
    ( spl0_671
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f19592,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_254
    | ~ spl0_671 ),
    inference(superposition,[],[f19307,f3689]) ).

fof(f19307,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_671 ),
    inference(avatar_component_clause,[],[f19306]) ).

fof(f27567,plain,
    ( spl0_807
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_568
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f16198,f16150,f13761,f8722,f1364,f27565]) ).

fof(f27565,plain,
    ( spl0_807
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f16150,plain,
    ( spl0_592
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f16198,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_568
    | ~ spl0_592 ),
    inference(forward_demodulation,[],[f16194,f8841]) ).

fof(f16194,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_568
    | ~ spl0_592 ),
    inference(superposition,[],[f16151,f13762]) ).

fof(f16151,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_592 ),
    inference(avatar_component_clause,[],[f16150]) ).

fof(f26858,plain,
    ( spl0_806
    | ~ spl0_81
    | ~ spl0_422 ),
    inference(avatar_split_clause,[],[f8808,f8722,f1230,f26856]) ).

fof(f8808,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_Olift(X0,X1),X1) = c_Lambda_Olift(c_Lambda_Olift(X0,X1),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_81
    | ~ spl0_422 ),
    inference(resolution,[],[f8723,f1231]) ).

fof(f26854,plain,
    ( spl0_805
    | ~ spl0_63
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8503,f7788,f1146,f26852]) ).

fof(f26852,plain,
    ( spl0_805
  <=> ! [X0] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),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_805])]) ).

fof(f8503,plain,
    ( ! [X0] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_63
    | ~ spl0_411 ),
    inference(forward_demodulation,[],[f8352,f1147]) ).

fof(f8352,plain,
    ( ! [X0] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_63
    | ~ spl0_411 ),
    inference(superposition,[],[f7789,f1147]) ).

fof(f26836,plain,
    ( spl0_804
    | ~ spl0_41
    | ~ spl0_65
    | ~ spl0_251
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6038,f5762,f3676,f1154,f1058,f26834]) ).

fof(f26834,plain,
    ( spl0_804
  <=> ! [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_804])]) ).

fof(f1154,plain,
    ( spl0_65
  <=> ! [X29,X10] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X10),X29,X10) = X29 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f6038,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_41
    | ~ spl0_65
    | ~ spl0_251
    | ~ spl0_329 ),
    inference(forward_demodulation,[],[f6026,f4173]) ).

fof(f6026,plain,
    ( ! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),X1,X0) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_65
    | ~ spl0_329 ),
    inference(superposition,[],[f5763,f1155]) ).

fof(f1155,plain,
    ( ! [X10,X29] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X10),X29,X10) = X29
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f1154]) ).

fof(f26832,plain,
    ( spl0_803
    | ~ spl0_24
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f5715,f5619,f976,f26830]) ).

fof(f26830,plain,
    ( spl0_803
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f976,plain,
    ( spl0_24
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f5619,plain,
    ( spl0_316
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f5715,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_316 ),
    inference(resolution,[],[f5620,f978]) ).

fof(f978,plain,
    ( class_Ring__and__Field_Osemiring__1(tc_nat)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f976]) ).

fof(f5620,plain,
    ( ! [X3,X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f5619]) ).

fof(f26828,plain,
    ( spl0_802
    | ~ spl0_32
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f5678,f5611,f1016,f26826]) ).

fof(f26826,plain,
    ( spl0_802
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f5611,plain,
    ( spl0_314
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f5678,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_314 ),
    inference(resolution,[],[f5612,f1018]) ).

fof(f5612,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0),X5,X0) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f5611]) ).

fof(f26824,plain,
    ( spl0_801
    | ~ spl0_32
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f5677,f5607,f1016,f26822]) ).

fof(f26822,plain,
    ( spl0_801
  <=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).

fof(f5607,plain,
    ( spl0_313
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f5677,plain,
    ( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_313 ),
    inference(resolution,[],[f5608,f1018]) ).

fof(f5608,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0),X5,X0) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f5607]) ).

fof(f26820,plain,
    ( spl0_800
    | ~ spl0_17
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f5676,f5603,f941,f26818]) ).

fof(f26818,plain,
    ( spl0_800
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).

fof(f5603,plain,
    ( spl0_312
  <=> ! [X24,X0,X25,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f5676,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_312 ),
    inference(resolution,[],[f5604,f943]) ).

fof(f5604,plain,
    ( ! [X0,X24,X22,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X25,X0),X0) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f5603]) ).

fof(f26816,plain,
    ( spl0_799
    | ~ spl0_17
    | ~ spl0_18
    | ~ spl0_309
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f5674,f5595,f5591,f946,f941,f26814]) ).

fof(f26814,plain,
    ( spl0_799
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f946,plain,
    ( spl0_18
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f5591,plain,
    ( spl0_309
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f5595,plain,
    ( spl0_310
  <=> ! [X24,X0,X23,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,X0),X24,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),X23,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f5674,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_18
    | ~ spl0_309
    | ~ spl0_310 ),
    inference(forward_demodulation,[],[f5673,f5672]) ).

fof(f5672,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
    | ~ spl0_18
    | ~ spl0_309 ),
    inference(resolution,[],[f5592,f948]) ).

fof(f948,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f946]) ).

fof(f5592,plain,
    ( ! [X2,X0,X6,X5] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) )
    | ~ spl0_309 ),
    inference(avatar_component_clause,[],[f5591]) ).

fof(f5673,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X1,tc_nat)
    | ~ spl0_17
    | ~ spl0_310 ),
    inference(resolution,[],[f5596,f943]) ).

fof(f5596,plain,
    ( ! [X0,X24,X22,X23] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,X0),X24,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),X23,X0) )
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f5595]) ).

fof(f26812,plain,
    ( spl0_798
    | ~ spl0_18
    | ~ spl0_309 ),
    inference(avatar_split_clause,[],[f5672,f5591,f946,f26810]) ).

fof(f26810,plain,
    ( spl0_798
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f26808,plain,
    ( spl0_797
    | ~ spl0_24
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f5671,f5587,f976,f26806]) ).

fof(f26806,plain,
    ( spl0_797
  <=> ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f5587,plain,
    ( spl0_308
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f5671,plain,
    ( ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_308 ),
    inference(resolution,[],[f5588,f978]) ).

fof(f5588,plain,
    ( ! [X3,X0,X4] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) )
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f5587]) ).

fof(f26804,plain,
    ( spl0_796
    | ~ spl0_64
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5645,f5551,f1150,f26802]) ).

fof(f26802,plain,
    ( spl0_796
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_796])]) ).

fof(f5645,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_64
    | ~ spl0_299 ),
    inference(superposition,[],[f5552,f1151]) ).

fof(f26800,plain,
    ( spl0_795
    | ~ spl0_63
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5640,f5551,f1146,f26798]) ).

fof(f26798,plain,
    ( spl0_795
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_795])]) ).

fof(f5640,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_63
    | ~ spl0_299 ),
    inference(superposition,[],[f5552,f1147]) ).

fof(f26784,plain,
    ( spl0_794
    | ~ spl0_64
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f5638,f5551,f1150,f26782]) ).

fof(f26782,plain,
    ( spl0_794
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_794])]) ).

fof(f5638,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) != 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_64
    | ~ spl0_299 ),
    inference(superposition,[],[f5552,f1151]) ).

fof(f26780,plain,
    ( spl0_793
    | ~ spl0_41
    | ~ spl0_106
    | ~ spl0_188
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5310,f4538,f3676,f2169,f1346,f1058,f26778]) ).

fof(f26778,plain,
    ( spl0_793
  <=> ! [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,X2)
        | ~ c_lessequals(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f5310,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,X2)
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_41
    | ~ spl0_106
    | ~ spl0_188
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5309,f1347]) ).

fof(f5309,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_41
    | ~ spl0_188
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5269,f4173]) ).

fof(f5269,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1,X2)
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_188
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f2170]) ).

fof(f26776,plain,
    ( spl0_792
    | ~ spl0_41
    | ~ spl0_106
    | ~ spl0_194
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5308,f4538,f3676,f2193,f1346,f1058,f26774]) ).

fof(f26774,plain,
    ( spl0_792
  <=> ! [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,X2)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f5308,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,X2)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_41
    | ~ spl0_106
    | ~ spl0_194
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5307,f1347]) ).

fof(f5307,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Osubst(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1,X2) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_41
    | ~ spl0_194
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5268,f4173]) ).

fof(f5268,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1,X2)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_194
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f2194]) ).

fof(f26772,plain,
    ( spl0_791
    | ~ spl0_77
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5255,f4534,f1214,f26770]) ).

fof(f26770,plain,
    ( spl0_791
  <=> ! [X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X0,X1)),X2,X1) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X3,X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f5255,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X3,c_Lambda_Olift(X0,X1)),X2,X1) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X3,X2,X1),X0)
    | ~ spl0_77
    | ~ spl0_285 ),
    inference(superposition,[],[f4535,f1215]) ).

fof(f26768,plain,
    ( spl0_790
    | ~ spl0_77
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5253,f4534,f1214,f26766]) ).

fof(f26766,plain,
    ( spl0_790
  <=> ! [X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3),X2,X1) = c_Lambda_OdB_OApp(X0,c_Lambda_Osubst(X3,X2,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f5253,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(X0,X1),X3),X2,X1) = c_Lambda_OdB_OApp(X0,c_Lambda_Osubst(X3,X2,X1))
    | ~ spl0_77
    | ~ spl0_285 ),
    inference(superposition,[],[f4535,f1215]) ).

fof(f26764,plain,
    ( spl0_789
    | ~ spl0_58
    | ~ spl0_247
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4654,f4458,f3660,f1126,f26762]) ).

fof(f26762,plain,
    ( spl0_789
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f4654,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_58
    | ~ spl0_247
    | ~ spl0_266 ),
    inference(forward_demodulation,[],[f4643,f3661]) ).

fof(f4643,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat),X1,tc_nat) )
    | ~ spl0_58
    | ~ spl0_266 ),
    inference(resolution,[],[f4459,f1127]) ).

fof(f26760,plain,
    ( spl0_788
    | ~ spl0_248
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4382,f3704,f3664,f26758]) ).

fof(f26758,plain,
    ( spl0_788
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f4382,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ spl0_248
    | ~ spl0_258 ),
    inference(superposition,[],[f3705,f3665]) ).

fof(f26756,plain,
    ( spl0_787
    | ~ spl0_86
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f4365,f3696,f1265,f26754]) ).

fof(f26754,plain,
    ( spl0_787
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f3696,plain,
    ( spl0_256
  <=> ! [X4,X3] :
        ( X3 = X4
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f4365,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 )
    | ~ spl0_86
    | ~ spl0_256 ),
    inference(superposition,[],[f3697,f1266]) ).

fof(f3697,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | X3 = X4 )
    | ~ spl0_256 ),
    inference(avatar_component_clause,[],[f3696]) ).

fof(f26752,plain,
    ( spl0_786
    | ~ spl0_86
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f4331,f3692,f1265,f26750]) ).

fof(f26750,plain,
    ( spl0_786
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f3692,plain,
    ( spl0_255
  <=> ! [X4,X3] :
        ( X3 = X4
        | ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f4331,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1 )
    | ~ spl0_86
    | ~ spl0_255 ),
    inference(superposition,[],[f3693,f1266]) ).

fof(f3693,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f3692]) ).

fof(f26748,plain,
    ( spl0_785
    | ~ spl0_86
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4291,f3688,f1265,f26746]) ).

fof(f26746,plain,
    ( spl0_785
  <=> ! [X2,X0,X1] : c_Lambda_Olift(c_Lambda_Oliftn(X0,X1,X2),X2) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f4291,plain,
    ( ! [X2,X0,X1] : c_Lambda_Olift(c_Lambda_Oliftn(X0,X1,X2),X2) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,X2)
    | ~ spl0_86
    | ~ spl0_254 ),
    inference(superposition,[],[f3689,f1266]) ).

fof(f26744,plain,
    ( spl0_784
    | ~ spl0_522
    | ~ spl0_732 ),
    inference(avatar_split_clause,[],[f26511,f26414,f12338,f26742]) ).

fof(f26742,plain,
    ( spl0_784
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f26414,plain,
    ( spl0_732
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f26511,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X1),X2))
    | ~ spl0_522
    | ~ spl0_732 ),
    inference(superposition,[],[f26415,f12339]) ).

fof(f26415,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X0),X2))
    | ~ spl0_732 ),
    inference(avatar_component_clause,[],[f26414]) ).

fof(f26740,plain,
    ( spl0_783
    | ~ spl0_106
    | ~ spl0_188
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4245,f3680,f2169,f1346,f26738]) ).

fof(f26738,plain,
    ( spl0_783
  <=> ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X1
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f4245,plain,
    ( ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X1
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_106
    | ~ spl0_188
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4215,f1347]) ).

fof(f4215,plain,
    ( ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_188
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f2170]) ).

fof(f26736,plain,
    ( spl0_782
    | ~ spl0_106
    | ~ spl0_194
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4244,f3680,f2193,f1346,f26734]) ).

fof(f26734,plain,
    ( spl0_782
  <=> ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X1
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f4244,plain,
    ( ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X1
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_106
    | ~ spl0_194
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4214,f1347]) ).

fof(f4214,plain,
    ( ! [X0,X1] :
        ( c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_194
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f2194]) ).

fof(f26635,plain,
    ( spl0_781
    | ~ spl0_568
    | ~ spl0_780 ),
    inference(avatar_split_clause,[],[f26631,f26628,f13761,f26633]) ).

fof(f26633,plain,
    ( spl0_781
  <=> ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f26628,plain,
    ( spl0_780
  <=> ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).

fof(f26631,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_568
    | ~ spl0_780 ),
    inference(forward_demodulation,[],[f26629,f13762]) ).

fof(f26629,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_780 ),
    inference(avatar_component_clause,[],[f26628]) ).

fof(f26630,plain,
    ( spl0_780
    | ~ spl0_70
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4170,f3676,f1186,f26628]) ).

fof(f4170,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_70
    | ~ spl0_251 ),
    inference(resolution,[],[f3677,f1187]) ).

fof(f26626,plain,
    ( spl0_779
    | ~ spl0_86
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4082,f3668,f1265,f26624]) ).

fof(f26624,plain,
    ( spl0_779
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).

fof(f4082,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_249 ),
    inference(superposition,[],[f3669,f1266]) ).

fof(f26622,plain,
    ( spl0_778
    | ~ spl0_106
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4049,f3664,f1346,f26620]) ).

fof(f26620,plain,
    ( spl0_778
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f4049,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X0,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ spl0_106
    | ~ spl0_248 ),
    inference(superposition,[],[f3665,f1347]) ).

fof(f26618,plain,
    ( spl0_777
    | ~ spl0_107
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3970,f3660,f1352,f26616]) ).

fof(f26616,plain,
    ( spl0_777
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f3970,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = X2
    | ~ spl0_107
    | ~ spl0_247 ),
    inference(superposition,[],[f1353,f3661]) ).

fof(f26614,plain,
    ( spl0_776
    | ~ spl0_106
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3969,f3660,f1346,f26612]) ).

fof(f26612,plain,
    ( spl0_776
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f3969,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat)
    | ~ spl0_106
    | ~ spl0_247 ),
    inference(superposition,[],[f1347,f3661]) ).

fof(f26610,plain,
    ( spl0_775
    | ~ spl0_86
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3952,f3660,f1265,f26608]) ).

fof(f26608,plain,
    ( spl0_775
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f3952,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
    | ~ spl0_86
    | ~ spl0_247 ),
    inference(superposition,[],[f3661,f1266]) ).

fof(f26606,plain,
    ( spl0_774
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_641 ),
    inference(avatar_split_clause,[],[f19231,f19129,f12350,f8722,f1230,f26604]) ).

fof(f26604,plain,
    ( spl0_774
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f19129,plain,
    ( spl0_641
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f19231,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X1))
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_641 ),
    inference(forward_demodulation,[],[f19226,f8808]) ).

fof(f19226,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1))
    | ~ spl0_525
    | ~ spl0_641 ),
    inference(superposition,[],[f19130,f12351]) ).

fof(f19130,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X1))
    | ~ spl0_641 ),
    inference(avatar_component_clause,[],[f19129]) ).

fof(f26602,plain,
    ( spl0_773
    | ~ spl0_107
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3856,f3655,f1352,f26600]) ).

fof(f26600,plain,
    ( spl0_773
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).

fof(f3856,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X0,tc_nat)
    | ~ spl0_107
    | ~ spl0_246 ),
    inference(superposition,[],[f1353,f3656]) ).

fof(f26598,plain,
    ( spl0_772
    | ~ spl0_106
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3855,f3655,f1346,f26596]) ).

fof(f26596,plain,
    ( spl0_772
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f3855,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0
    | ~ spl0_106
    | ~ spl0_246 ),
    inference(superposition,[],[f1347,f3656]) ).

fof(f26594,plain,
    ( spl0_771
    | ~ spl0_86
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3837,f3655,f1265,f26592]) ).

fof(f26592,plain,
    ( spl0_771
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).

fof(f3837,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat)
    | ~ spl0_86
    | ~ spl0_246 ),
    inference(superposition,[],[f3656,f1266]) ).

fof(f26590,plain,
    ( spl0_770
    | ~ spl0_86
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3832,f3655,f1265,f26588]) ).

fof(f26588,plain,
    ( spl0_770
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f3832,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_246 ),
    inference(superposition,[],[f3656,f1266]) ).

fof(f26586,plain,
    ( spl0_769
    | ~ spl0_44
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3820,f3651,f1070,f26584]) ).

fof(f26584,plain,
    ( spl0_769
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f3820,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_44
    | ~ spl0_245 ),
    inference(superposition,[],[f1071,f3652]) ).

fof(f26582,plain,
    ( spl0_768
    | ~ spl0_86
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3815,f3651,f1265,f26580]) ).

fof(f26580,plain,
    ( spl0_768
  <=> ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X0) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f3815,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OAbs(X2),X0) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,X2,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)))
    | ~ spl0_86
    | ~ spl0_245 ),
    inference(superposition,[],[f3652,f1266]) ).

fof(f26578,plain,
    ( spl0_767
    | ~ spl0_70
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3781,f3647,f1186,f26576]) ).

fof(f26576,plain,
    ( spl0_767
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).

fof(f3781,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X2) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))
        | c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_70
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1187]) ).

fof(f26574,plain,
    ( spl0_766
    | ~ spl0_130
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f3488,f2862,f1524,f26572]) ).

fof(f26572,plain,
    ( spl0_766
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X0,tc_nat)
        | c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f3488,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X0,tc_nat)
        | c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_130
    | ~ spl0_233 ),
    inference(forward_demodulation,[],[f3481,f287]) ).

fof(f3481,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) )
    | ~ spl0_130
    | ~ spl0_233 ),
    inference(superposition,[],[f2863,f1525]) ).

fof(f26570,plain,
    ( spl0_765
    | ~ spl0_99
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f3420,f2846,f1318,f26568]) ).

fof(f26568,plain,
    ( spl0_765
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).

fof(f3420,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_229 ),
    inference(resolution,[],[f2847,f1319]) ).

fof(f26566,plain,
    ( spl0_764
    | ~ spl0_99
    | ~ spl0_228 ),
    inference(avatar_split_clause,[],[f3394,f2842,f1318,f26564]) ).

fof(f26564,plain,
    ( spl0_764
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).

fof(f3394,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_228 ),
    inference(resolution,[],[f2843,f1319]) ).

fof(f26556,plain,
    ( spl0_763
    | ~ spl0_99
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3368,f2838,f1318,f26554]) ).

fof(f26554,plain,
    ( spl0_763
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f3368,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,c_Nat_Osemiring__1__class_Oof__nat(X2,X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_99
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f1319]) ).

fof(f26552,plain,
    ( spl0_762
    | ~ spl0_99
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3342,f2834,f1318,f26550]) ).

fof(f26550,plain,
    ( spl0_762
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f3342,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1319]) ).

fof(f26548,plain,
    ( spl0_761
    | ~ spl0_99
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3312,f2830,f1318,f26546]) ).

fof(f26546,plain,
    ( spl0_761
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f3312,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_99
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1319]) ).

fof(f26544,plain,
    ( spl0_760
    | ~ spl0_99
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f3286,f2826,f1318,f26542]) ).

fof(f26542,plain,
    ( spl0_760
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X2,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).

fof(f3286,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X1),X2,X1)
        | ~ class_Orderings_Oorder(X1)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_99
    | ~ spl0_224 ),
    inference(resolution,[],[f2827,f1319]) ).

fof(f26540,plain,
    ( spl0_759
    | ~ spl0_130
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3144,f2802,f1524,f26538]) ).

fof(f26538,plain,
    ( spl0_759
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f3144,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_130
    | ~ spl0_218 ),
    inference(superposition,[],[f2803,f1525]) ).

fof(f26536,plain,
    ( spl0_758
    | ~ spl0_111
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2710,f2506,f1368,f26534]) ).

fof(f2710,plain,
    ( ! [X0] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_111
    | ~ spl0_203 ),
    inference(resolution,[],[f2507,f1369]) ).

fof(f26532,plain,
    ( spl0_757
    | ~ spl0_121
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f2705,f2506,f1486,f26530]) ).

fof(f2705,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 )
    | ~ spl0_121
    | ~ spl0_203 ),
    inference(resolution,[],[f2507,f1487]) ).

fof(f26528,plain,
    ( spl0_756
    | ~ spl0_62
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f2614,f2494,f1142,f26526]) ).

fof(f26526,plain,
    ( spl0_756
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f2494,plain,
    ( spl0_200
  <=> ! [X4,X19] :
        ( ~ c_lessequals(X19,X4,tc_nat)
        | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X4,X19,tc_nat),tc_nat) = X19 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f2614,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_62
    | ~ spl0_200 ),
    inference(resolution,[],[f2495,f1143]) ).

fof(f2495,plain,
    ( ! [X19,X4] :
        ( ~ c_lessequals(X19,X4,tc_nat)
        | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X4,X19,tc_nat),tc_nat) = X19 )
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f2494]) ).

fof(f26524,plain,
    ( spl0_755
    | ~ spl0_61
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f2613,f2494,f1138,f26522]) ).

fof(f26522,plain,
    ( spl0_755
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f2613,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_200 ),
    inference(resolution,[],[f2495,f1139]) ).

fof(f26520,plain,
    ( spl0_754
    | ~ spl0_62
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2537,f2479,f1142,f26518]) ).

fof(f2479,plain,
    ( spl0_197
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f2537,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_62
    | ~ spl0_197 ),
    inference(resolution,[],[f2480,f1143]) ).

fof(f2480,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f2479]) ).

fof(f26500,plain,
    ( spl0_753
    | ~ spl0_61
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2536,f2479,f1138,f26498]) ).

fof(f2536,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_61
    | ~ spl0_197 ),
    inference(resolution,[],[f2480,f1139]) ).

fof(f26496,plain,
    ( spl0_752
    | ~ spl0_152
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2469,f2193,f1741,f26494]) ).

fof(f26494,plain,
    ( spl0_752
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f2469,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_152
    | ~ spl0_194 ),
    inference(resolution,[],[f2194,f1742]) ).

fof(f26492,plain,
    ( spl0_751
    | ~ spl0_163
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2456,f2193,f1785,f26490]) ).

fof(f26490,plain,
    ( spl0_751
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X1) = c_Lambda_Olift(c_Lambda_OdB_OVar(X1),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f2456,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),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_163
    | ~ spl0_194 ),
    inference(resolution,[],[f2194,f1786]) ).

fof(f26488,plain,
    ( spl0_750
    | ~ spl0_158
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2446,f2189,f1765,f26486]) ).

fof(f26486,plain,
    ( spl0_750
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f2446,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_193 ),
    inference(resolution,[],[f2190,f1766]) ).

fof(f26484,plain,
    ( spl0_749
    | ~ spl0_161
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2445,f2189,f1777,f26482]) ).

fof(f26482,plain,
    ( spl0_749
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f2445,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) )
    | ~ spl0_161
    | ~ spl0_193 ),
    inference(resolution,[],[f2190,f1778]) ).

fof(f26480,plain,
    ( spl0_748
    | ~ spl0_153
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f2427,f2185,f1745,f26478]) ).

fof(f26478,plain,
    ( spl0_748
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f2427,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) )
    | ~ spl0_153
    | ~ spl0_192 ),
    inference(resolution,[],[f2186,f1746]) ).

fof(f26476,plain,
    ( spl0_747
    | ~ spl0_164
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2414,f2181,f1789,f26474]) ).

fof(f26474,plain,
    ( spl0_747
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).

fof(f2414,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_164
    | ~ spl0_191 ),
    inference(resolution,[],[f2182,f1790]) ).

fof(f26472,plain,
    ( spl0_746
    | ~ spl0_153
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f2396,f2177,f1745,f26470]) ).

fof(f26470,plain,
    ( spl0_746
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).

fof(f2396,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) )
    | ~ spl0_153
    | ~ spl0_190 ),
    inference(resolution,[],[f2178,f1746]) ).

fof(f26468,plain,
    ( spl0_745
    | ~ spl0_164
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2383,f2173,f1789,f26466]) ).

fof(f26466,plain,
    ( spl0_745
  <=> ! [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,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).

fof(f2383,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,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_164
    | ~ spl0_189 ),
    inference(resolution,[],[f2174,f1790]) ).

fof(f26464,plain,
    ( spl0_744
    | ~ spl0_152
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2366,f2169,f1741,f26462]) ).

fof(f26462,plain,
    ( spl0_744
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).

fof(f2366,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_152
    | ~ spl0_188 ),
    inference(resolution,[],[f2170,f1742]) ).

fof(f26460,plain,
    ( spl0_743
    | ~ spl0_568
    | ~ spl0_726 ),
    inference(avatar_split_clause,[],[f26069,f25123,f13761,f26458]) ).

fof(f26458,plain,
    ( spl0_743
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f26069,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),X0),X1))
    | ~ spl0_568
    | ~ spl0_726 ),
    inference(superposition,[],[f25124,f13762]) ).

fof(f26456,plain,
    ( spl0_742
    | ~ spl0_163
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2353,f2169,f1785,f26454]) ).

fof(f26454,plain,
    ( spl0_742
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).

fof(f2353,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )
    | ~ spl0_163
    | ~ spl0_188 ),
    inference(resolution,[],[f2170,f1786]) ).

fof(f26452,plain,
    ( spl0_741
    | ~ spl0_158
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2345,f2165,f1765,f26450]) ).

fof(f26450,plain,
    ( spl0_741
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).

fof(f2345,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) )
    | ~ spl0_158
    | ~ spl0_187 ),
    inference(resolution,[],[f2166,f1766]) ).

fof(f26448,plain,
    ( spl0_740
    | ~ spl0_161
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2344,f2165,f1777,f26446]) ).

fof(f26446,plain,
    ( spl0_740
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f2344,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) )
    | ~ spl0_161
    | ~ spl0_187 ),
    inference(resolution,[],[f2166,f1778]) ).

fof(f26444,plain,
    ( spl0_739
    | ~ spl0_169
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2314,f2157,f1809,f26442]) ).

fof(f26442,plain,
    ( spl0_739
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f2314,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_169
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1810]) ).

fof(f26440,plain,
    ( spl0_738
    | ~ spl0_168
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2313,f2157,f1805,f26438]) ).

fof(f26438,plain,
    ( spl0_738
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f2313,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat))
    | ~ spl0_168
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1806]) ).

fof(f26436,plain,
    ( spl0_737
    | ~ spl0_150
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2312,f2157,f1733,f26434]) ).

fof(f26434,plain,
    ( spl0_737
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f2312,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_150
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1734]) ).

fof(f26432,plain,
    ( spl0_736
    | ~ spl0_151
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2311,f2157,f1737,f26430]) ).

fof(f26430,plain,
    ( spl0_736
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f2311,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_151
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1738]) ).

fof(f26428,plain,
    ( spl0_735
    | ~ spl0_165
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2272,f2145,f1793,f26426]) ).

fof(f26426,plain,
    ( spl0_735
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X2)
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).

fof(f2272,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X2)
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | X0 = X2 )
    | ~ spl0_165
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1794]) ).

fof(f26424,plain,
    ( spl0_734
    | ~ spl0_169
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2271,f2145,f1809,f26422]) ).

fof(f26422,plain,
    ( spl0_734
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f2271,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat))
    | ~ spl0_169
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1810]) ).

fof(f26420,plain,
    ( spl0_733
    | ~ spl0_168
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2270,f2145,f1805,f26418]) ).

fof(f26418,plain,
    ( spl0_733
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f2270,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat))
    | ~ spl0_168
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1806]) ).

fof(f26416,plain,
    ( spl0_732
    | ~ spl0_86
    | ~ spl0_726 ),
    inference(avatar_split_clause,[],[f26059,f25123,f1265,f26414]) ).

fof(f26059,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X0),X2))
    | ~ spl0_86
    | ~ spl0_726 ),
    inference(superposition,[],[f25124,f1266]) ).

fof(f26412,plain,
    ( spl0_731
    | ~ spl0_150
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2269,f2145,f1733,f26410]) ).

fof(f26410,plain,
    ( spl0_731
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f2269,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_150
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1734]) ).

fof(f26408,plain,
    ( spl0_730
    | ~ spl0_151
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2268,f2145,f1737,f26406]) ).

fof(f26406,plain,
    ( spl0_730
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f2268,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_151
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1738]) ).

fof(f26404,plain,
    ( spl0_729
    | ~ spl0_158
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2244,f2120,f1765,f26402]) ).

fof(f26402,plain,
    ( spl0_729
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X3,X2,tc_nat)
        | ~ c_lessequals(X3,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f2244,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X3,X2,tc_nat)
        | ~ c_lessequals(X3,X1,tc_nat) )
    | ~ spl0_158
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f1766]) ).

fof(f26400,plain,
    ( spl0_728
    | ~ spl0_161
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2243,f2120,f1777,f26398]) ).

fof(f26398,plain,
    ( spl0_728
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X3,X2,tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).

fof(f2243,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X3,X2,tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat) )
    | ~ spl0_161
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f1778]) ).

fof(f26396,plain,
    ( spl0_727
    | ~ spl0_153
    | ~ spl0_173 ),
    inference(avatar_split_clause,[],[f2200,f2108,f1745,f26394]) ).

fof(f26394,plain,
    ( spl0_727
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X0,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).

fof(f2200,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X0,tc_nat),X0,tc_nat) )
    | ~ spl0_153
    | ~ spl0_173 ),
    inference(resolution,[],[f2109,f1746]) ).

fof(f25125,plain,
    ( spl0_726
    | ~ spl0_522
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f21649,f20382,f12338,f25123]) ).

fof(f20382,plain,
    ( spl0_723
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f21649,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X1),X2))
    | ~ spl0_522
    | ~ spl0_723 ),
    inference(superposition,[],[f20383,f12339]) ).

fof(f20383,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X2))
    | ~ spl0_723 ),
    inference(avatar_component_clause,[],[f20382]) ).

fof(f22716,plain,
    ( spl0_725
    | ~ spl0_461
    | ~ spl0_723 ),
    inference(avatar_split_clause,[],[f21654,f20382,f10383,f22714]) ).

fof(f22714,plain,
    ( spl0_725
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).

fof(f21654,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X0),X1))
    | ~ spl0_461
    | ~ spl0_723 ),
    inference(superposition,[],[f20383,f10384]) ).

fof(f21165,plain,
    ( spl0_724
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f16199,f16150,f12350,f8722,f1230,f21163]) ).

fof(f21163,plain,
    ( spl0_724
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f16199,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_592 ),
    inference(forward_demodulation,[],[f16195,f8808]) ).

fof(f16195,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_525
    | ~ spl0_592 ),
    inference(superposition,[],[f16151,f12351]) ).

fof(f20384,plain,
    ( spl0_723
    | ~ spl0_254
    | ~ spl0_578 ),
    inference(avatar_split_clause,[],[f15301,f14665,f3688,f20382]) ).

fof(f14665,plain,
    ( spl0_578
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f15301,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X1),X2))
    | ~ spl0_254
    | ~ spl0_578 ),
    inference(superposition,[],[f14666,f3689]) ).

fof(f14666,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X2))
    | ~ spl0_578 ),
    inference(avatar_component_clause,[],[f14665]) ).

fof(f19857,plain,
    ( spl0_722
    | ~ spl0_38
    | ~ spl0_86
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f5822,f5734,f1265,f1046,f19855]) ).

fof(f19855,plain,
    ( spl0_722
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f1046,plain,
    ( spl0_38
  <=> ! [X4] : c_lessequals(X4,X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f5822,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_38
    | ~ spl0_86
    | ~ spl0_322 ),
    inference(forward_demodulation,[],[f5797,f1266]) ).

fof(f5797,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X0,tc_nat),X1,tc_nat) )
    | ~ spl0_38
    | ~ spl0_322 ),
    inference(resolution,[],[f5735,f1047]) ).

fof(f1047,plain,
    ( ! [X4] : c_lessequals(X4,X4,tc_nat)
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f1046]) ).

fof(f19808,plain,
    ( spl0_721
    | ~ spl0_25
    | ~ spl0_37
    | ~ spl0_291 ),
    inference(avatar_split_clause,[],[f5432,f4558,f1041,f981,f19806]) ).

fof(f19806,plain,
    ( spl0_721
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f981,plain,
    ( spl0_25
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f4558,plain,
    ( spl0_291
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Osemiring__0(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f5432,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__0(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) )
    | ~ spl0_37
    | ~ spl0_291 ),
    inference(resolution,[],[f4559,f1043]) ).

fof(f4559,plain,
    ( ! [X0,X4] :
        ( ~ class_Power_Opower(X0)
        | ~ class_Ring__and__Field_Osemiring__0(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) )
    | ~ spl0_291 ),
    inference(avatar_component_clause,[],[f4558]) ).

fof(f19804,plain,
    ( spl0_720
    | ~ spl0_41
    | ~ spl0_106
    | ~ spl0_166
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5321,f4538,f3676,f1797,f1346,f1058,f19802]) ).

fof(f19802,plain,
    ( spl0_720
  <=> ! [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_720])]) ).

fof(f5321,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_41
    | ~ spl0_106
    | ~ spl0_166
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5320,f1347]) ).

fof(f5320,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = 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_41
    | ~ spl0_166
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5300,f4173]) ).

fof(f5300,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat))
    | ~ spl0_166
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f1798]) ).

fof(f19796,plain,
    ( spl0_719
    | ~ spl0_65
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5254,f4534,f1154,f19794]) ).

fof(f19794,plain,
    ( spl0_719
  <=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X0)),X1,X0) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X1,X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f5254,plain,
    ( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X0)),X1,X0) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X1,X0),X1)
    | ~ spl0_65
    | ~ spl0_285 ),
    inference(superposition,[],[f4535,f1155]) ).

fof(f19792,plain,
    ( spl0_718
    | ~ spl0_65
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5252,f4534,f1154,f19790]) ).

fof(f19790,plain,
    ( spl0_718
  <=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X2),X1,X0) = c_Lambda_OdB_OApp(X1,c_Lambda_Osubst(X2,X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).

fof(f5252,plain,
    ( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X2),X1,X0) = c_Lambda_OdB_OApp(X1,c_Lambda_Osubst(X2,X1,X0))
    | ~ spl0_65
    | ~ spl0_285 ),
    inference(superposition,[],[f4535,f1155]) ).

fof(f19747,plain,
    ( spl0_717
    | ~ spl0_25
    | ~ spl0_37
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f4921,f4490,f1041,f981,f19745]) ).

fof(f19745,plain,
    ( spl0_717
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f4490,plain,
    ( spl0_274
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Osemiring__0(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f4921,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__0(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_37
    | ~ spl0_274 ),
    inference(resolution,[],[f4491,f1043]) ).

fof(f4491,plain,
    ( ! [X0,X4] :
        ( ~ class_Power_Opower(X0)
        | ~ class_Ring__and__Field_Osemiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X4,X0) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f4490]) ).

fof(f19743,plain,
    ( spl0_716
    | ~ spl0_64
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4652,f4458,f1150,f19741]) ).

fof(f19741,plain,
    ( spl0_716
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f4652,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_64
    | ~ spl0_266 ),
    inference(superposition,[],[f4459,f1151]) ).

fof(f19739,plain,
    ( spl0_715
    | ~ spl0_17
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f4569,f4450,f941,f19737]) ).

fof(f19737,plain,
    ( spl0_715
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f4450,plain,
    ( spl0_264
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X3,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f4569,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
    | ~ spl0_17
    | ~ spl0_264 ),
    inference(resolution,[],[f4451,f943]) ).

fof(f4451,plain,
    ( ! [X3,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X3,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X3,X0) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f4450]) ).

fof(f19735,plain,
    ( spl0_714
    | ~ spl0_51
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4300,f3688,f1098,f19733]) ).

fof(f19733,plain,
    ( spl0_714
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).

fof(f1098,plain,
    ( spl0_51
  <=> ! [X9,X19] :
        ( ~ c_InductTermi_OIT(X9)
        | c_InductTermi_OIT(c_Lambda_Olift(X9,X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f4300,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) )
    | ~ spl0_51
    | ~ spl0_254 ),
    inference(superposition,[],[f1099,f3689]) ).

fof(f1099,plain,
    ( ! [X19,X9] :
        ( c_InductTermi_OIT(c_Lambda_Olift(X9,X19))
        | ~ c_InductTermi_OIT(X9) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f19731,plain,
    ( spl0_713
    | ~ spl0_106
    | ~ spl0_166
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4253,f3680,f1797,f1346,f19729]) ).

fof(f19729,plain,
    ( spl0_713
  <=> ! [X0,X1] : c_List_Olast(c_List_Oupt(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).

fof(f4253,plain,
    ( ! [X0,X1] : c_List_Olast(c_List_Oupt(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0
    | ~ spl0_106
    | ~ spl0_166
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4239,f1347]) ).

fof(f4239,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_List_Olast(c_List_Oupt(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat)
    | ~ spl0_166
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1798]) ).

fof(f19727,plain,
    ( spl0_712
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4162,f3672,f1797,f1265,f19725]) ).

fof(f19725,plain,
    ( spl0_712
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f4162,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_250 ),
    inference(forward_demodulation,[],[f4145,f1266]) ).

fof(f4145,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_166
    | ~ spl0_250 ),
    inference(superposition,[],[f1798,f3673]) ).

fof(f19723,plain,
    ( spl0_711
    | ~ spl0_164
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4144,f3672,f1789,f19721]) ).

fof(f19721,plain,
    ( spl0_711
  <=> ! [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(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f4144,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(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_250 ),
    inference(superposition,[],[f1790,f3673]) ).

fof(f19719,plain,
    ( spl0_710
    | ~ spl0_568
    | ~ spl0_629 ),
    inference(avatar_split_clause,[],[f18477,f17744,f13761,f19717]) ).

fof(f19717,plain,
    ( spl0_710
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f18477,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1))
    | ~ spl0_568
    | ~ spl0_629 ),
    inference(superposition,[],[f17745,f13762]) ).

fof(f19715,plain,
    ( spl0_709
    | ~ spl0_233
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4140,f3672,f2862,f19713]) ).

fof(f19713,plain,
    ( spl0_709
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).

fof(f4140,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X0,tc_nat) )
    | ~ spl0_233
    | ~ spl0_250 ),
    inference(superposition,[],[f2863,f3673]) ).

fof(f19711,plain,
    ( spl0_708
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4118,f3668,f1797,f1265,f19709]) ).

fof(f19709,plain,
    ( spl0_708
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f4118,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_166
    | ~ spl0_249 ),
    inference(forward_demodulation,[],[f4105,f1266]) ).

fof(f4105,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_166
    | ~ spl0_249 ),
    inference(superposition,[],[f1798,f3669]) ).

fof(f19707,plain,
    ( spl0_707
    | ~ spl0_164
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4104,f3668,f1789,f19705]) ).

fof(f19705,plain,
    ( spl0_707
  <=> ! [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(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f4104,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(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
    | ~ spl0_164
    | ~ spl0_249 ),
    inference(superposition,[],[f1790,f3669]) ).

fof(f19703,plain,
    ( spl0_706
    | ~ spl0_81
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4011,f3660,f1230,f19701]) ).

fof(f19701,plain,
    ( spl0_706
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f4011,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_81
    | ~ spl0_247 ),
    inference(superposition,[],[f1231,f3661]) ).

fof(f19699,plain,
    ( spl0_705
    | ~ spl0_80
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4010,f3660,f1226,f19697]) ).

fof(f19697,plain,
    ( spl0_705
  <=> ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f4010,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_80
    | ~ spl0_247 ),
    inference(superposition,[],[f1227,f3661]) ).

fof(f19695,plain,
    ( spl0_704
    | ~ spl0_169
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3983,f3660,f1809,f19693]) ).

fof(f19693,plain,
    ( spl0_704
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).

fof(f3983,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_169
    | ~ spl0_247 ),
    inference(superposition,[],[f1810,f3661]) ).

fof(f19691,plain,
    ( spl0_703
    | ~ spl0_159
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3979,f3660,f1769,f19689]) ).

fof(f19689,plain,
    ( spl0_703
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(X2,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).

fof(f3979,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(X2,X3,tc_nat) )
    | ~ spl0_159
    | ~ spl0_247 ),
    inference(superposition,[],[f1770,f3661]) ).

fof(f19687,plain,
    ( spl0_702
    | ~ spl0_158
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3978,f3660,f1765,f19685]) ).

fof(f19685,plain,
    ( spl0_702
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).

fof(f3978,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_247 ),
    inference(superposition,[],[f1766,f3661]) ).

fof(f19683,plain,
    ( spl0_701
    | ~ spl0_150
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3975,f3660,f1733,f19681]) ).

fof(f19681,plain,
    ( spl0_701
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f3975,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
    | ~ spl0_150
    | ~ spl0_247 ),
    inference(superposition,[],[f1734,f3661]) ).

fof(f19679,plain,
    ( spl0_700
    | ~ spl0_147
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3974,f3660,f1721,f19677]) ).

fof(f19677,plain,
    ( spl0_700
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).

fof(f3974,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
    | ~ spl0_147
    | ~ spl0_247 ),
    inference(superposition,[],[f1722,f3661]) ).

fof(f19671,plain,
    ( spl0_699
    | ~ spl0_161
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3867,f3655,f1777,f19669]) ).

fof(f19669,plain,
    ( spl0_699
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f3867,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X3,X0,tc_nat) )
    | ~ spl0_161
    | ~ spl0_246 ),
    inference(superposition,[],[f1778,f3656]) ).

fof(f19667,plain,
    ( spl0_698
    | ~ spl0_160
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3866,f3655,f1773,f19665]) ).

fof(f19665,plain,
    ( spl0_698
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f3866,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_lessequals(X0,X3,tc_nat) )
    | ~ spl0_160
    | ~ spl0_246 ),
    inference(superposition,[],[f1774,f3656]) ).

fof(f19663,plain,
    ( spl0_697
    | ~ spl0_152
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3863,f3655,f1741,f19661]) ).

fof(f19661,plain,
    ( spl0_697
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f3863,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
    | ~ spl0_152
    | ~ spl0_246 ),
    inference(superposition,[],[f1742,f3656]) ).

fof(f19659,plain,
    ( spl0_696
    | ~ spl0_151
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3862,f3655,f1737,f19657]) ).

fof(f19657,plain,
    ( spl0_696
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f3862,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat) )
    | ~ spl0_151
    | ~ spl0_246 ),
    inference(superposition,[],[f1738,f3656]) ).

fof(f19655,plain,
    ( spl0_695
    | ~ spl0_146
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3859,f3655,f1717,f19653]) ).

fof(f19653,plain,
    ( spl0_695
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f3859,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_146
    | ~ spl0_246 ),
    inference(superposition,[],[f1718,f3656]) ).

fof(f19650,plain,
    ( spl0_694
    | ~ spl0_81
    | ~ spl0_86
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3630,f2886,f1265,f1230,f19648]) ).

fof(f19648,plain,
    ( spl0_694
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f3630,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_81
    | ~ spl0_86
    | ~ spl0_239 ),
    inference(forward_demodulation,[],[f3611,f1266]) ).

fof(f3611,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_81
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f1231]) ).

fof(f19646,plain,
    ( spl0_693
    | ~ spl0_86
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3626,f2886,f1265,f19644]) ).

fof(f19644,plain,
    ( spl0_693
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),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_693])]) ).

fof(f3626,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_86
    | ~ spl0_239 ),
    inference(superposition,[],[f2887,f1266]) ).

fof(f19642,plain,
    ( spl0_692
    | ~ spl0_223
    | ~ spl0_239 ),
    inference(avatar_split_clause,[],[f3610,f2886,f2822,f19640]) ).

fof(f19640,plain,
    ( spl0_692
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f2822,plain,
    ( spl0_223
  <=> ! [X4,X3,X10] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f3610,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_223
    | ~ spl0_239 ),
    inference(resolution,[],[f2887,f2823]) ).

fof(f2823,plain,
    ( ! [X3,X10,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2822]) ).

fof(f19601,plain,
    ( ~ spl0_16
    | spl0_691
    | ~ spl0_70
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f3562,f2874,f1186,f19599,f936]) ).

fof(f19599,plain,
    ( spl0_691
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f3562,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_236 ),
    inference(resolution,[],[f2875,f1187]) ).

fof(f19586,plain,
    ( spl0_690
    | ~ spl0_67
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f3419,f2846,f1173,f19584]) ).

fof(f19584,plain,
    ( spl0_690
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f1173,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f3419,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67
    | ~ spl0_229 ),
    inference(resolution,[],[f2847,f1174]) ).

fof(f1174,plain,
    ( ! [X0] :
        ( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1173]) ).

fof(f19582,plain,
    ( spl0_689
    | ~ spl0_67
    | ~ spl0_228 ),
    inference(avatar_split_clause,[],[f3393,f2842,f1173,f19580]) ).

fof(f19580,plain,
    ( spl0_689
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,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_689])]) ).

fof(f3393,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67
    | ~ spl0_228 ),
    inference(resolution,[],[f2843,f1174]) ).

fof(f19578,plain,
    ( spl0_688
    | ~ spl0_67
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3367,f2838,f1173,f19576]) ).

fof(f19576,plain,
    ( spl0_688
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f3367,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
        | ~ class_Orderings_Opreorder(X1)
        | c_lessequals(X0,c_HOL_Oone__class_Oone(X1),X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_67
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f1174]) ).

fof(f19574,plain,
    ( spl0_687
    | ~ spl0_67
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3341,f2834,f1173,f19572]) ).

fof(f19572,plain,
    ( spl0_687
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f3341,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1174]) ).

fof(f19469,plain,
    ( spl0_686
    | ~ spl0_36
    | ~ spl0_72
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3326,f2834,f1194,f1036,f19467]) ).

fof(f19467,plain,
    ( spl0_686
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f3326,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_72
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1195]) ).

fof(f19465,plain,
    ( spl0_685
    | ~ spl0_67
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3311,f2830,f1173,f19463]) ).

fof(f19463,plain,
    ( spl0_685
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,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_685])]) ).

fof(f3311,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1174]) ).

fof(f19360,plain,
    ( spl0_684
    | ~ spl0_36
    | ~ spl0_72
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3296,f2830,f1194,f1036,f19358]) ).

fof(f19358,plain,
    ( spl0_684
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f3296,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_72
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1195]) ).

fof(f19356,plain,
    ( spl0_683
    | ~ spl0_67
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f3285,f2826,f1173,f19354]) ).

fof(f19354,plain,
    ( spl0_683
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f3285,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_67
    | ~ spl0_224 ),
    inference(resolution,[],[f2827,f1174]) ).

fof(f19352,plain,
    ( spl0_682
    | ~ spl0_568
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f16107,f15848,f13761,f19350]) ).

fof(f19350,plain,
    ( spl0_682
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f16107,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_568
    | ~ spl0_579 ),
    inference(superposition,[],[f15849,f13762]) ).

fof(f19348,plain,
    ( spl0_681
    | ~ spl0_70
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f3245,f2822,f1186,f19346]) ).

fof(f19346,plain,
    ( spl0_681
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f3245,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_223 ),
    inference(resolution,[],[f2823,f1187]) ).

fof(f19344,plain,
    ( spl0_680
    | ~ spl0_86
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f3228,f2818,f1265,f19342]) ).

fof(f19342,plain,
    ( spl0_680
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).

fof(f3228,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_222 ),
    inference(superposition,[],[f2819,f1266]) ).

fof(f19340,plain,
    ( spl0_679
    | ~ spl0_86
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f3224,f2818,f1265,f19338]) ).

fof(f19338,plain,
    ( spl0_679
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).

fof(f3224,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_222 ),
    inference(superposition,[],[f2819,f1266]) ).

fof(f19336,plain,
    ( spl0_678
    | ~ spl0_86
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f3206,f2814,f1265,f19334]) ).

fof(f19334,plain,
    ( spl0_678
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f2814,plain,
    ( spl0_221
  <=> ! [X18,X19,X10] :
        ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f3206,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_221 ),
    inference(superposition,[],[f2815,f1266]) ).

fof(f2815,plain,
    ( ! [X10,X18,X19] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat) )
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f2814]) ).

fof(f19332,plain,
    ( spl0_677
    | ~ spl0_86
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f3202,f2814,f1265,f19330]) ).

fof(f19330,plain,
    ( spl0_677
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f3202,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_221 ),
    inference(superposition,[],[f2815,f1266]) ).

fof(f19328,plain,
    ( spl0_676
    | ~ spl0_70
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f3192,f2814,f1186,f19326]) ).

fof(f19326,plain,
    ( spl0_676
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f3192,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_221 ),
    inference(resolution,[],[f2815,f1187]) ).

fof(f19324,plain,
    ( spl0_675
    | ~ spl0_86
    | ~ spl0_205
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f3177,f2810,f2750,f1265,f19322]) ).

fof(f19322,plain,
    ( spl0_675
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f3177,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_205
    | ~ spl0_220 ),
    inference(forward_demodulation,[],[f3152,f1266]) ).

fof(f3152,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat),tc_nat) )
    | ~ spl0_205
    | ~ spl0_220 ),
    inference(resolution,[],[f2811,f2751]) ).

fof(f19320,plain,
    ( spl0_674
    | ~ spl0_107
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f3170,f2810,f1352,f19318]) ).

fof(f19318,plain,
    ( spl0_674
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f3170,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_107
    | ~ spl0_220 ),
    inference(superposition,[],[f2811,f1353]) ).

fof(f19316,plain,
    ( spl0_673
    | ~ spl0_106
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f3169,f2810,f1346,f19314]) ).

fof(f19314,plain,
    ( spl0_673
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f3169,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) )
    | ~ spl0_106
    | ~ spl0_220 ),
    inference(superposition,[],[f2811,f1347]) ).

fof(f19312,plain,
    ( spl0_672
    | ~ spl0_107
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3147,f2802,f1352,f19310]) ).

fof(f19310,plain,
    ( spl0_672
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f3147,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_107
    | ~ spl0_218 ),
    inference(superposition,[],[f2803,f1353]) ).

fof(f19308,plain,
    ( spl0_671
    | ~ spl0_522
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f16106,f15848,f12338,f19306]) ).

fof(f16106,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X2))
    | ~ spl0_522
    | ~ spl0_579 ),
    inference(superposition,[],[f15849,f12339]) ).

fof(f19304,plain,
    ( spl0_670
    | ~ spl0_106
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3140,f2802,f1346,f19302]) ).

fof(f19302,plain,
    ( spl0_670
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
        | ~ c_lessequals(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f3140,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
        | ~ c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_106
    | ~ spl0_218 ),
    inference(superposition,[],[f2803,f1347]) ).

fof(f19300,plain,
    ( spl0_669
    | ~ spl0_205
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3123,f2802,f2750,f19298]) ).

fof(f19298,plain,
    ( spl0_669
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f3123,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat),tc_nat) )
    | ~ spl0_205
    | ~ spl0_218 ),
    inference(resolution,[],[f2803,f2751]) ).

fof(f19296,plain,
    ( spl0_668
    | ~ spl0_206
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f3062,f2782,f2754,f19294]) ).

fof(f19294,plain,
    ( spl0_668
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f3062,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat),X2,tc_nat) )
    | ~ spl0_206
    | ~ spl0_213 ),
    inference(resolution,[],[f2783,f2755]) ).

fof(f19292,plain,
    ( spl0_667
    | ~ spl0_86
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3053,f2778,f1265,f19290]) ).

fof(f19290,plain,
    ( spl0_667
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_lessequals(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f2778,plain,
    ( spl0_212
  <=> ! [X4,X3,X10] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f3053,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_lessequals(X2,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_212 ),
    inference(superposition,[],[f2779,f1266]) ).

fof(f2779,plain,
    ( ! [X3,X10,X4] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat)
        | c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_212 ),
    inference(avatar_component_clause,[],[f2778]) ).

fof(f19288,plain,
    ( spl0_666
    | ~ spl0_86
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3049,f2778,f1265,f19286]) ).

fof(f19286,plain,
    ( spl0_666
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_lessequals(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f3049,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
        | c_lessequals(X1,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_212 ),
    inference(superposition,[],[f2779,f1266]) ).

fof(f19284,plain,
    ( spl0_665
    | ~ spl0_72
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3044,f2778,f1194,f19282]) ).

fof(f19282,plain,
    ( spl0_665
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f3044,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) )
    | ~ spl0_72
    | ~ spl0_212 ),
    inference(resolution,[],[f2779,f1195]) ).

fof(f19280,plain,
    ( spl0_664
    | ~ spl0_86
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f3025,f2774,f1265,f19278]) ).

fof(f19278,plain,
    ( spl0_664
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f3025,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | ~ c_lessequals(X2,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_211 ),
    inference(superposition,[],[f2775,f1266]) ).

fof(f19239,plain,
    ( ~ spl0_16
    | spl0_663
    | ~ spl0_72
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f2955,f2762,f1194,f19237,f936]) ).

fof(f19237,plain,
    ( spl0_663
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f2955,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
        | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),tc_nat) )
    | ~ spl0_72
    | ~ spl0_208 ),
    inference(resolution,[],[f2763,f1195]) ).

fof(f19235,plain,
    ( spl0_662
    | ~ spl0_86
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2939,f2754,f1265,f19233]) ).

fof(f19233,plain,
    ( spl0_662
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f2939,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_206 ),
    inference(superposition,[],[f2755,f1266]) ).

fof(f19223,plain,
    ( spl0_661
    | ~ spl0_72
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2931,f2754,f1194,f19221]) ).

fof(f19221,plain,
    ( spl0_661
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f2931,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_72
    | ~ spl0_206 ),
    inference(resolution,[],[f2755,f1195]) ).

fof(f19219,plain,
    ( spl0_660
    | ~ spl0_107
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2911,f2750,f1352,f19217]) ).

fof(f19217,plain,
    ( spl0_660
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f2911,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X1,X2,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) )
    | ~ spl0_107
    | ~ spl0_205 ),
    inference(superposition,[],[f2751,f1353]) ).

fof(f19215,plain,
    ( spl0_659
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2898,f2750,f1194,f19213]) ).

fof(f19213,plain,
    ( spl0_659
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_lessequals(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f2898,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | c_lessequals(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_72
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1195]) ).

fof(f19211,plain,
    ( spl0_658
    | ~ spl0_139
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2648,f2498,f1560,f19209]) ).

fof(f19209,plain,
    ( spl0_658
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
        | c_Lambda_Olift(X0,X1) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f2648,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
        | c_Lambda_Olift(X0,X1) = X3 )
    | ~ spl0_139
    | ~ spl0_201 ),
    inference(superposition,[],[f1561,f2499]) ).

fof(f19207,plain,
    ( spl0_657
    | ~ spl0_138
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2646,f2498,f1556,f19205]) ).

fof(f19205,plain,
    ( spl0_657
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
        | c_Lambda_Olift(X2,X1) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f2646,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
        | c_Lambda_Olift(X2,X1) = X4 )
    | ~ spl0_138
    | ~ spl0_201 ),
    inference(superposition,[],[f1557,f2499]) ).

fof(f19203,plain,
    ( spl0_656
    | ~ spl0_121
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2457,f2193,f1486,f19201]) ).

fof(f19201,plain,
    ( spl0_656
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f2457,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X1 )
    | ~ spl0_121
    | ~ spl0_194 ),
    inference(resolution,[],[f2194,f1487]) ).

fof(f19199,plain,
    ( spl0_655
    | ~ spl0_121
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2354,f2169,f1486,f19197]) ).

fof(f19197,plain,
    ( spl0_655
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f2354,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_188 ),
    inference(resolution,[],[f2170,f1487]) ).

fof(f19195,plain,
    ( spl0_654
    | ~ spl0_110
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2319,f2157,f1364,f19193]) ).

fof(f19193,plain,
    ( spl0_654
  <=> ! [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_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f2319,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,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_110
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1365]) ).

fof(f19191,plain,
    ( spl0_653
    | ~ spl0_95
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2318,f2157,f1301,f19189]) ).

fof(f19189,plain,
    ( spl0_653
  <=> ! [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_653])]) ).

fof(f2318,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_95
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1302]) ).

fof(f19187,plain,
    ( spl0_652
    | ~ spl0_110
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2278,f2145,f1364,f19185]) ).

fof(f19185,plain,
    ( spl0_652
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f2278,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_110
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1365]) ).

fof(f19171,plain,
    ( spl0_651
    | ~ spl0_95
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2277,f2145,f1301,f19169]) ).

fof(f19169,plain,
    ( spl0_651
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f2277,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_95
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1302]) ).

fof(f19167,plain,
    ( spl0_650
    | ~ spl0_122
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2265,f2141,f1492,f19165]) ).

fof(f19165,plain,
    ( spl0_650
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f2265,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) )
    | ~ spl0_122
    | ~ spl0_181 ),
    inference(resolution,[],[f2142,f1493]) ).

fof(f19163,plain,
    ( spl0_649
    | ~ spl0_123
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2264,f2141,f1496,f19161]) ).

fof(f19161,plain,
    ( spl0_649
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f2264,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) )
    | ~ spl0_123
    | ~ spl0_181 ),
    inference(resolution,[],[f2142,f1497]) ).

fof(f19159,plain,
    ( spl0_648
    | ~ spl0_141
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2263,f2141,f1568,f19157]) ).

fof(f19157,plain,
    ( spl0_648
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f2263,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_141
    | ~ spl0_181 ),
    inference(resolution,[],[f2142,f1569]) ).

fof(f19155,plain,
    ( spl0_647
    | ~ spl0_142
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2262,f2141,f1572,f19153]) ).

fof(f19153,plain,
    ( spl0_647
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f2262,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_142
    | ~ spl0_181 ),
    inference(resolution,[],[f2142,f1573]) ).

fof(f19151,plain,
    ( spl0_646
    | ~ spl0_143
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2261,f2141,f1578,f19149]) ).

fof(f19149,plain,
    ( spl0_646
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f2261,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_143
    | ~ spl0_181 ),
    inference(resolution,[],[f2142,f1579]) ).

fof(f19147,plain,
    ( spl0_645
    | ~ spl0_152
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2098,f1809,f1741,f19145]) ).

fof(f19145,plain,
    ( spl0_645
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f2098,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_152
    | ~ spl0_169 ),
    inference(resolution,[],[f1810,f1742]) ).

fof(f19143,plain,
    ( spl0_644
    | ~ spl0_163
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2090,f1809,f1785,f19141]) ).

fof(f19141,plain,
    ( spl0_644
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f2090,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat))
    | ~ spl0_163
    | ~ spl0_169 ),
    inference(resolution,[],[f1810,f1786]) ).

fof(f19139,plain,
    ( spl0_643
    | ~ spl0_163
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2076,f1805,f1785,f19137]) ).

fof(f19137,plain,
    ( spl0_643
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f2076,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat))
    | ~ spl0_163
    | ~ spl0_168 ),
    inference(resolution,[],[f1806,f1786]) ).

fof(f19135,plain,
    ( spl0_642
    | ~ spl0_163
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2018,f1793,f1785,f19133]) ).

fof(f19133,plain,
    ( spl0_642
  <=> ! [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_642])]) ).

fof(f2018,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_163
    | ~ spl0_165 ),
    inference(resolution,[],[f1794,f1786]) ).

fof(f19131,plain,
    ( spl0_641
    | ~ spl0_525
    | ~ spl0_629 ),
    inference(avatar_split_clause,[],[f18478,f17744,f12350,f19129]) ).

fof(f18478,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oone__class_Oone(tc_nat)),X1))
    | ~ spl0_525
    | ~ spl0_629 ),
    inference(superposition,[],[f17745,f12351]) ).

fof(f19127,plain,
    ( spl0_640
    | ~ spl0_150
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1991,f1785,f1733,f19125]) ).

fof(f19125,plain,
    ( spl0_640
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f1991,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_150
    | ~ spl0_163 ),
    inference(resolution,[],[f1786,f1734]) ).

fof(f19123,plain,
    ( spl0_639
    | ~ spl0_151
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1990,f1785,f1737,f19121]) ).

fof(f19121,plain,
    ( spl0_639
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f1990,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_151
    | ~ spl0_163 ),
    inference(resolution,[],[f1786,f1738]) ).

fof(f19119,plain,
    ( spl0_638
    | ~ spl0_153
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1959,f1777,f1745,f19117]) ).

fof(f19117,plain,
    ( spl0_638
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f1959,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_161 ),
    inference(resolution,[],[f1778,f1746]) ).

fof(f19115,plain,
    ( spl0_637
    | ~ spl0_159
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1957,f1777,f1769,f19113]) ).

fof(f19113,plain,
    ( spl0_637
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f1957,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) )
    | ~ spl0_159
    | ~ spl0_161 ),
    inference(resolution,[],[f1778,f1770]) ).

fof(f19111,plain,
    ( spl0_636
    | ~ spl0_160
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1956,f1777,f1773,f19109]) ).

fof(f19109,plain,
    ( spl0_636
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1956,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) )
    | ~ spl0_160
    | ~ spl0_161 ),
    inference(resolution,[],[f1778,f1774]) ).

fof(f19107,plain,
    ( spl0_635
    | ~ spl0_158
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1949,f1773,f1765,f19105]) ).

fof(f19105,plain,
    ( spl0_635
  <=> ! [X0,X3,X2,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f1949,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_160 ),
    inference(resolution,[],[f1774,f1766]) ).

fof(f19103,plain,
    ( spl0_634
    | ~ spl0_158
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1933,f1769,f1765,f19101]) ).

fof(f19101,plain,
    ( spl0_634
  <=> ! [X2,X0,X1,X3] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f1933,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X2,tc_nat) )
    | ~ spl0_158
    | ~ spl0_159 ),
    inference(resolution,[],[f1770,f1766]) ).

fof(f19099,plain,
    ( spl0_633
    | ~ spl0_153
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1915,f1765,f1745,f19097]) ).

fof(f19097,plain,
    ( spl0_633
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f1915,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_153
    | ~ spl0_158 ),
    inference(resolution,[],[f1766,f1746]) ).

fof(f19095,plain,
    ( spl0_632
    | ~ spl0_150
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1861,f1741,f1733,f19093]) ).

fof(f19093,plain,
    ( spl0_632
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f1861,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2,tc_nat) )
    | ~ spl0_150
    | ~ spl0_152 ),
    inference(resolution,[],[f1742,f1734]) ).

fof(f19091,plain,
    ( spl0_631
    | ~ spl0_151
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1860,f1741,f1737,f19089]) ).

fof(f19089,plain,
    ( spl0_631
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f1860,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) )
    | ~ spl0_151
    | ~ spl0_152 ),
    inference(resolution,[],[f1742,f1738]) ).

fof(f19087,plain,
    ( spl0_630
    | ~ spl0_522
    | ~ spl0_629 ),
    inference(avatar_split_clause,[],[f18476,f17744,f12338,f19085]) ).

fof(f19085,plain,
    ( spl0_630
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f18476,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X1),X2))
    | ~ spl0_522
    | ~ spl0_629 ),
    inference(superposition,[],[f17745,f12339]) ).

fof(f17746,plain,
    ( spl0_629
    | ~ spl0_86
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f17218,f16549,f1265,f17744]) ).

fof(f17218,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X0),X2))
    | ~ spl0_86
    | ~ spl0_618 ),
    inference(superposition,[],[f16550,f1266]) ).

fof(f16591,plain,
    ( ~ spl0_4
    | spl0_628
    | ~ spl0_58
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f7510,f6682,f1126,f16589,f876]) ).

fof(f16589,plain,
    ( spl0_628
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f7510,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) )
    | ~ spl0_58
    | ~ spl0_387 ),
    inference(resolution,[],[f6683,f1127]) ).

fof(f16587,plain,
    ( spl0_627
    | ~ spl0_56
    | ~ spl0_346 ),
    inference(avatar_split_clause,[],[f6443,f6171,f1118,f16585]) ).

fof(f16585,plain,
    ( spl0_627
  <=> ! [X0] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f1118,plain,
    ( spl0_56
  <=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f6443,plain,
    ( ! [X0] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_56
    | ~ spl0_346 ),
    inference(resolution,[],[f6172,f1119]) ).

fof(f1119,plain,
    ( ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f1118]) ).

fof(f16583,plain,
    ( spl0_626
    | ~ spl0_59
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f6400,f6167,f1130,f16581]) ).

fof(f16581,plain,
    ( spl0_626
  <=> ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f6167,plain,
    ( spl0_345
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f6400,plain,
    ( ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_59
    | ~ spl0_345 ),
    inference(resolution,[],[f6168,f1131]) ).

fof(f6168,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_345 ),
    inference(avatar_component_clause,[],[f6167]) ).

fof(f16579,plain,
    ( spl0_625
    | ~ spl0_45
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f5720,f5623,f1074,f16577]) ).

fof(f16577,plain,
    ( spl0_625
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Oorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f1074,plain,
    ( spl0_45
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f5623,plain,
    ( spl0_317
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f5720,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_45
    | ~ spl0_317 ),
    inference(resolution,[],[f5624,f1075]) ).

fof(f1075,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,X1,X0)
        | ~ class_Orderings_Oorder(X0) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f1074]) ).

fof(f5624,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f5623]) ).

fof(f16575,plain,
    ( spl0_624
    | ~ spl0_46
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f5719,f5623,f1078,f16573]) ).

fof(f16573,plain,
    ( spl0_624
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f1078,plain,
    ( spl0_46
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f5719,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_46
    | ~ spl0_317 ),
    inference(resolution,[],[f5624,f1079]) ).

fof(f1079,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,X1,X0)
        | ~ class_Orderings_Opreorder(X0) )
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f1078]) ).

fof(f16571,plain,
    ( spl0_623
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_95
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f5479,f4562,f1301,f1265,f1146,f16569]) ).

fof(f16569,plain,
    ( spl0_623
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f5479,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_95
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5478,f1147]) ).

fof(f5478,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_86
    | ~ spl0_95
    | ~ spl0_292 ),
    inference(forward_demodulation,[],[f5458,f1266]) ).

fof(f5458,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_95
    | ~ spl0_292 ),
    inference(resolution,[],[f4563,f1302]) ).

fof(f16567,plain,
    ( spl0_622
    | ~ spl0_64
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f5411,f4550,f1150,f16565]) ).

fof(f16565,plain,
    ( spl0_622
  <=> ! [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_622])]) ).

fof(f5411,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_64
    | ~ spl0_289 ),
    inference(superposition,[],[f4551,f1151]) ).

fof(f16563,plain,
    ( spl0_621
    | ~ spl0_61
    | ~ spl0_258 ),
    inference(avatar_split_clause,[],[f4388,f3704,f1138,f16561]) ).

fof(f16561,plain,
    ( spl0_621
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f4388,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_258 ),
    inference(superposition,[],[f1139,f3705]) ).

fof(f16559,plain,
    ( spl0_620
    | ~ spl0_61
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4057,f3664,f1138,f16557]) ).

fof(f16557,plain,
    ( spl0_620
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f4057,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_248 ),
    inference(superposition,[],[f1139,f3665]) ).

fof(f16555,plain,
    ( spl0_619
    | ~ spl0_53
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f4053,f3664,f1106,f16553]) ).

fof(f16553,plain,
    ( spl0_619
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f4053,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_53
    | ~ spl0_248 ),
    inference(superposition,[],[f3665,f1107]) ).

fof(f16551,plain,
    ( spl0_618
    | ~ spl0_522
    | ~ spl0_578 ),
    inference(avatar_split_clause,[],[f15300,f14665,f12338,f16549]) ).

fof(f15300,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),X1),X2))
    | ~ spl0_522
    | ~ spl0_578 ),
    inference(superposition,[],[f14666,f12339]) ).

fof(f16547,plain,
    ( spl0_617
    | ~ spl0_66
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4008,f3660,f1158,f16545]) ).

fof(f16545,plain,
    ( spl0_617
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f4008,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_66
    | ~ spl0_247 ),
    inference(superposition,[],[f1159,f3661]) ).

fof(f16543,plain,
    ( spl0_616
    | ~ spl0_58
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3965,f3660,f1126,f16541]) ).

fof(f16541,plain,
    ( spl0_616
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f3965,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_58
    | ~ spl0_247 ),
    inference(superposition,[],[f1127,f3661]) ).

fof(f16539,plain,
    ( spl0_615
    | ~ spl0_55
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f3963,f3660,f1114,f16537]) ).

fof(f16537,plain,
    ( spl0_615
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f1114,plain,
    ( spl0_55
  <=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f3963,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_247 ),
    inference(superposition,[],[f1115,f3661]) ).

fof(f1115,plain,
    ( ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f1114]) ).

fof(f16535,plain,
    ( spl0_614
    | ~ spl0_130
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3858,f3655,f1524,f16533]) ).

fof(f16533,plain,
    ( spl0_614
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f3858,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_130
    | ~ spl0_246 ),
    inference(superposition,[],[f1525,f3656]) ).

fof(f16531,plain,
    ( spl0_613
    | ~ spl0_59
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3852,f3655,f1130,f16529]) ).

fof(f16529,plain,
    ( spl0_613
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f3852,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ spl0_59
    | ~ spl0_246 ),
    inference(superposition,[],[f1131,f3656]) ).

fof(f16527,plain,
    ( spl0_612
    | ~ spl0_56
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3850,f3655,f1118,f16525]) ).

fof(f16525,plain,
    ( spl0_612
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f3850,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_246 ),
    inference(superposition,[],[f1119,f3656]) ).

fof(f16523,plain,
    ( spl0_611
    | ~ spl0_64
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3817,f3651,f1150,f16521]) ).

fof(f16521,plain,
    ( spl0_611
  <=> ! [X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X0,X1,c_HOL_Oone__class_Oone(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f3817,plain,
    ( ! [X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X0,X1,c_HOL_Oone__class_Oone(tc_nat)))
    | ~ spl0_64
    | ~ spl0_245 ),
    inference(superposition,[],[f3652,f1151]) ).

fof(f16479,plain,
    ( ~ spl0_34
    | spl0_610
    | ~ spl0_62
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3348,f2838,f1142,f16477,f1026]) ).

fof(f16477,plain,
    ( spl0_610
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f3348,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f1143]) ).

fof(f16426,plain,
    ( spl0_609
    | ~ spl0_525
    | ~ spl0_568
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f14143,f13785,f13761,f12350,f16424]) ).

fof(f13785,plain,
    ( spl0_574
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f14143,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X0),X1))
    | ~ spl0_525
    | ~ spl0_568
    | ~ spl0_574 ),
    inference(forward_demodulation,[],[f14139,f13762]) ).

fof(f14139,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X0),X1))
    | ~ spl0_525
    | ~ spl0_574 ),
    inference(superposition,[],[f13786,f12351]) ).

fof(f13786,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X1))
    | ~ spl0_574 ),
    inference(avatar_component_clause,[],[f13785]) ).

fof(f16422,plain,
    ( ~ spl0_34
    | spl0_608
    | ~ spl0_61
    | ~ spl0_227 ),
    inference(avatar_split_clause,[],[f3347,f2838,f1138,f16420,f1026]) ).

fof(f16420,plain,
    ( spl0_608
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f3347,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_61
    | ~ spl0_227 ),
    inference(resolution,[],[f2839,f1139]) ).

fof(f16385,plain,
    ( spl0_607
    | ~ spl0_36
    | ~ spl0_62
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3322,f2834,f1142,f1036,f16383]) ).

fof(f16383,plain,
    ( spl0_607
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f3322,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1143]) ).

fof(f16338,plain,
    ( spl0_606
    | ~ spl0_36
    | ~ spl0_61
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f3321,f2834,f1138,f1036,f16336]) ).

fof(f16336,plain,
    ( spl0_606
  <=> ! [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_606])]) ).

fof(f3321,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ 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_61
    | ~ spl0_226 ),
    inference(resolution,[],[f2835,f1139]) ).

fof(f16273,plain,
    ( spl0_605
    | ~ spl0_36
    | ~ spl0_62
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f3292,f2830,f1142,f1036,f16271]) ).

fof(f16271,plain,
    ( spl0_605
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f3292,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_225 ),
    inference(resolution,[],[f2831,f1143]) ).

fof(f16207,plain,
    ( ~ spl0_16
    | spl0_604
    | ~ spl0_95
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f3109,f2790,f1301,f16205,f936]) ).

fof(f16205,plain,
    ( spl0_604
  <=> ! [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_604])]) ).

fof(f3109,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_95
    | ~ spl0_215 ),
    inference(resolution,[],[f2791,f1302]) ).

fof(f16203,plain,
    ( spl0_603
    | ~ spl0_62
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2927,f2754,f1142,f16201]) ).

fof(f16201,plain,
    ( spl0_603
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f2927,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),X0,tc_nat)
    | ~ spl0_62
    | ~ spl0_206 ),
    inference(resolution,[],[f2755,f1143]) ).

fof(f16192,plain,
    ( spl0_602
    | ~ spl0_56
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2917,f2750,f1265,f1118,f16190]) ).

fof(f16190,plain,
    ( spl0_602
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f2917,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(forward_demodulation,[],[f2903,f1266]) ).

fof(f2903,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),X2,tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1119]) ).

fof(f16188,plain,
    ( spl0_601
    | ~ spl0_55
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2916,f2750,f1265,f1114,f16186]) ).

fof(f16186,plain,
    ( spl0_601
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f2916,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(forward_demodulation,[],[f2902,f1266]) ).

fof(f2902,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1115]) ).

fof(f16184,plain,
    ( spl0_600
    | ~ spl0_44
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2741,f2510,f1070,f16182]) ).

fof(f16182,plain,
    ( spl0_600
  <=> ! [X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1))
        | ~ c_InductTermi_OIT(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f2741,plain,
    ( ! [X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1))
        | ~ c_InductTermi_OIT(c_Lambda_Olift(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
    | ~ spl0_44
    | ~ spl0_204 ),
    inference(superposition,[],[f1071,f2511]) ).

fof(f16180,plain,
    ( spl0_599
    | ~ spl0_86
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2737,f2510,f1265,f16178]) ).

fof(f16178,plain,
    ( spl0_599
  <=> ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X0) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f2737,plain,
    ( ! [X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X1),X0) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)))
    | ~ spl0_86
    | ~ spl0_204 ),
    inference(superposition,[],[f2511,f1266]) ).

fof(f16176,plain,
    ( spl0_598
    | ~ spl0_72
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f2618,f2494,f1194,f16174]) ).

fof(f16174,plain,
    ( spl0_598
  <=> ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f2618,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_72
    | ~ spl0_200 ),
    inference(resolution,[],[f2495,f1195]) ).

fof(f16172,plain,
    ( spl0_597
    | ~ spl0_72
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f2541,f2479,f1194,f16170]) ).

fof(f16170,plain,
    ( spl0_597
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f2541,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_72
    | ~ spl0_197 ),
    inference(resolution,[],[f2480,f1195]) ).

fof(f16168,plain,
    ( spl0_596
    | ~ spl0_121
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2091,f1809,f1486,f16166]) ).

fof(f16166,plain,
    ( spl0_596
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f2091,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_121
    | ~ spl0_169 ),
    inference(resolution,[],[f1810,f1487]) ).

fof(f16164,plain,
    ( spl0_595
    | ~ spl0_121
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2077,f1805,f1486,f16162]) ).

fof(f16162,plain,
    ( spl0_595
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f2077,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_121
    | ~ spl0_168 ),
    inference(resolution,[],[f1806,f1487]) ).

fof(f16160,plain,
    ( spl0_594
    | ~ spl0_111
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2022,f1793,f1368,f16158]) ).

fof(f16158,plain,
    ( spl0_594
  <=> ! [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_594])]) ).

fof(f2022,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_111
    | ~ spl0_165 ),
    inference(resolution,[],[f1794,f1369]) ).

fof(f16156,plain,
    ( spl0_593
    | ~ spl0_121
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2019,f1793,f1486,f16154]) ).

fof(f16154,plain,
    ( spl0_593
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f2019,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_165 ),
    inference(resolution,[],[f1794,f1487]) ).

fof(f16152,plain,
    ( spl0_592
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_532
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f15838,f13761,f13604,f8722,f1364,f16150]) ).

fof(f13604,plain,
    ( spl0_532
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f15838,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_110
    | ~ spl0_422
    | ~ spl0_532
    | ~ spl0_568 ),
    inference(forward_demodulation,[],[f15826,f8841]) ).

fof(f15826,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1))
    | ~ spl0_532
    | ~ spl0_568 ),
    inference(superposition,[],[f13605,f13762]) ).

fof(f13605,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X1))
    | ~ spl0_532 ),
    inference(avatar_component_clause,[],[f13604]) ).

fof(f16148,plain,
    ( spl0_591
    | ~ spl0_110
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1987,f1785,f1364,f16146]) ).

fof(f16146,plain,
    ( spl0_591
  <=> ! [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)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f1987,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)),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_110
    | ~ spl0_163 ),
    inference(resolution,[],[f1786,f1365]) ).

fof(f16144,plain,
    ( spl0_590
    | ~ spl0_95
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1986,f1785,f1301,f16142]) ).

fof(f16142,plain,
    ( spl0_590
  <=> ! [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_590])]) ).

fof(f1986,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_95
    | ~ spl0_163 ),
    inference(resolution,[],[f1786,f1302]) ).

fof(f16140,plain,
    ( spl0_589
    | ~ spl0_56
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1979,f1781,f1118,f16138]) ).

fof(f16138,plain,
    ( spl0_589
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f1979,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_56
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1119]) ).

fof(f16136,plain,
    ( spl0_588
    | ~ spl0_55
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1978,f1781,f1114,f16134]) ).

fof(f16134,plain,
    ( spl0_588
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1978,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_55
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1115]) ).

fof(f16132,plain,
    ( spl0_587
    | ~ spl0_62
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1970,f1781,f1142,f16130]) ).

fof(f16130,plain,
    ( spl0_587
  <=> ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f1970,plain,
    ( ! [X0,X1] :
        ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_62
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1143]) ).

fof(f16128,plain,
    ( spl0_586
    | ~ spl0_61
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1969,f1781,f1138,f16126]) ).

fof(f16126,plain,
    ( spl0_586
  <=> ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f1969,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_61
    | ~ spl0_162 ),
    inference(resolution,[],[f1782,f1139]) ).

fof(f16124,plain,
    ( spl0_585
    | ~ spl0_56
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1910,f1761,f1118,f16122]) ).

fof(f16122,plain,
    ( spl0_585
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f1910,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 )
    | ~ spl0_56
    | ~ spl0_157 ),
    inference(resolution,[],[f1762,f1119]) ).

fof(f16120,plain,
    ( spl0_584
    | ~ spl0_55
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1909,f1761,f1114,f16118]) ).

fof(f16118,plain,
    ( spl0_584
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f1909,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
    | ~ spl0_55
    | ~ spl0_157 ),
    inference(resolution,[],[f1762,f1115]) ).

fof(f16116,plain,
    ( spl0_583
    | ~ spl0_62
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1901,f1761,f1142,f16114]) ).

fof(f16114,plain,
    ( spl0_583
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f1901,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
        | c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
    | ~ spl0_62
    | ~ spl0_157 ),
    inference(resolution,[],[f1762,f1143]) ).

fof(f16112,plain,
    ( spl0_582
    | ~ spl0_61
    | ~ spl0_157 ),
    inference(avatar_split_clause,[],[f1900,f1761,f1138,f16110]) ).

fof(f16110,plain,
    ( spl0_582
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f1900,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 )
    | ~ spl0_61
    | ~ spl0_157 ),
    inference(resolution,[],[f1762,f1139]) ).

fof(f16105,plain,
    ( spl0_581
    | ~ spl0_121
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1841,f1737,f1486,f16103]) ).

fof(f16103,plain,
    ( spl0_581
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f1841,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_151 ),
    inference(resolution,[],[f1738,f1487]) ).

fof(f16101,plain,
    ( spl0_580
    | ~ spl0_121
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1823,f1733,f1486,f16099]) ).

fof(f16099,plain,
    ( spl0_580
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1823,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = X0 )
    | ~ spl0_121
    | ~ spl0_150 ),
    inference(resolution,[],[f1734,f1487]) ).

fof(f15850,plain,
    ( spl0_579
    | ~ spl0_2
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f15803,f13761,f867,f15848]) ).

fof(f15803,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)),X1))
    | ~ spl0_2
    | ~ spl0_568 ),
    inference(superposition,[],[f868,f13762]) ).

fof(f14667,plain,
    ( spl0_578
    | ~ spl0_254
    | ~ spl0_553 ),
    inference(avatar_split_clause,[],[f13739,f13693,f3688,f14665]) ).

fof(f13693,plain,
    ( spl0_553
  <=> ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f13739,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1),X1),X2))
    | ~ spl0_254
    | ~ spl0_553 ),
    inference(superposition,[],[f13694,f3689]) ).

fof(f13694,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2))
    | ~ spl0_553 ),
    inference(avatar_component_clause,[],[f13693]) ).

fof(f13799,plain,
    ( spl0_577
    | ~ spl0_59
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8392,f7788,f1130,f13797]) ).

fof(f13797,plain,
    ( spl0_577
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f8392,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_59
    | ~ spl0_411 ),
    inference(superposition,[],[f1131,f7789]) ).

fof(f13795,plain,
    ( spl0_576
    | ~ spl0_56
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8390,f7788,f1118,f13793]) ).

fof(f13793,plain,
    ( spl0_576
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f8390,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_56
    | ~ spl0_411 ),
    inference(superposition,[],[f1119,f7789]) ).

fof(f13791,plain,
    ( spl0_575
    | ~ spl0_110
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f8365,f7788,f1364,f13789]) ).

fof(f13789,plain,
    ( spl0_575
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f8365,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_110
    | ~ spl0_411 ),
    inference(superposition,[],[f1365,f7789]) ).

fof(f13787,plain,
    ( spl0_574
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f13651,f13604,f12350,f8722,f1230,f13785]) ).

fof(f13651,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X0),X1))
    | ~ spl0_81
    | ~ spl0_422
    | ~ spl0_525
    | ~ spl0_532 ),
    inference(forward_demodulation,[],[f13648,f8808]) ).

fof(f13648,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1))
    | ~ spl0_525
    | ~ spl0_532 ),
    inference(superposition,[],[f13605,f12351]) ).

fof(f13783,plain,
    ( spl0_573
    | ~ spl0_71
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f5658,f5555,f1190,f13781]) ).

fof(f13781,plain,
    ( spl0_573
  <=> ! [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_573])]) ).

fof(f1190,plain,
    ( spl0_71
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f5658,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_71
    | ~ spl0_300 ),
    inference(trivial_inequality_removal,[],[f5655]) ).

fof(f5655,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_71
    | ~ spl0_300 ),
    inference(superposition,[],[f5556,f1191]) ).

fof(f1191,plain,
    ( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f1190]) ).

fof(f13779,plain,
    ( spl0_572
    | ~ spl0_39
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f4625,f4458,f1050,f13777]) ).

fof(f13777,plain,
    ( spl0_572
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f4625,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_39
    | ~ spl0_266 ),
    inference(resolution,[],[f4459,f1051]) ).

fof(f13775,plain,
    ( spl0_571
    | ~ spl0_150
    | ~ spl0_256 ),
    inference(avatar_split_clause,[],[f4347,f3696,f1733,f13773]) ).

fof(f13773,plain,
    ( spl0_571
  <=> ! [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_571])]) ).

fof(f4347,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_150
    | ~ spl0_256 ),
    inference(resolution,[],[f3697,f1734]) ).

fof(f13771,plain,
    ( spl0_570
    | ~ spl0_150
    | ~ spl0_255 ),
    inference(avatar_split_clause,[],[f4313,f3692,f1733,f13769]) ).

fof(f13769,plain,
    ( spl0_570
  <=> ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f4313,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | X0 = X1
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_150
    | ~ spl0_255 ),
    inference(resolution,[],[f3693,f1734]) ).

fof(f13767,plain,
    ( spl0_569
    | ~ spl0_106
    | ~ spl0_110
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4248,f3680,f1364,f1346,f13765]) ).

fof(f13765,plain,
    ( spl0_569
  <=> ! [X0] : c_List_Olast(c_List_Oupt(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f4248,plain,
    ( ! [X0] : c_List_Olast(c_List_Oupt(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0
    | ~ spl0_106
    | ~ spl0_110
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4231,f1347]) ).

fof(f4231,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_List_Olast(c_List_Oupt(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat)
    | ~ spl0_110
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1365]) ).

fof(f13763,plain,
    ( spl0_568
    | ~ spl0_41
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4173,f3676,f1058,f13761]) ).

fof(f13759,plain,
    ( spl0_567
    | ~ spl0_110
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4012,f3660,f1364,f13757]) ).

fof(f13757,plain,
    ( spl0_567
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f4012,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_110
    | ~ spl0_247 ),
    inference(superposition,[],[f1365,f3661]) ).

fof(f13755,plain,
    ( spl0_566
    | ~ spl0_41
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3784,f3647,f1058,f13753]) ).

fof(f13753,plain,
    ( spl0_566
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f3784,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat))
    | ~ spl0_41
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1059]) ).

fof(f13751,plain,
    ( spl0_565
    | ~ spl0_189
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f3239,f2822,f2173,f13749]) ).

fof(f13749,plain,
    ( spl0_565
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f3239,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_189
    | ~ spl0_223 ),
    inference(resolution,[],[f2823,f2174]) ).

fof(f13747,plain,
    ( spl0_564
    | ~ spl0_191
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f3238,f2822,f2181,f13745]) ).

fof(f13745,plain,
    ( spl0_564
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f3238,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_191
    | ~ spl0_223 ),
    inference(resolution,[],[f2823,f2182]) ).

fof(f13735,plain,
    ( spl0_563
    | ~ spl0_188
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f3212,f2818,f2169,f13733]) ).

fof(f13733,plain,
    ( spl0_563
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f3212,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_188
    | ~ spl0_222 ),
    inference(resolution,[],[f2819,f2170]) ).

fof(f13731,plain,
    ( spl0_562
    | ~ spl0_194
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f3211,f2818,f2193,f13729]) ).

fof(f13729,plain,
    ( spl0_562
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f3211,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_194
    | ~ spl0_222 ),
    inference(resolution,[],[f2819,f2194]) ).

fof(f13727,plain,
    ( spl0_561
    | ~ spl0_54
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f3137,f2802,f1110,f13725]) ).

fof(f13725,plain,
    ( spl0_561
  <=> ! [X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f3137,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_54
    | ~ spl0_218 ),
    inference(superposition,[],[f2803,f1111]) ).

fof(f13723,plain,
    ( spl0_560
    | ~ spl0_32
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f3122,f2798,f1016,f13721]) ).

fof(f13721,plain,
    ( spl0_560
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f2798,plain,
    ( spl0_217
  <=> ! [X5,X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f3122,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_217 ),
    inference(resolution,[],[f2799,f1018]) ).

fof(f2799,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X0),X5,X0) )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f2798]) ).

fof(f13719,plain,
    ( spl0_559
    | ~ spl0_32
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f3121,f2794,f1016,f13717]) ).

fof(f13717,plain,
    ( spl0_559
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f2794,plain,
    ( spl0_216
  <=> ! [X5,X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f3121,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_216 ),
    inference(resolution,[],[f2795,f1018]) ).

fof(f2795,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X5,X0) )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2794]) ).

fof(f13715,plain,
    ( spl0_558
    | ~ spl0_63
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f3079,f2782,f1146,f13713]) ).

fof(f13713,plain,
    ( spl0_558
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f3079,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_63
    | ~ spl0_213 ),
    inference(superposition,[],[f2783,f1147]) ).

fof(f13711,plain,
    ( spl0_557
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f3059,f2782,f2165,f13709]) ).

fof(f13709,plain,
    ( spl0_557
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f3059,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(resolution,[],[f2783,f2166]) ).

fof(f13707,plain,
    ( spl0_556
    | ~ spl0_193
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f3058,f2782,f2189,f13705]) ).

fof(f13705,plain,
    ( spl0_556
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f3058,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_193
    | ~ spl0_213 ),
    inference(resolution,[],[f2783,f2190]) ).

fof(f13703,plain,
    ( spl0_555
    | ~ spl0_190
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3043,f2778,f2177,f13701]) ).

fof(f13701,plain,
    ( spl0_555
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f3043,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_190
    | ~ spl0_212 ),
    inference(resolution,[],[f2779,f2178]) ).

fof(f13699,plain,
    ( spl0_554
    | ~ spl0_192
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3042,f2778,f2185,f13697]) ).

fof(f13697,plain,
    ( spl0_554
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f3042,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) )
    | ~ spl0_192
    | ~ spl0_212 ),
    inference(resolution,[],[f2779,f2186]) ).

fof(f13695,plain,
    ( spl0_553
    | ~ spl0_2
    | ~ spl0_522 ),
    inference(avatar_split_clause,[],[f13440,f12338,f867,f13693]) ).

fof(f13440,plain,
    ( ! [X2,X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2))
    | ~ spl0_2
    | ~ spl0_522 ),
    inference(superposition,[],[f868,f12339]) ).

fof(f13691,plain,
    ( spl0_552
    | ~ spl0_64
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f3027,f2774,f1150,f13689]) ).

fof(f13689,plain,
    ( spl0_552
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f3027,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_64
    | ~ spl0_211 ),
    inference(superposition,[],[f2775,f1151]) ).

fof(f13687,plain,
    ( spl0_551
    | ~ spl0_32
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f2950,f2758,f1016,f13685]) ).

fof(f13685,plain,
    ( spl0_551
  <=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f2758,plain,
    ( spl0_207
  <=> ! [X5,X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f2950,plain,
    ( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_207 ),
    inference(resolution,[],[f2759,f1018]) ).

fof(f2759,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X5,X0),X5,X0) )
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f2758]) ).

fof(f13683,plain,
    ( spl0_550
    | ~ spl0_86
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2470,f2193,f1265,f13681]) ).

fof(f13681,plain,
    ( spl0_550
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f2470,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_194 ),
    inference(superposition,[],[f2194,f1266]) ).

fof(f13679,plain,
    ( spl0_549
    | ~ spl0_86
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2447,f2189,f1265,f13677]) ).

fof(f13677,plain,
    ( spl0_549
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f2447,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_193 ),
    inference(superposition,[],[f2190,f1266]) ).

fof(f13675,plain,
    ( spl0_548
    | ~ spl0_86
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f2430,f2185,f1265,f13673]) ).

fof(f13673,plain,
    ( spl0_548
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f2430,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_192 ),
    inference(superposition,[],[f2186,f1266]) ).

fof(f13671,plain,
    ( spl0_547
    | ~ spl0_86
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2416,f2181,f1265,f13669]) ).

fof(f13669,plain,
    ( spl0_547
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f2416,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_191 ),
    inference(superposition,[],[f2182,f1266]) ).

fof(f13667,plain,
    ( spl0_546
    | ~ spl0_86
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f2399,f2177,f1265,f13665]) ).

fof(f13665,plain,
    ( spl0_546
  <=> ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f2399,plain,
    ( ! [X0,X1] :
        ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_190 ),
    inference(superposition,[],[f2178,f1266]) ).

fof(f13663,plain,
    ( spl0_545
    | ~ spl0_86
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2385,f2173,f1265,f13661]) ).

fof(f13661,plain,
    ( spl0_545
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f2385,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_86
    | ~ spl0_189 ),
    inference(superposition,[],[f2174,f1266]) ).

fof(f13659,plain,
    ( spl0_544
    | ~ spl0_86
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2367,f2169,f1265,f13657]) ).

fof(f13657,plain,
    ( spl0_544
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f2367,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_188 ),
    inference(superposition,[],[f2170,f1266]) ).

fof(f13655,plain,
    ( spl0_543
    | ~ spl0_86
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2346,f2165,f1265,f13653]) ).

fof(f13653,plain,
    ( spl0_543
  <=> ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f2346,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_86
    | ~ spl0_187 ),
    inference(superposition,[],[f2166,f1266]) ).

fof(f13646,plain,
    ( spl0_542
    | ~ spl0_81
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f2309,f2157,f1230,f13644]) ).

fof(f13644,plain,
    ( spl0_542
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f2309,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_81
    | ~ spl0_185 ),
    inference(resolution,[],[f2158,f1231]) ).

fof(f13642,plain,
    ( spl0_541
    | ~ spl0_107
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f2308,f2153,f1352,f13640]) ).

fof(f13640,plain,
    ( spl0_541
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f2308,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_107
    | ~ spl0_184 ),
    inference(superposition,[],[f2154,f1353]) ).

fof(f13638,plain,
    ( spl0_540
    | ~ spl0_106
    | ~ spl0_184 ),
    inference(avatar_split_clause,[],[f2307,f2153,f1346,f13636]) ).

fof(f13636,plain,
    ( spl0_540
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f2307,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_106
    | ~ spl0_184 ),
    inference(superposition,[],[f2154,f1347]) ).

fof(f13634,plain,
    ( spl0_539
    | ~ spl0_81
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2266,f2145,f1230,f13632]) ).

fof(f13632,plain,
    ( spl0_539
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f2266,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_81
    | ~ spl0_182 ),
    inference(resolution,[],[f2146,f1231]) ).

fof(f13630,plain,
    ( spl0_538
    | ~ spl0_72
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2236,f2120,f1194,f13628]) ).

fof(f13628,plain,
    ( spl0_538
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f2236,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X2,X1,tc_nat)
        | c_lessequals(X0,X2,tc_nat) )
    | ~ spl0_72
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f1195]) ).

fof(f13626,plain,
    ( spl0_537
    | ~ spl0_86
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2216,f2116,f1265,f13624]) ).

fof(f13624,plain,
    ( spl0_537
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f2216,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_86
    | ~ spl0_175 ),
    inference(superposition,[],[f2117,f1266]) ).

fof(f13622,plain,
    ( spl0_536
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1998,f1789,f1368,f13620]) ).

fof(f13620,plain,
    ( spl0_536
  <=> ! [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_536])]) ).

fof(f1998,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_111
    | ~ spl0_164 ),
    inference(resolution,[],[f1790,f1369]) ).

fof(f13618,plain,
    ( spl0_535
    | ~ spl0_140
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1710,f1578,f1564,f13616]) ).

fof(f13616,plain,
    ( spl0_535
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
        | ~ class_Orderings_Opreorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1710,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
        | ~ class_Orderings_Opreorder(X1)
        | ~ class_Ring__and__Field_Oordered__semidom(X1) )
    | ~ spl0_140
    | ~ spl0_143 ),
    inference(resolution,[],[f1579,f1565]) ).

fof(f13614,plain,
    ( spl0_534
    | ~ spl0_140
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1702,f1572,f1564,f13612]) ).

fof(f13612,plain,
    ( spl0_534
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f1702,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_140
    | ~ spl0_142 ),
    inference(resolution,[],[f1573,f1565]) ).

fof(f13610,plain,
    ( spl0_533
    | ~ spl0_140
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1695,f1568,f1564,f13608]) ).

fof(f13608,plain,
    ( spl0_533
  <=> ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f1695,plain,
    ( ! [X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
        | ~ class_Ring__and__Field_Oordered__semidom(X0) )
    | ~ spl0_140
    | ~ spl0_141 ),
    inference(resolution,[],[f1569,f1565]) ).

fof(f13606,plain,
    ( spl0_532
    | ~ spl0_2
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f13535,f12350,f867,f13604]) ).

fof(f13535,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0),X1))
    | ~ spl0_2
    | ~ spl0_525 ),
    inference(superposition,[],[f868,f12351]) ).

fof(f13602,plain,
    ( spl0_531
    | ~ spl0_122
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1686,f1564,f1492,f13600]) ).

fof(f13600,plain,
    ( spl0_531
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f1686,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Oorder(X0)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) )
    | ~ spl0_122
    | ~ spl0_140 ),
    inference(resolution,[],[f1565,f1493]) ).

fof(f13598,plain,
    ( spl0_530
    | ~ spl0_123
    | ~ spl0_140 ),
    inference(avatar_split_clause,[],[f1685,f1564,f1496,f13596]) ).

fof(f13596,plain,
    ( spl0_530
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f1685,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) )
    | ~ spl0_123
    | ~ spl0_140 ),
    inference(resolution,[],[f1565,f1497]) ).

fof(f13303,plain,
    ( spl0_529
    | ~ spl0_40
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f13084,f12298,f1054,f13301]) ).

fof(f13301,plain,
    ( spl0_529
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f1054,plain,
    ( spl0_40
  <=> ! [X9,X19] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X19),X9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f12298,plain,
    ( spl0_512
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f13084,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
    | ~ spl0_40
    | ~ spl0_512 ),
    inference(resolution,[],[f12299,f1055]) ).

fof(f1055,plain,
    ( ! [X19,X9] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X19),X9)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f1054]) ).

fof(f12299,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) )
    | ~ spl0_512 ),
    inference(avatar_component_clause,[],[f12298]) ).

fof(f12541,plain,
    ( spl0_528
    | ~ spl0_56
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f11652,f10982,f1118,f12539]) ).

fof(f12539,plain,
    ( spl0_528
  <=> ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f10982,plain,
    ( spl0_484
  <=> ! [X0] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f11652,plain,
    ( ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_484 ),
    inference(resolution,[],[f10983,f1119]) ).

fof(f10983,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_484 ),
    inference(avatar_component_clause,[],[f10982]) ).

fof(f12360,plain,
    ( spl0_527
    | ~ spl0_41
    | ~ spl0_81
    | ~ spl0_106
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f5304,f4538,f3676,f1346,f1230,f1058,f12358]) ).

fof(f12358,plain,
    ( spl0_527
  <=> ! [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_527])]) ).

fof(f5304,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_41
    | ~ spl0_81
    | ~ spl0_106
    | ~ spl0_251
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5303,f4173]) ).

fof(f5303,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1,X0)
    | ~ spl0_81
    | ~ spl0_106
    | ~ spl0_286 ),
    inference(forward_demodulation,[],[f5266,f1347]) ).

fof(f5266,plain,
    ( ! [X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X1,X0) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_81
    | ~ spl0_286 ),
    inference(resolution,[],[f4539,f1231]) ).

fof(f12356,plain,
    ( spl0_526
    | ~ spl0_81
    | ~ spl0_106
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f4242,f3680,f1346,f1230,f12354]) ).

fof(f12354,plain,
    ( spl0_526
  <=> ! [X0] : c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f4242,plain,
    ( ! [X0] : c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat) = X0
    | ~ spl0_81
    | ~ spl0_106
    | ~ spl0_252 ),
    inference(forward_demodulation,[],[f4212,f1347]) ).

fof(f4212,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_List_Olast(c_List_Oupt(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),tc_nat)
    | ~ spl0_81
    | ~ spl0_252 ),
    inference(resolution,[],[f3681,f1231]) ).

fof(f12352,plain,
    ( spl0_525
    | ~ spl0_39
    | ~ spl0_251 ),
    inference(avatar_split_clause,[],[f4165,f3676,f1050,f12350]) ).

fof(f12348,plain,
    ( spl0_524
    | ~ spl0_79
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f4009,f3660,f1222,f12346]) ).

fof(f12346,plain,
    ( spl0_524
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f1222,plain,
    ( spl0_79
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f4009,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
    | ~ spl0_79
    | ~ spl0_247 ),
    inference(superposition,[],[f1223,f3661]) ).

fof(f1223,plain,
    ( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f1222]) ).

fof(f12344,plain,
    ( spl0_523
    | ~ spl0_168
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f3891,f3655,f1805,f12342]) ).

fof(f12342,plain,
    ( spl0_523
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f3891,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_168
    | ~ spl0_246 ),
    inference(superposition,[],[f1806,f3656]) ).

fof(f12340,plain,
    ( spl0_522
    | ~ spl0_39
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f3776,f3647,f1050,f12338]) ).

fof(f3776,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1)
    | ~ spl0_39
    | ~ spl0_244 ),
    inference(resolution,[],[f3648,f1051]) ).

fof(f12336,plain,
    ( spl0_521
    | ~ spl0_55
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f11651,f10982,f1114,f12334]) ).

fof(f12334,plain,
    ( spl0_521
  <=> ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f11651,plain,
    ( ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_484 ),
    inference(resolution,[],[f10983,f1115]) ).

fof(f12332,plain,
    ( spl0_520
    | ~ spl0_152
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f3237,f2822,f1741,f12330]) ).

fof(f12330,plain,
    ( spl0_520
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f3237,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_152
    | ~ spl0_223 ),
    inference(resolution,[],[f2823,f1742]) ).

fof(f12328,plain,
    ( spl0_519
    | ~ spl0_169
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f3216,f2818,f1809,f12326]) ).

fof(f12326,plain,
    ( spl0_519
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f3216,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),tc_nat)
    | ~ spl0_169
    | ~ spl0_222 ),
    inference(resolution,[],[f2819,f1810]) ).

fof(f12324,plain,
    ( spl0_518
    | ~ spl0_161
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f3036,f2778,f1777,f12322]) ).

fof(f12322,plain,
    ( spl0_518
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f3036,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X2,tc_nat) )
    | ~ spl0_161
    | ~ spl0_212 ),
    inference(resolution,[],[f2779,f1778]) ).

fof(f12320,plain,
    ( spl0_517
    | ~ spl0_158
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f2923,f2754,f1765,f12318]) ).

fof(f12318,plain,
    ( spl0_517
  <=> ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f2923,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
        | ~ c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_158
    | ~ spl0_206 ),
    inference(resolution,[],[f2755,f1766]) ).

fof(f12316,plain,
    ( spl0_516
    | ~ spl0_64
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2739,f2510,f1150,f12314]) ).

fof(f12314,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f2739,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_64
    | ~ spl0_204 ),
    inference(superposition,[],[f2511,f1151]) ).

fof(f12312,plain,
    ( spl0_515
    | ~ spl0_56
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2444,f2189,f1118,f12310]) ).

fof(f12310,plain,
    ( spl0_515
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f2444,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_193 ),
    inference(resolution,[],[f2190,f1119]) ).

fof(f12308,plain,
    ( spl0_514
    | ~ spl0_56
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2343,f2165,f1118,f12306]) ).

fof(f12306,plain,
    ( spl0_514
  <=> ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f2343,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_56
    | ~ spl0_187 ),
    inference(resolution,[],[f2166,f1119]) ).

fof(f12304,plain,
    ( spl0_513
    | ~ spl0_77
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2330,f2161,f1214,f12302]) ).

fof(f12302,plain,
    ( spl0_513
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X3,X2,X1),X0)
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f2161,plain,
    ( spl0_186
  <=> ! [X9,X27,X19,X30] :
        ( ~ c_Lambda_Obeta(X30,X27)
        | c_Lambda_Obeta(c_Lambda_Osubst(X30,X9,X19),c_Lambda_Osubst(X27,X9,X19)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f2330,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X3,X2,X1),X0)
        | ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) )
    | ~ spl0_77
    | ~ spl0_186 ),
    inference(superposition,[],[f2162,f1215]) ).

fof(f2162,plain,
    ( ! [X19,X9,X27,X30] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X30,X9,X19),c_Lambda_Osubst(X27,X9,X19))
        | ~ c_Lambda_Obeta(X30,X27) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f2161]) ).

fof(f12300,plain,
    ( spl0_512
    | ~ spl0_77
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2328,f2161,f1214,f12298]) ).

fof(f2328,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) )
    | ~ spl0_77
    | ~ spl0_186 ),
    inference(superposition,[],[f2162,f1215]) ).

fof(f12296,plain,
    ( spl0_511
    | ~ spl0_95
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2283,f2149,f1301,f12294]) ).

fof(f12294,plain,
    ( spl0_511
  <=> ! [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_511])]) ).

fof(f2283,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_95
    | ~ spl0_183 ),
    inference(resolution,[],[f2150,f1302]) ).

fof(f12292,plain,
    ( spl0_510
    | ~ spl0_77
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f11640,f10978,f1214,f12290]) ).

fof(f12290,plain,
    ( spl0_510
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Obeta(X0,X2)
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),c_Lambda_OdB_OVar(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).

fof(f10978,plain,
    ( spl0_483
  <=> ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
        | ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f11640,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(X0,X2)
        | ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),c_Lambda_OdB_OVar(X1)) )
    | ~ spl0_77
    | ~ spl0_483 ),
    inference(superposition,[],[f10979,f1215]) ).

fof(f10979,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
        | ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f10978]) ).

fof(f12288,plain,
    ( spl0_509
    | ~ spl0_62
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2232,f2120,f1142,f12286]) ).

fof(f12286,plain,
    ( spl0_509
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f2232,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_62
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f1143]) ).

fof(f12284,plain,
    ( spl0_508
    | ~ spl0_61
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2231,f2120,f1138,f12282]) ).

fof(f12282,plain,
    ( spl0_508
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f2231,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_61
    | ~ spl0_176 ),
    inference(resolution,[],[f2121,f1139]) ).

fof(f12280,plain,
    ( spl0_507
    | ~ spl0_86
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2070,f1797,f1265,f12278]) ).

fof(f12278,plain,
    ( spl0_507
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f2070,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_166 ),
    inference(superposition,[],[f1798,f1266]) ).

fof(f12276,plain,
    ( spl0_506
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1996,f1789,f1186,f12274]) ).

fof(f12274,plain,
    ( spl0_506
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f1996,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_70
    | ~ spl0_164 ),
    inference(resolution,[],[f1790,f1187]) ).

fof(f12272,plain,
    ( spl0_505
    | ~ spl0_81
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1988,f1785,f1230,f12270]) ).

fof(f12270,plain,
    ( spl0_505
  <=> ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f1988,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
    | ~ spl0_81
    | ~ spl0_163 ),
    inference(resolution,[],[f1786,f1231]) ).

fof(f12268,plain,
    ( spl0_504
    | ~ spl0_80
    | ~ spl0_86
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1966,f1777,f1265,f1226,f12266]) ).

fof(f12266,plain,
    ( spl0_504
  <=> ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f1966,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X0,tc_nat)
    | ~ spl0_80
    | ~ spl0_86
    | ~ spl0_161 ),
    inference(forward_demodulation,[],[f1955,f1266]) ).

fof(f1955,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
    | ~ spl0_80
    | ~ spl0_161 ),
    inference(resolution,[],[f1778,f1227]) ).

fof(f12264,plain,
    ( spl0_503
    | ~ spl0_72
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f1943,f1773,f1194,f12262]) ).

fof(f12262,plain,
    ( spl0_503
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f1943,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_72
    | ~ spl0_160 ),
    inference(resolution,[],[f1774,f1195]) ).

fof(f12260,plain,
    ( spl0_502
    | ~ spl0_72
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1927,f1769,f1194,f12258]) ).

fof(f12258,plain,
    ( spl0_502
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f1927,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) )
    | ~ spl0_72
    | ~ spl0_159 ),
    inference(resolution,[],[f1770,f1195]) ).

fof(f12256,plain,
    ( spl0_501
    | ~ spl0_80
    | ~ spl0_86
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1922,f1765,f1265,f1226,f12254]) ).

fof(f12254,plain,
    ( spl0_501
  <=> ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1922,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_80
    | ~ spl0_86
    | ~ spl0_158 ),
    inference(forward_demodulation,[],[f1913,f1266]) ).

fof(f1913,plain,
    ( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_80
    | ~ spl0_158 ),
    inference(resolution,[],[f1766,f1227]) ).

fof(f12252,plain,
    ( spl0_500
    | ~ spl0_107
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1893,f1749,f1352,f12250]) ).

fof(f12250,plain,
    ( spl0_500
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X1
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f1893,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X1
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) )
    | ~ spl0_107
    | ~ spl0_154 ),
    inference(superposition,[],[f1750,f1353]) ).

fof(f12145,plain,
    ( spl0_499
    | ~ spl0_106
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1892,f1749,f1346,f12143]) ).

fof(f12143,plain,
    ( spl0_499
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X0
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f1892,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X0
        | c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) )
    | ~ spl0_106
    | ~ spl0_154 ),
    inference(superposition,[],[f1750,f1347]) ).

fof(f12141,plain,
    ( spl0_498
    | ~ spl0_72
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1876,f1745,f1194,f12139]) ).

fof(f12139,plain,
    ( spl0_498
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f1876,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_72
    | ~ spl0_153 ),
    inference(resolution,[],[f1746,f1195]) ).

fof(f12137,plain,
    ( spl0_497
    | ~ spl0_86
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1864,f1741,f1265,f12135]) ).

fof(f12135,plain,
    ( spl0_497
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1864,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_86
    | ~ spl0_152 ),
    inference(superposition,[],[f1742,f1266]) ).

fof(f12133,plain,
    ( spl0_496
    | ~ spl0_70
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1842,f1737,f1186,f12131]) ).

fof(f12131,plain,
    ( spl0_496
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f1842,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_151 ),
    inference(resolution,[],[f1738,f1187]) ).

fof(f12129,plain,
    ( spl0_495
    | ~ spl0_70
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1824,f1733,f1186,f12127]) ).

fof(f12127,plain,
    ( spl0_495
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f1824,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_70
    | ~ spl0_150 ),
    inference(resolution,[],[f1734,f1187]) ).

fof(f12125,plain,
    ( spl0_494
    | ~ spl0_78
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1673,f1536,f1218,f12123]) ).

fof(f12123,plain,
    ( spl0_494
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
        | ~ c_Lambda_Obeta(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f1673,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
        | ~ c_Lambda_Obeta(X0,X1) )
    | ~ spl0_78
    | ~ spl0_133 ),
    inference(resolution,[],[f1537,f1219]) ).

fof(f11020,plain,
    ( spl0_493
    | ~ spl0_331
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f10462,f10343,f5770,f11018]) ).

fof(f11018,plain,
    ( spl0_493
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_lessequals(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f5770,plain,
    ( spl0_331
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f10343,plain,
    ( spl0_451
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f10462,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
        | c_lessequals(X0,X1,tc_nat) )
    | ~ spl0_331
    | ~ spl0_451 ),
    inference(resolution,[],[f10344,f5771]) ).

fof(f5771,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f5770]) ).

fof(f10344,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_451 ),
    inference(avatar_component_clause,[],[f10343]) ).

fof(f11016,plain,
    ( spl0_492
    | ~ spl0_278
    | ~ spl0_281 ),
    inference(avatar_split_clause,[],[f5127,f4518,f4506,f11014]) ).

fof(f11014,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f5127,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_278
    | ~ spl0_281 ),
    inference(duplicate_literal_removal,[],[f5091]) ).

fof(f5091,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_278
    | ~ spl0_281 ),
    inference(resolution,[],[f4519,f4507]) ).

fof(f11012,plain,
    ( spl0_491
    | ~ spl0_269
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f4774,f4474,f4470,f11010]) ).

fof(f11010,plain,
    ( spl0_491
  <=> ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f4774,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1) )
    | ~ spl0_269
    | ~ spl0_270 ),
    inference(duplicate_literal_removal,[],[f4739]) ).

fof(f4739,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_lessequals(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_lessequals(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_269
    | ~ spl0_270 ),
    inference(resolution,[],[f4475,f4471]) ).

fof(f11008,plain,
    ( spl0_490
    | ~ spl0_61
    | ~ spl0_250 ),
    inference(avatar_split_clause,[],[f4142,f3672,f1138,f11006]) ).

fof(f11006,plain,
    ( spl0_490
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f4142,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_250 ),
    inference(superposition,[],[f1139,f3673]) ).

fof(f11004,plain,
    ( spl0_489
    | ~ spl0_61
    | ~ spl0_249 ),
    inference(avatar_split_clause,[],[f4102,f3668,f1138,f11002]) ).

fof(f11002,plain,
    ( spl0_489
  <=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f4102,plain,
    ( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_61
    | ~ spl0_249 ),
    inference(superposition,[],[f1139,f3669]) ).

fof(f11000,plain,
    ( spl0_488
    | ~ spl0_38
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f2912,f2750,f1265,f1046,f10998]) ).

fof(f10998,plain,
    ( spl0_488
  <=> ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f2912,plain,
    ( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
    | ~ spl0_38
    | ~ spl0_86
    | ~ spl0_205 ),
    inference(forward_demodulation,[],[f2894,f1266]) ).

fof(f2894,plain,
    ( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat),tc_nat)
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(resolution,[],[f2751,f1047]) ).

fof(f10996,plain,
    ( spl0_487
    | ~ spl0_64
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f2472,f2193,f1150,f10994]) ).

fof(f10994,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f2472,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_64
    | ~ spl0_194 ),
    inference(superposition,[],[f2194,f1151]) ).

fof(f10992,plain,
    ( spl0_486
    | ~ spl0_64
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2449,f2189,f1150,f10990]) ).

fof(f10990,plain,
    ( spl0_486
  <=> ! [X0] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(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_486])]) ).

fof(f2449,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
    | ~ spl0_64
    | ~ spl0_193 ),
    inference(superposition,[],[f2190,f1151]) ).

fof(f10988,plain,
    ( spl0_485
    | ~ spl0_64
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f2369,f2169,f1150,f10986]) ).

fof(f10986,plain,
    ( spl0_485
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f2369,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
        | ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_64
    | ~ spl0_188 ),
    inference(superposition,[],[f2170,f1151]) ).

fof(f10984,plain,
    ( spl0_484
    | ~ spl0_64
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f2348,f2165,f1150,f10982]) ).

fof(f2348,plain,
    ( ! [X0] :
        ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_64
    | ~ spl0_187 ),
    inference(superposition,[],[f2166,f1151]) ).

fof(f10980,plain,
    ( spl0_483
    | ~ spl0_65
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2329,f2161,f1154,f10978]) ).

fof(f2329,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
        | ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) )
    | ~ spl0_65
    | ~ spl0_186 ),
    inference(superposition,[],[f2162,f1155]) ).

fof(f10976,plain,
    ( spl0_482
    | ~ spl0_111
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f8768,f5770,f1368,f10974]) ).

fof(f10974,plain,
    ( spl0_482
  <=> ! [X0] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f8768,plain,
    ( ! [X0] :
        ( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_111
    | ~ spl0_331 ),
    inference(resolution,[],[f5771,f1369]) ).

fof(f10972,plain,
    ( spl0_481
    | ~ spl0_63
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f2249,f2137,f1146,f10970]) ).

fof(f10970,plain,
    ( spl0_481
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f2249,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
        | X0 = X1 )
    | ~ spl0_63
    | ~ spl0_180 ),
    inference(superposition,[],[f2138,f1147]) ).

fof(f10968,plain,
    ( spl0_480
    | ~ spl0_32
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f2248,f2133,f1016,f10966]) ).

fof(f10966,plain,
    ( spl0_480
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f2133,plain,
    ( spl0_179
  <=> ! [X5,X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f2248,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat)
    | ~ spl0_32
    | ~ spl0_179 ),
    inference(resolution,[],[f2134,f1018]) ).

fof(f2134,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X0),X5,X0) )
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f2133]) ).

fof(f10964,plain,
    ( spl0_479
    | ~ spl0_32
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f2247,f2124,f1016,f10962]) ).

fof(f10962,plain,
    ( spl0_479
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f2124,plain,
    ( spl0_177
  <=> ! [X5,X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f2247,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat)
    | ~ spl0_32
    | ~ spl0_177 ),
    inference(resolution,[],[f2125,f1018]) ).

fof(f2125,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X5,X0) )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f2124]) ).

fof(f10960,plain,
    ( spl0_478
    | ~ spl0_64
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2218,f2116,f1150,f10958]) ).

fof(f10958,plain,
    ( spl0_478
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f2218,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
        | X0 = X1 )
    | ~ spl0_64
    | ~ spl0_175 ),
    inference(superposition,[],[f2117,f1151]) ).

fof(f10956,plain,
    ( spl0_477
    | ~ spl0_55
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1938,f1769,f1114,f10954]) ).

fof(f10954,plain,
    ( spl0_477
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f1938,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_159 ),
    inference(forward_demodulation,[],[f1931,f287]) ).

fof(f1931,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_159 ),
    inference(resolution,[],[f1770,f1115]) ).

fof(f10952,plain,
    ( spl0_476
    | ~ spl0_56
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1932,f1769,f1118,f10950]) ).

fof(f10950,plain,
    ( spl0_476
  <=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f1932,plain,
    ( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_159 ),
    inference(resolution,[],[f1770,f1119]) ).

fof(f10948,plain,
    ( spl0_475
    | ~ spl0_62
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1872,f1745,f1142,f10946]) ).

fof(f10946,plain,
    ( spl0_475
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f1872,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat)
    | ~ spl0_62
    | ~ spl0_153 ),
    inference(resolution,[],[f1746,f1143]) ).

fof(f10944,plain,
    ( spl0_474
    | ~ spl0_61
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1871,f1745,f1138,f10942]) ).

fof(f10942,plain,
    ( spl0_474
  <=> ! [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_474])]) ).

fof(f1871,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_61
    | ~ spl0_153 ),
    inference(resolution,[],[f1746,f1139]) ).

fof(f10940,plain,
    ( spl0_473
    | ~ spl0_58
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1839,f1733,f1126,f10938]) ).

fof(f10938,plain,
    ( spl0_473
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f1839,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_58
    | ~ spl0_150 ),
    inference(forward_demodulation,[],[f1833,f287]) ).

fof(f1833,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
    | ~ spl0_58
    | ~ spl0_150 ),
    inference(resolution,[],[f1734,f1127]) ).

fof(f10936,plain,
    ( spl0_472
    | ~ spl0_59
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1834,f1733,f1130,f10934]) ).

fof(f10934,plain,
    ( spl0_472
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f1834,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat)
    | ~ spl0_59
    | ~ spl0_150 ),
    inference(resolution,[],[f1734,f1131]) ).

fof(f10932,plain,
    ( spl0_471
    | ~ spl0_204
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f3658,f3316,f2510,f10930]) ).

fof(f10930,plain,
    ( spl0_471
  <=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f3316,plain,
    ( spl0_240
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f3658,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1),X3)
    | ~ spl0_204
    | ~ spl0_240 ),
    inference(superposition,[],[f3317,f2511]) ).

fof(f3317,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f3316]) ).

fof(f10928,plain,
    ( spl0_470
    | ~ spl0_128
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1672,f1528,f1516,f10926]) ).

fof(f10926,plain,
    ( spl0_470
  <=> ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f1672,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2) )
    | ~ spl0_128
    | ~ spl0_131 ),
    inference(duplicate_literal_removal,[],[f1663]) ).

fof(f1663,plain,
    ( ! [X2,X0,X1] :
        ( c_lessequals(X1,X0,X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ class_Orderings_Olinorder(X2)
        | ~ c_HOL_Oord__class_Oless(X1,X0,X2) )
    | ~ spl0_128
    | ~ spl0_131 ),
    inference(resolution,[],[f1529,f1517]) ).

fof(f10924,plain,
    ( spl0_469
    | ~ spl0_86
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1654,f1524,f1265,f10922]) ).

fof(f10922,plain,
    ( spl0_469
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f1654,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_130 ),
    inference(superposition,[],[f1525,f1266]) ).

fof(f10920,plain,
    ( spl0_468
    | ~ spl0_81
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1595,f1486,f1230,f10918]) ).

fof(f10918,plain,
    ( spl0_468
  <=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f1595,plain,
    ( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0
    | ~ spl0_81
    | ~ spl0_121 ),
    inference(resolution,[],[f1487,f1231]) ).

fof(f10916,plain,
    ( spl0_467
    | ~ spl0_86
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1582,f1458,f1265,f10914]) ).

fof(f10914,plain,
    ( spl0_467
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f1582,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_86
    | ~ spl0_114 ),
    inference(superposition,[],[f1459,f1266]) ).

fof(f10405,plain,
    ( spl0_466
    | ~ spl0_50
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6030,f5762,f1094,f10403]) ).

fof(f10403,plain,
    ( spl0_466
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_Lambda_OdB_OApp(X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f1094,plain,
    ( spl0_50
  <=> ! [X36,X39,X35] : c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OAbs(X39) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f6030,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_Lambda_OdB_OApp(X3,X4)
    | ~ spl0_50
    | ~ spl0_329 ),
    inference(superposition,[],[f1095,f5763]) ).

fof(f1095,plain,
    ( ! [X39,X36,X35] : c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OAbs(X39)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f1094]) ).

fof(f10401,plain,
    ( spl0_465
    | ~ spl0_52
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5257,f4534,f1102,f10399]) ).

fof(f10399,plain,
    ( spl0_465
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f1102,plain,
    ( spl0_52
  <=> ! [X38,X37,X12] : c_Lambda_OdB_OApp(X37,X38) != c_Lambda_OdB_OVar(X12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f5257,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
    | ~ spl0_52
    | ~ spl0_285 ),
    inference(superposition,[],[f1103,f4535]) ).

fof(f1103,plain,
    ( ! [X38,X37,X12] : c_Lambda_OdB_OApp(X37,X38) != c_Lambda_OdB_OVar(X12)
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f1102]) ).

fof(f10397,plain,
    ( spl0_464
    | ~ spl0_50
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f5256,f4534,f1094,f10395]) ).

fof(f10395,plain,
    ( spl0_464
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f5256,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
    | ~ spl0_50
    | ~ spl0_285 ),
    inference(superposition,[],[f1095,f4535]) ).

fof(f10393,plain,
    ( spl0_463
    | ~ spl0_52
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f5186,f4526,f1102,f10391]) ).

fof(f10391,plain,
    ( spl0_463
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OVar(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f5186,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OVar(X4)
    | ~ spl0_52
    | ~ spl0_283 ),
    inference(superposition,[],[f1103,f4527]) ).

fof(f10389,plain,
    ( spl0_462
    | ~ spl0_50
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f5185,f4526,f1094,f10387]) ).

fof(f10387,plain,
    ( spl0_462
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OAbs(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f5185,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) != c_Lambda_OdB_OAbs(X4)
    | ~ spl0_50
    | ~ spl0_283 ),
    inference(superposition,[],[f1095,f4527]) ).

fof(f10385,plain,
    ( spl0_461
    | ~ spl0_57
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f4303,f3688,f1265,f1146,f1122,f10383]) ).

fof(f1122,plain,
    ( spl0_57
  <=> ! [X9,X10] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X9,X10) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f4303,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
    | ~ spl0_57
    | ~ spl0_63
    | ~ spl0_86
    | ~ spl0_254 ),
    inference(forward_demodulation,[],[f4302,f1147]) ).

fof(f4302,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,X1)
    | ~ spl0_57
    | ~ spl0_86
    | ~ spl0_254 ),
    inference(forward_demodulation,[],[f4289,f1266]) ).

fof(f4289,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X1)
    | ~ spl0_57
    | ~ spl0_254 ),
    inference(superposition,[],[f3689,f1123]) ).

fof(f1123,plain,
    ( ! [X10,X9] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X9,X10) = X9
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f1122]) ).

fof(f10381,plain,
    ( spl0_460
    | ~ spl0_50
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3821,f3651,f1094,f10379]) ).

fof(f10379,plain,
    ( spl0_460
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OApp(X3,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f3821,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OApp(X3,X4)
    | ~ spl0_50
    | ~ spl0_245 ),
    inference(superposition,[],[f1095,f3652]) ).

fof(f10377,plain,
    ( spl0_459
    | ~ spl0_159
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f2421,f2185,f1769,f10375]) ).

fof(f10375,plain,
    ( spl0_459
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f2421,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) )
    | ~ spl0_159
    | ~ spl0_192 ),
    inference(resolution,[],[f2186,f1770]) ).

fof(f10373,plain,
    ( spl0_458
    | ~ spl0_150
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f2406,f2181,f1733,f10371]) ).

fof(f10371,plain,
    ( spl0_458
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f2406,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
    | ~ spl0_150
    | ~ spl0_191 ),
    inference(resolution,[],[f2182,f1734]) ).

fof(f10369,plain,
    ( spl0_457
    | ~ spl0_159
    | ~ spl0_190 ),
    inference(avatar_split_clause,[],[f2390,f2177,f1769,f10367]) ).

fof(f10367,plain,
    ( spl0_457
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f2390,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) )
    | ~ spl0_159
    | ~ spl0_190 ),
    inference(resolution,[],[f2178,f1770]) ).

fof(f10365,plain,
    ( spl0_456
    | ~ spl0_109
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f3830,f3700,f1360,f10363]) ).

fof(f10363,plain,
    ( spl0_456
  <=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))))),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f3700,plain,
    ( spl0_257
  <=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f3830,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))))),X1)
    | ~ spl0_109
    | ~ spl0_257 ),
    inference(resolution,[],[f3701,f1361]) ).

fof(f3701,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))),X1)
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f3700]) ).

fof(f10361,plain,
    ( spl0_455
    | ~ spl0_150
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2375,f2173,f1733,f10359]) ).

fof(f10359,plain,
    ( spl0_455
  <=> ! [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_455])]) ).

fof(f2375,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_150
    | ~ spl0_189 ),
    inference(resolution,[],[f2174,f1734]) ).

fof(f10357,plain,
    ( spl0_454
    | ~ spl0_63
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1918,f1765,f1146,f10355]) ).

fof(f10355,plain,
    ( spl0_454
  <=> ! [X0,X1] :
        ( c_lessequals(X1,X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1918,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X1,X0,tc_nat)
        | ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_63
    | ~ spl0_158 ),
    inference(superposition,[],[f1766,f1147]) ).

fof(f10353,plain,
    ( spl0_453
    | ~ spl0_17
    | ~ spl0_155 ),
    inference(avatar_split_clause,[],[f1897,f1753,f941,f10351]) ).

fof(f10351,plain,
    ( spl0_453
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1753,plain,
    ( spl0_155
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X2,X5,X0) = c_HOL_Otimes__class_Otimes(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1897,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
    | ~ spl0_17
    | ~ spl0_155 ),
    inference(resolution,[],[f1754,f943]) ).

fof(f1754,plain,
    ( ! [X2,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X2,X5,X0) = c_HOL_Otimes__class_Otimes(X5,X2,X0) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1753]) ).

fof(f10349,plain,
    ( spl0_452
    | ~ spl0_54
    | ~ spl0_154 ),
    inference(avatar_split_clause,[],[f1889,f1749,f1110,f10347]) ).

fof(f10347,plain,
    ( spl0_452
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X0
        | c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f1889,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != X0
        | c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
    | ~ spl0_54
    | ~ spl0_154 ),
    inference(superposition,[],[f1750,f1111]) ).

fof(f10345,plain,
    ( spl0_451
    | ~ spl0_64
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1866,f1741,f1150,f10343]) ).

fof(f1866,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_64
    | ~ spl0_152 ),
    inference(superposition,[],[f1742,f1151]) ).

fof(f10341,plain,
    ( spl0_450
    | ~ spl0_77
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1680,f1552,f1214,f10339]) ).

fof(f10339,plain,
    ( spl0_450
  <=> ! [X0,X1] : c_Lambda_Obeta(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_450])]) ).

fof(f1680,plain,
    ( ! [X0,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat))),X1),X0)
    | ~ spl0_77
    | ~ spl0_137 ),
    inference(superposition,[],[f1553,f1215]) ).

fof(f10337,plain,
    ( spl0_449
    | ~ spl0_86
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f1451,f1364,f1265,f10335]) ).

fof(f10335,plain,
    ( spl0_449
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1451,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
    | ~ spl0_86
    | ~ spl0_110 ),
    inference(superposition,[],[f1365,f1266]) ).

fof(f10249,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f67,f10247]) ).

fof(f10247,plain,
    ( spl0_448
  <=> ! [X5,X17,X16,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X6,X0) != c_Divides_Odiv__class_Omod(X17,X6,X0)
        | c_Divides_Odiv__class_Omod(X5,X6,X0) != c_Divides_Odiv__class_Omod(X16,X6,X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f67,axiom,
    ! [X2,X0,X6,X16,X17,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X6,X0) != c_Divides_Odiv__class_Omod(X17,X6,X0)
      | c_Divides_Odiv__class_Omod(X5,X6,X0) != c_Divides_Odiv__class_Omod(X16,X6,X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X17,X16,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

fof(f10245,plain,
    spl0_447,
    inference(avatar_split_clause,[],[f39,f10243]) ).

fof(f10243,plain,
    ( spl0_447
  <=> ! [X5,X17,X16,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,X6,X0) != c_Divides_Odiv__class_Omod(X17,X6,X0)
        | c_Divides_Odiv__class_Omod(X5,X6,X0) != c_Divides_Odiv__class_Omod(X16,X6,X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f39,axiom,
    ! [X2,X0,X6,X16,X17,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X6,X0) != c_Divides_Odiv__class_Omod(X17,X6,X0)
      | c_Divides_Odiv__class_Omod(X5,X6,X0) != c_Divides_Odiv__class_Omod(X16,X6,X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X17,X16,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

fof(f10175,plain,
    spl0_446,
    inference(avatar_split_clause,[],[f820,f10173]) ).

fof(f10173,plain,
    ( spl0_446
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X2 = X5
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) != c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f820,plain,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X2 = X5
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) != c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f537,f149,f149]) ).

fof(f149,axiom,
    ! [X4] : c_Suc(X4) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

fof(f537,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X2 = X5
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_Power_Opower__class_Opower(X2,c_Suc(X4),X0) != c_Power_Opower__class_Opower(X5,c_Suc(X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

fof(f10171,plain,
    spl0_445,
    inference(avatar_split_clause,[],[f799,f10169]) ).

fof(f10169,plain,
    ( spl0_445
  <=> ! [X18,X33,X9,X29,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_Lambda_Osubst(c_Lambda_Osubst(X9,X29,X19),X33,X18) = c_Lambda_Osubst(c_Lambda_Osubst(X9,c_Lambda_Olift(X33,X19),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Osubst(X29,X33,X18),X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f799,plain,
    ! [X29,X18,X19,X9,X33] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Osubst(c_Lambda_Osubst(X9,X29,X19),X33,X18) = c_Lambda_Osubst(c_Lambda_Osubst(X9,c_Lambda_Olift(X33,X19),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Osubst(X29,X33,X18),X19) ),
    inference(definition_unfolding,[],[f594,f149]) ).

fof(f594,axiom,
    ! [X29,X18,X19,X9,X33] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Osubst(c_Lambda_Osubst(X9,c_Lambda_Olift(X33,X19),c_Suc(X18)),c_Lambda_Osubst(X29,X33,X18),X19) = c_Lambda_Osubst(c_Lambda_Osubst(X9,X29,X19),X33,X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).

fof(f9938,plain,
    spl0_444,
    inference(avatar_split_clause,[],[f539,f9936]) ).

fof(f9936,plain,
    ( spl0_444
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(X6,X15,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f539,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(X6,X15,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

fof(f9934,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f538,f9932]) ).

fof(f9932,plain,
    ( spl0_443
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Opordered__semiring(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(X6,X15,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f538,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Opordered__semiring(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(X6,X15,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

fof(f9930,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f423,f9928]) ).

fof(f9928,plain,
    ( spl0_442
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f423,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

fof(f9926,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f253,f9924]) ).

fof(f9924,plain,
    ( spl0_441
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f253,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

fof(f9922,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f252,f9920]) ).

fof(f9920,plain,
    ( spl0_440
  <=> ! [X5,X2,X0,X6,X15] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_lessequals(X6,X15,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f252,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_lessequals(X6,X15,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

fof(f9918,plain,
    spl0_439,
    inference(avatar_split_clause,[],[f129,f9916]) ).

fof(f9916,plain,
    ( spl0_439
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f129,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

fof(f9876,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f818,f9874]) ).

fof(f9874,plain,
    ( spl0_438
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f818,plain,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_Power_Opower__class_Opower(X5,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ),
    inference(definition_unfolding,[],[f243,f149,f149]) ).

fof(f243,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X2,c_Suc(X4),X0),c_Power_Opower__class_Opower(X5,c_Suc(X4),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

fof(f9872,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f508,f9870]) ).

fof(f9870,plain,
    ( spl0_437
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X2 = X5
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_Power_Opower__class_Opower(X2,X4,X0) != c_Power_Opower__class_Opower(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f508,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X2 = X5
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_Power_Opower__class_Opower(X2,X4,X0) != c_Power_Opower__class_Opower(X5,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

fof(f9218,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f836,f9216]) ).

fof(f836,plain,
    ! [X3,X10,X18] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat),X3,tc_nat)
      | ~ c_lessequals(X10,X18,tc_nat) ),
    inference(forward_demodulation,[],[f771,f90]) ).

fof(f90,axiom,
    ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

fof(f771,plain,
    ! [X3,X10,X18] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f135,f149,f149]) ).

fof(f135,axiom,
    ! [X3,X10,X18] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat)),X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X18),c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

fof(f9214,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f835,f9212]) ).

fof(f9212,plain,
    ( spl0_435
  <=> ! [X18,X3,X10] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X10,X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f835,plain,
    ! [X3,X10,X18] :
      ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X10,X18,tc_nat) ),
    inference(forward_demodulation,[],[f770,f90]) ).

fof(f770,plain,
    ! [X3,X10,X18] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f225,f149,f149]) ).

fof(f225,axiom,
    ! [X3,X10,X18] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(X3,c_Suc(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_Suc(X18),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

fof(f9210,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f797,f9208]) ).

fof(f9208,plain,
    ( spl0_434
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f797,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f158,f149,f149,f149]) ).

fof(f158,axiom,
    ! [X3,X4] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X3,X4,tc_nat)) = X4
      | c_Divides_Odiv__class_Omod(c_Suc(X3),X4,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X3,X4,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

fof(f9206,plain,
    ( spl0_433
    | ~ spl0_43
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f6028,f5762,f1066,f9204]) ).

fof(f9204,plain,
    ( spl0_433
  <=> ! [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_433])]) ).

fof(f1066,plain,
    ( spl0_43
  <=> ! [X12,X39] : c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OVar(X12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f6028,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X0),X1,X2) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_43
    | ~ spl0_329 ),
    inference(superposition,[],[f1067,f5763]) ).

fof(f1067,plain,
    ( ! [X39,X12] : c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OVar(X12)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f1066]) ).

fof(f9202,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f598,f9200]) ).

fof(f9200,plain,
    ( spl0_432
  <=> ! [X18,X9,X27,X19] :
        ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Osubst(X9,X27,X18),X19) = c_Lambda_Osubst(c_Lambda_Olift(X9,X19),c_Lambda_Olift(X27,X19),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f598,axiom,
    ! [X18,X19,X9,X27] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Olift(c_Lambda_Osubst(X9,X27,X18),X19) = c_Lambda_Osubst(c_Lambda_Olift(X9,X19),c_Lambda_Olift(X27,X19),c_HOL_Oplus__class_Oplus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).

fof(f9198,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f585,f9196]) ).

fof(f9196,plain,
    ( spl0_431
  <=> ! [X18,X9,X27,X19] :
        ( ~ c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
        | c_Lambda_Olift(c_Lambda_Osubst(X9,X27,X18),X19) = c_Lambda_Osubst(c_Lambda_Olift(X9,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X27,X19),X18) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f585,axiom,
    ! [X18,X19,X9,X27] :
      ( ~ c_HOL_Oord__class_Oless(X18,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Olift(c_Lambda_Osubst(X9,X27,X18),X19) = c_Lambda_Osubst(c_Lambda_Olift(X9,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(X27,X19),X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).

fof(f9098,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f607,f9096]) ).

fof(f9096,plain,
    ( spl0_430
  <=> ! [X2,X4,X0,X28] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X28,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X28,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f607,axiom,
    ! [X2,X28,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X28,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X28,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

fof(f9094,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f356,f9092]) ).

fof(f9092,plain,
    ( spl0_429
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f356,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

fof(f9090,plain,
    spl0_428,
    inference(avatar_split_clause,[],[f351,f9088]) ).

fof(f9088,plain,
    ( spl0_428
  <=> ! [X5,X0,X14,X6,X2] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X14,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,X0),X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X14,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f351,axiom,
    ! [X2,X0,X6,X14,X5] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X14,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X14,X0),X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X14,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f9086,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f103,f9084]) ).

fof(f9084,plain,
    ( spl0_427
  <=> ! [X2,X4,X0,X28] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X4,X28,tc_nat)
        | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_Power_Opower__class_Opower(X2,X28,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f103,axiom,
    ! [X2,X28,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X4,X28,tc_nat)
      | ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_Power_Opower__class_Opower(X2,X28,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

fof(f9055,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f518,f9053]) ).

fof(f9053,plain,
    ( spl0_426
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f518,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

fof(f9028,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f819,f9026]) ).

fof(f9026,plain,
    ( spl0_425
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f819,plain,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_HOL_Oone__class_Oone(X0),X0) ),
    inference(definition_unfolding,[],[f283,f149]) ).

fof(f283,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,c_Suc(X4),X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

fof(f8732,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f844,f8730]) ).

fof(f8730,plain,
    ( spl0_424
  <=> ! [X4,X3,X10] :
        ( c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat),tc_nat)
        | ~ c_lessequals(X10,X3,tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f844,plain,
    ! [X3,X10,X4] :
      ( c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X10,c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat),tc_nat)
      | ~ c_lessequals(X10,X3,tc_nat)
      | ~ c_lessequals(X10,X4,tc_nat) ),
    inference(forward_demodulation,[],[f362,f330]) ).

fof(f362,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X10,X3,tc_nat)
      | ~ c_lessequals(X10,X4,tc_nat)
      | c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

fof(f8728,plain,
    spl0_423,
    inference(avatar_split_clause,[],[f831,f8726]) ).

fof(f831,plain,
    ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f754,f330]) ).

fof(f754,plain,
    ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f503,f149,f149]) ).

fof(f503,axiom,
    ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X10),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X10,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

fof(f8724,plain,
    spl0_422,
    inference(avatar_split_clause,[],[f798,f8722]) ).

fof(f798,plain,
    ! [X10,X19,X9] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Olift(c_Lambda_Olift(X9,X10),X19) = c_Lambda_Olift(c_Lambda_Olift(X9,X19),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    inference(definition_unfolding,[],[f584,f149]) ).

fof(f584,axiom,
    ! [X10,X19,X9] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
      | c_Lambda_Olift(c_Lambda_Olift(X9,X19),c_Suc(X10)) = c_Lambda_Olift(c_Lambda_Olift(X9,X10),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).

fof(f8720,plain,
    spl0_421,
    inference(avatar_split_clause,[],[f506,f8718]) ).

fof(f8718,plain,
    ( spl0_421
  <=> ! [X2,X6,X0,X5,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Oplus__class_Oplus(X6,X15,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f506,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Oplus__class_Oplus(X6,X15,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f8716,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f177,f8714]) ).

fof(f8714,plain,
    ( spl0_420
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X6,X0),c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f177,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X6,X0),c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

fof(f8712,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f70,f8710]) ).

fof(f8710,plain,
    ( spl0_419
  <=> ! [X24,X0,X22,X23,X25] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,X0),c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),c_HOL_Otimes__class_Otimes(X23,X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f70,axiom,
    ! [X0,X24,X22,X25,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,X0),c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),c_HOL_Otimes__class_Otimes(X23,X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f8708,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f22,f8706]) ).

fof(f8706,plain,
    ( spl0_418
  <=> ! [X11,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f22,axiom,
    ! [X0,X11,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

fof(f8635,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f21,f8633]) ).

fof(f8633,plain,
    ( spl0_417
  <=> ! [X0,X11,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X11
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f21,axiom,
    ! [X0,X11,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X11
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

fof(f8631,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f15,f8629]) ).

fof(f8629,plain,
    ( spl0_416
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X6,X0),c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f15,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X6,X0),c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

fof(f8547,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f640,f8545]) ).

fof(f8545,plain,
    ( spl0_415
  <=> ! [X4,X3,X10] :
        ( ~ c_lessequals(X10,X3,tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f640,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X10,X3,tc_nat)
      | ~ c_lessequals(X10,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

fof(f8543,plain,
    spl0_414,
    inference(avatar_split_clause,[],[f328,f8541]) ).

fof(f8541,plain,
    ( spl0_414
  <=> ! [X4,X3,X10] :
        ( ~ c_lessequals(X10,X3,tc_nat)
        | ~ c_lessequals(X10,X4,tc_nat)
        | c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f328,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X10,X3,tc_nat)
      | ~ c_lessequals(X10,X4,tc_nat)
      | c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X10,tc_nat),c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

fof(f7974,plain,
    ( spl0_413
    | ~ spl0_62
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f7745,f5668,f1142,f7972]) ).

fof(f5668,plain,
    ( spl0_319
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f7745,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
    | ~ spl0_62
    | ~ spl0_319 ),
    inference(resolution,[],[f5669,f1143]) ).

fof(f5669,plain,
    ( ! [X0,X1] :
        ( ~ c_lessequals(X1,X0,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f5668]) ).

fof(f7794,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f796,f7792]) ).

fof(f7792,plain,
    ( spl0_412
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f796,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f495,f149,f149]) ).

fof(f495,axiom,
    ! [X3,X4] :
      ( c_Suc(c_Divides_Odiv__class_Omod(X3,X4,tc_nat)) != X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

fof(f7790,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f780,f7788]) ).

fof(f780,plain,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f186,f149]) ).

fof(f186,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

fof(f7786,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f645,f7784]) ).

fof(f7784,plain,
    ( spl0_410
  <=> ! [X4,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f645,axiom,
    ! [X2,X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X3,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

fof(f7741,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f642,f7739]) ).

fof(f7739,plain,
    ( spl0_409
  <=> ! [X11,X0,X5,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X11,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
        | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f642,axiom,
    ! [X0,X11,X1,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

fof(f7737,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f572,f7735]) ).

fof(f7735,plain,
    ( spl0_408
  <=> ! [X11,X0,X5,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X1,X11,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
        | c_lessequals(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f572,axiom,
    ! [X0,X11,X1,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X1,X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
      | c_lessequals(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

fof(f7733,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f571,f7731]) ).

fof(f7731,plain,
    ( spl0_407
  <=> ! [X11,X0,X5,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(X1,X11,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
        | ~ c_lessequals(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f571,axiom,
    ! [X0,X11,X1,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X1,X11,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
      | ~ c_lessequals(c_Power_Opower__class_Opower(X5,X1,X0),c_Power_Opower__class_Opower(X5,X11,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).

fof(f7729,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f536,f7727]) ).

fof(f7727,plain,
    ( spl0_406
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f536,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

fof(f7725,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f533,f7723]) ).

fof(f7723,plain,
    ( spl0_405
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f533,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

fof(f7721,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f529,f7719]) ).

fof(f7719,plain,
    ( spl0_404
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f529,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

fof(f7717,plain,
    spl0_403,
    inference(avatar_split_clause,[],[f388,f7715]) ).

fof(f7715,plain,
    ( spl0_403
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Omult__mono1(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f388,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Omult__mono1(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

fof(f7713,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f387,f7711]) ).

fof(f7711,plain,
    ( spl0_402
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Omult__mono(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f387,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Omult__mono(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

fof(f7709,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f386,f7707]) ).

fof(f7707,plain,
    ( spl0_401
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Omult__mono(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f386,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Omult__mono(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

fof(f7705,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f344,f7703]) ).

fof(f7703,plain,
    ( spl0_400
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_lessequals(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f344,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

fof(f7701,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f343,f7699]) ).

fof(f7699,plain,
    ( spl0_399
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_lessequals(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f343,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

fof(f7697,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f331,f7695]) ).

fof(f7695,plain,
    ( spl0_398
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f331,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

fof(f7693,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f324,f7691]) ).

fof(f7691,plain,
    ( spl0_397
  <=> ! [X2,X4,X0,X28] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(X4,X28,tc_nat)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_lessequals(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X2,X28,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f324,axiom,
    ! [X2,X28,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X4,X28,tc_nat)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_lessequals(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X2,X28,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).

fof(f7689,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f51,f7687]) ).

fof(f7687,plain,
    ( spl0_396
  <=> ! [X4,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f51,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

fof(f7685,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f7,f7683]) ).

fof(f7683,plain,
    ( spl0_395
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f7,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

fof(f7681,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f6,f7679]) ).

fof(f7679,plain,
    ( spl0_394
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f6,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

fof(f7677,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f5,f7675]) ).

fof(f7675,plain,
    ( spl0_393
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f5,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

fof(f7673,plain,
    spl0_392,
    inference(avatar_split_clause,[],[f4,f7671]) ).

fof(f7671,plain,
    ( spl0_392
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f4,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

fof(f6700,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f828,f6698]) ).

fof(f828,plain,
    ! [X3,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X3,X4,tc_nat),tc_nat),X4,tc_nat),
    inference(forward_demodulation,[],[f750,f90]) ).

fof(f750,plain,
    ! [X3,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
    inference(definition_unfolding,[],[f396,f149,f149]) ).

fof(f396,axiom,
    ! [X3,X4] : c_Divides_Odiv__class_Omod(c_Suc(X3),X4,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X3,X4,tc_nat)),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

fof(f6696,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f599,f6694]) ).

fof(f6694,plain,
    ( spl0_390
  <=> ! [X4,X0,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f599,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

fof(f6692,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f582,f6690]) ).

fof(f6690,plain,
    ( spl0_389
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f582,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

fof(f6688,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f574,f6686]) ).

fof(f574,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_lessequals(X6,X15,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

fof(f6684,plain,
    spl0_387,
    inference(avatar_split_clause,[],[f573,f6682]) ).

fof(f573,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

fof(f6680,plain,
    spl0_386,
    inference(avatar_split_clause,[],[f500,f6678]) ).

fof(f500,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).

fof(f6676,plain,
    spl0_385,
    inference(avatar_split_clause,[],[f499,f6674]) ).

fof(f499,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).

fof(f6672,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f479,f6670]) ).

fof(f479,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X11,X21,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f6668,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f478,f6666]) ).

fof(f6666,plain,
    ( spl0_383
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f478,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f6659,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f477,f6657]) ).

fof(f477,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f6655,plain,
    spl0_381,
    inference(avatar_split_clause,[],[f468,f6653]) ).

fof(f468,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X2,X0),c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) = c_HOL_Otimes__class_Otimes(X6,c_Divides_Odiv__class_Omod(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

fof(f6651,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f467,f6649]) ).

fof(f467,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X6,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X2,X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

fof(f6647,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f460,f6645]) ).

fof(f6645,plain,
    ( spl0_379
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f460,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

fof(f6643,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f444,f6641]) ).

fof(f444,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X5,X6,X0),X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

fof(f6639,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f443,f6637]) ).

fof(f443,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X2,X6,X0),X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).

fof(f6635,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f442,f6633]) ).

fof(f6633,plain,
    ( spl0_376
  <=> ! [X11,X0,X8,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X11,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X11,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f442,axiom,
    ! [X0,X11,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X11,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X11,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

fof(f6631,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f441,f6629]) ).

fof(f441,axiom,
    ! [X2,X0,X4,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X5,X0),X4,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),c_Power_Opower__class_Opower(X5,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

fof(f6627,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f409,f6625]) ).

fof(f6625,plain,
    ( spl0_374
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f409,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

fof(f6623,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f383,f6621]) ).

fof(f6621,plain,
    ( spl0_373
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f383,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X2,X4,X0),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

fof(f6602,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f375,f6600]) ).

fof(f6600,plain,
    ( spl0_372
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f375,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

fof(f6598,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f372,f6596]) ).

fof(f6596,plain,
    ( spl0_371
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
        | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f372,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

fof(f6594,plain,
    spl0_370,
    inference(avatar_split_clause,[],[f367,f6592]) ).

fof(f6592,plain,
    ( spl0_370
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f367,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

fof(f6590,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f366,f6588]) ).

fof(f6588,plain,
    ( spl0_369
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f366,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

fof(f6586,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f355,f6584]) ).

fof(f6584,plain,
    ( spl0_368
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f355,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f6582,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f332,f6580]) ).

fof(f332,axiom,
    ! [X3,X10,X4] :
      ( X3 = X4
      | ~ c_lessequals(X10,X3,tc_nat)
      | ~ c_lessequals(X10,X4,tc_nat)
      | c_HOL_Ominus__class_Ominus(X3,X10,tc_nat) != c_HOL_Ominus__class_Ominus(X4,X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

fof(f6578,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f323,f6576]) ).

fof(f323,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

fof(f6574,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f296,f6572]) ).

fof(f6572,plain,
    ( spl0_365
  <=> ! [X4,X0,X3,X2] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f296,axiom,
    ! [X2,X3,X0,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X3,X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).

fof(f6570,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f270,f6568]) ).

fof(f6568,plain,
    ( spl0_364
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f270,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

fof(f6566,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f269,f6564]) ).

fof(f6564,plain,
    ( spl0_363
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f269,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

fof(f6530,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f257,f6528]) ).

fof(f6528,plain,
    ( spl0_362
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f257,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

fof(f6526,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f213,f6524]) ).

fof(f6524,plain,
    ( spl0_361
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f213,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X15,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f6522,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f195,f6520]) ).

fof(f6520,plain,
    ( spl0_360
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f195,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f6518,plain,
    spl0_359,
    inference(avatar_split_clause,[],[f178,f6516]) ).

fof(f6516,plain,
    ( spl0_359
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f178,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

fof(f6514,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f168,f6512]) ).

fof(f6512,plain,
    ( spl0_358
  <=> ! [X15,X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
        | ~ c_lessequals(X2,X5,X0)
        | ~ c_lessequals(X6,X15,X0)
        | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f168,axiom,
    ! [X2,X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X5,X0)
      | ~ c_lessequals(X6,X15,X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

fof(f6510,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f142,f6508]) ).

fof(f142,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X5,X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

fof(f6506,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f114,f6504]) ).

fof(f6504,plain,
    ( spl0_356
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X5,X6,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f114,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X5,X6,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

fof(f6502,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f113,f6500]) ).

fof(f6500,plain,
    ( spl0_355
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_lessequals(X5,X2,X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
        | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f113,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X5,X2,X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
      | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

fof(f6498,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f62,f6496]) ).

fof(f6496,plain,
    ( spl0_354
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f62,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

fof(f6494,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f61,f6492]) ).

fof(f6492,plain,
    ( spl0_353
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f61,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

fof(f6490,plain,
    ( spl0_352
    | ~ spl0_43
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f3819,f3651,f1066,f6488]) ).

fof(f6488,plain,
    ( spl0_352
  <=> ! [X2,X0,X1,X3] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OVar(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f3819,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_43
    | ~ spl0_245 ),
    inference(superposition,[],[f1067,f3652]) ).

fof(f6486,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f49,f6484]) ).

fof(f6484,plain,
    ( spl0_351
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f49,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

fof(f6482,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f48,f6480]) ).

fof(f6480,plain,
    ( spl0_350
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f48,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

fof(f6478,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f47,f6476]) ).

fof(f6476,plain,
    ( spl0_349
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f47,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

fof(f6474,plain,
    spl0_348,
    inference(avatar_split_clause,[],[f17,f6472]) ).

fof(f17,axiom,
    ! [X0,X1,X8,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X7,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).

fof(f6303,plain,
    ( spl0_347
    | ~ spl0_50
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2742,f2510,f1094,f6301]) ).

fof(f6301,plain,
    ( spl0_347
  <=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_Lambda_OdB_OApp(X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f2742,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1) != c_Lambda_OdB_OApp(X2,X3)
    | ~ spl0_50
    | ~ spl0_204 ),
    inference(superposition,[],[f1095,f2511]) ).

fof(f6173,plain,
    spl0_346,
    inference(avatar_split_clause,[],[f815,f6171]) ).

fof(f815,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
      | c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f520,f149,f149]) ).

fof(f520,axiom,
    ! [X3,X4] :
      ( c_Suc(X4) = X3
      | c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

fof(f6169,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f808,f6167]) ).

fof(f808,plain,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f378,f149,f149]) ).

fof(f378,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_Suc(X3) = X4
      | c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

fof(f6165,plain,
    spl0_344,
    inference(avatar_split_clause,[],[f801,f6163]) ).

fof(f801,plain,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ),
    inference(definition_unfolding,[],[f224,f149]) ).

fof(f224,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,c_Suc(X4),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

fof(f6161,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f639,f6159]) ).

fof(f6159,plain,
    ( spl0_343
  <=> ! [X4,X0,X3,X2] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | X3 = X4
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
        | c_Power_Opower__class_Opower(X2,X4,X0) != c_Power_Opower__class_Opower(X2,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f639,axiom,
    ! [X2,X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | X3 = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_Power_Opower__class_Opower(X2,X4,X0) != c_Power_Opower__class_Opower(X2,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

fof(f6157,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f247,f6155]) ).

fof(f6155,plain,
    ( spl0_342
  <=> ! [X2,X0,X4] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f247,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

fof(f6153,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f242,f6151]) ).

fof(f6151,plain,
    ( spl0_341
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X10,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f242,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

fof(f6149,plain,
    spl0_340,
    inference(avatar_split_clause,[],[f241,f6147]) ).

fof(f6147,plain,
    ( spl0_340
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X10,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f241,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Oplus__class_Oplus(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

fof(f6145,plain,
    spl0_339,
    inference(avatar_split_clause,[],[f183,f6143]) ).

fof(f6143,plain,
    ( spl0_339
  <=> ! [X18,X19,X10] :
        ( ~ c_lessequals(X10,X18,tc_nat)
        | c_HOL_Ominus__class_Ominus(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f183,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | c_HOL_Ominus__class_Ominus(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

fof(f6141,plain,
    ( spl0_338
    | ~ spl0_52
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2641,f2498,f1102,f6139]) ).

fof(f6139,plain,
    ( spl0_338
  <=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OVar(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f2641,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_52
    | ~ spl0_201 ),
    inference(superposition,[],[f1103,f2499]) ).

fof(f5899,plain,
    ( spl0_337
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f2640,f2498,f1094,f5897]) ).

fof(f5897,plain,
    ( spl0_337
  <=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OAbs(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f2640,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OAbs(X3)
    | ~ spl0_50
    | ~ spl0_201 ),
    inference(superposition,[],[f1095,f2499]) ).

fof(f5792,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f761,f5790]) ).

fof(f5790,plain,
    ( spl0_336
  <=> ! [X0,X1,X8] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f761,plain,
    ! [X0,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f261,f149]) ).

fof(f261,axiom,
    ! [X0,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

fof(f5788,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f758,f5786]) ).

fof(f5786,plain,
    ( spl0_335
  <=> ! [X4,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X4,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f758,plain,
    ! [X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X4,X0),X0) = c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f165,f149]) ).

fof(f165,axiom,
    ! [X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Power_Opower__class_Opower(X1,c_Suc(X4),X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

fof(f5784,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f757,f5782]) ).

fof(f757,plain,
    ! [X2,X0,X4] :
      ( ~ class_Power_Opower(X0)
      | c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f164,f149]) ).

fof(f164,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Power_Opower(X0)
      | c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) = c_Power_Opower__class_Opower(X2,c_Suc(X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).

fof(f5780,plain,
    spl0_333,
    inference(avatar_split_clause,[],[f756,f5778]) ).

fof(f756,plain,
    ! [X2,X0,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_Power_Opower__class_Opower(X2,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f163,f149]) ).

fof(f163,axiom,
    ! [X2,X0,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_Power_Opower__class_Opower(X2,c_Suc(X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

fof(f5776,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f610,f5774]) ).

fof(f610,axiom,
    ! [X3,X26,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X26,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

fof(f5772,plain,
    ( spl0_331
    | ~ spl0_192
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f2437,f2189,f2185,f5770]) ).

fof(f2437,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_192
    | ~ spl0_193 ),
    inference(resolution,[],[f2190,f2186]) ).

fof(f5768,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f596,f5766]) ).

fof(f596,axiom,
    ! [X2,X6,X5] :
      ( ~ c_lessequals(X6,X2,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X2,X5,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X6,tc_nat),c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

fof(f5764,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f595,f5762]) ).

fof(f595,axiom,
    ! [X10,X9,X27] : c_Lambda_Osubst(c_Lambda_OdB_OAbs(X9),X27,X10) = c_Lambda_OdB_OAbs(c_Lambda_Osubst(X9,c_Lambda_Olift(X27,c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).

fof(f5760,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f295,f5758]) ).

fof(f295,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

fof(f5756,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f276,f5754]) ).

fof(f276,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f5752,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f214,f5750]) ).

fof(f214,axiom,
    ! [X10,X18,X19,X26] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

fof(f5748,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f203,f5746]) ).

fof(f203,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

fof(f5744,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f182,f5742]) ).

fof(f182,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(f5740,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f167,f5738]) ).

fof(f167,axiom,
    ! [X10,X18,X19,X26] :
      ( ~ c_lessequals(X19,X18,tc_nat)
      | ~ c_lessequals(X10,X26,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X26,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

fof(f5736,plain,
    spl0_322,
    inference(avatar_split_clause,[],[f116,f5734]) ).

fof(f116,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X10,X18,tc_nat)
      | ~ c_lessequals(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

fof(f5732,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f81,f5730]) ).

fof(f81,axiom,
    ! [X2,X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(f5728,plain,
    ( spl0_320
    | ~ spl0_151
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2374,f2173,f1737,f5726]) ).

fof(f5726,plain,
    ( spl0_320
  <=> ! [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_320])]) ).

fof(f2374,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_151
    | ~ spl0_189 ),
    inference(resolution,[],[f2174,f1738]) ).

fof(f5670,plain,
    ( spl0_319
    | ~ spl0_188
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f2373,f2173,f2169,f5668]) ).

fof(f2373,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_lessequals(X1,X0,tc_nat) )
    | ~ spl0_188
    | ~ spl0_189 ),
    inference(resolution,[],[f2174,f2170]) ).

fof(f5629,plain,
    ( spl0_318
    | ~ spl0_65
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1679,f1552,f1154,f5627]) ).

fof(f5627,plain,
    ( spl0_318
  <=> ! [X0] : c_Lambda_Obeta(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_318])]) ).

fof(f1679,plain,
    ( ! [X0] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),X0),X0)
    | ~ spl0_65
    | ~ spl0_137 ),
    inference(superposition,[],[f1553,f1155]) ).

fof(f5625,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f821,f5623]) ).

fof(f821,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    inference(duplicate_literal_removal,[],[f175]) ).

fof(f175,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

fof(f5621,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f755,f5619]) ).

fof(f755,plain,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f336,f149]) ).

fof(f336,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X3),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

fof(f5617,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f652,f5615]) ).

fof(f5615,plain,
    ( spl0_315
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f652,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

fof(f5613,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f545,f5611]) ).

fof(f545,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

fof(f5609,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f544,f5607]) ).

fof(f544,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

fof(f5605,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f475,f5603]) ).

fof(f475,axiom,
    ! [X0,X24,X22,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(X24,c_HOL_Otimes__class_Otimes(X22,X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f5601,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f474,f5599]) ).

fof(f5599,plain,
    ( spl0_311
  <=> ! [X24,X0,X25,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f474,axiom,
    ! [X0,X24,X22,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X24,X25,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

fof(f5597,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f472,f5595]) ).

fof(f472,axiom,
    ! [X0,X24,X22,X23] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,X0),X24,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X24,X0),X23,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f5593,plain,
    spl0_309,
    inference(avatar_split_clause,[],[f471,f5591]) ).

fof(f471,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f5589,plain,
    spl0_308,
    inference(avatar_split_clause,[],[f438,f5587]) ).

fof(f438,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

fof(f5585,plain,
    ( spl0_307
    | ~ spl0_29
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1612,f1508,f1001,f5583]) ).

fof(f5583,plain,
    ( spl0_307
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f1508,plain,
    ( spl0_126
  <=> ! [X4,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f1612,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
    | ~ spl0_29
    | ~ spl0_126 ),
    inference(resolution,[],[f1509,f1003]) ).

fof(f1509,plain,
    ( ! [X0,X4] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X4,X0) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f1508]) ).

fof(f5581,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f293,f5579]) ).

fof(f5579,plain,
    ( spl0_306
  <=> ! [X15,X0,X6,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X6,X15,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X2,X15,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f293,axiom,
    ! [X2,X0,X6,X15] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X6,X15,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X2,X15,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f5577,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f292,f5575]) ).

fof(f5575,plain,
    ( spl0_305
  <=> ! [X6,X0,X5,X2] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X6,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f292,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X6,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f5573,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f290,f5571]) ).

fof(f5571,plain,
    ( spl0_304
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f290,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f5569,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f289,f5567]) ).

fof(f5567,plain,
    ( spl0_303
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f289,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f5565,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f288,f5563]) ).

fof(f5563,plain,
    ( spl0_302
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f288,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X5,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f5561,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f284,f5559]) ).

fof(f5559,plain,
    ( spl0_301
  <=> ! [X11,X0,X21,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X11,X21,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X11,X0),X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f284,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X11,X21,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X11,X0),X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f5557,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f206,f5555]) ).

fof(f206,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

fof(f5553,plain,
    spl0_299,
    inference(avatar_split_clause,[],[f89,f5551]) ).

fof(f89,axiom,
    ! [X3,X10,X26,X4] :
      ( ~ c_HOL_Oord__class_Oless(X10,X26,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oplus__class_Oplus(X3,X26,tc_nat) != c_HOL_Oplus__class_Oplus(X10,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

fof(f5549,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f37,f5547]) ).

fof(f5547,plain,
    ( spl0_298
  <=> ! [X5,X2,X0] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f37,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

fof(f5545,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f16,f5543]) ).

fof(f5543,plain,
    ( spl0_297
  <=> ! [X4,X0,X2] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f16,axiom,
    ! [X2,X0,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

fof(f5541,plain,
    ( spl0_296
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1610,f1500,f1041,f5539]) ).

fof(f5539,plain,
    ( spl0_296
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f1500,plain,
    ( spl0_124
  <=> ! [X2,X0] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1610,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_37
    | ~ spl0_124 ),
    inference(resolution,[],[f1501,f1043]) ).

fof(f1501,plain,
    ( ! [X2,X0] :
        ( ~ class_Power_Opower(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1500]) ).

fof(f5180,plain,
    ( spl0_295
    | ~ spl0_17
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f1586,f1466,f941,f5178]) ).

fof(f5178,plain,
    ( spl0_295
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f1466,plain,
    ( spl0_116
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1586,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_17
    | ~ spl0_116 ),
    inference(resolution,[],[f1467,f943]) ).

fof(f1467,plain,
    ( ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1466]) ).

fof(f4822,plain,
    ( spl0_294
    | ~ spl0_17
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1585,f1462,f941,f4820]) ).

fof(f4820,plain,
    ( spl0_294
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f1462,plain,
    ( spl0_115
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1585,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
    | ~ spl0_17
    | ~ spl0_115 ),
    inference(resolution,[],[f1463,f943]) ).

fof(f1463,plain,
    ( ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f1462]) ).

fof(f4568,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f839,f4566]) ).

fof(f4566,plain,
    ( spl0_293
  <=> ! [X4] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X4
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f839,plain,
    ! [X4] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    inference(forward_demodulation,[],[f792,f90]) ).

fof(f792,plain,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4 ),
    inference(definition_unfolding,[],[f627,f149]) ).

fof(f627,axiom,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

fof(f4564,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f807,f4562]) ).

fof(f807,plain,
    ! [X10,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X10,tc_nat) ),
    inference(definition_unfolding,[],[f228,f149]) ).

fof(f228,axiom,
    ! [X10,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X19),X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f4560,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f800,f4558]) ).

fof(f800,plain,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
    inference(definition_unfolding,[],[f127,f149]) ).

fof(f127,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

fof(f4556,plain,
    ( spl0_290
    | ~ spl0_62
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f1408,f1297,f1142,f4554]) ).

fof(f4554,plain,
    ( spl0_290
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f1297,plain,
    ( spl0_94
  <=> ! [X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1408,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
    | ~ spl0_62
    | ~ spl0_94 ),
    inference(resolution,[],[f1298,f1143]) ).

fof(f1298,plain,
    ( ! [X4] :
        ( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f1297]) ).

fof(f4552,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f794,f4550]) ).

fof(f794,plain,
    ! [X19,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f445,f149]) ).

fof(f445,axiom,
    ! [X19,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X19),tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

fof(f4548,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f790,f4546]) ).

fof(f4546,plain,
    ( spl0_288
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f790,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f576,f149,f149]) ).

fof(f576,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

fof(f4544,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f784,f4542]) ).

fof(f4542,plain,
    ( spl0_287
  <=> ! [X4,X3] :
        ( c_lessequals(X4,X3,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f784,plain,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f469,f149,f149]) ).

fof(f469,axiom,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

fof(f4540,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f669,f4538]) ).

fof(f669,axiom,
    ! [X29,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).

fof(f4536,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f661,f4534]) ).

fof(f661,axiom,
    ! [X10,X29,X9,X27] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X9,X29),X27,X10) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X9,X27,X10),c_Lambda_Osubst(X29,X27,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

fof(f4532,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f646,f4530]) ).

fof(f646,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

fof(f4528,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f512,f4526]) ).

fof(f512,axiom,
    ! [X10,X9,X27,X4] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X27,X10),c_Lambda_Oliftn(X4,X9,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

fof(f4524,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f402,f4522]) ).

fof(f402,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f4520,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f401,f4518]) ).

fof(f401,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f4516,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f400,f4514]) ).

fof(f400,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f4512,plain,
    ( spl0_279
    | ~ spl0_79
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1384,f1265,f1222,f4510]) ).

fof(f4510,plain,
    ( spl0_279
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f1384,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
    | ~ spl0_79
    | ~ spl0_86 ),
    inference(superposition,[],[f1223,f1266]) ).

fof(f4508,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f399,f4506]) ).

fof(f399,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X2,X5,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f4504,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f398,f4502]) ).

fof(f398,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f4500,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f397,f4498]) ).

fof(f397,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f4496,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f299,f4494]) ).

fof(f4494,plain,
    ( spl0_275
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | ~ class_Ring__and__Field_Omult__zero(X0)
        | ~ class_Power_Opower(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f299,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | ~ class_Ring__and__Field_Omult__zero(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

fof(f4492,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f256,f4490]) ).

fof(f256,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Osemiring__0(X0)
      | ~ class_Power_Opower(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

fof(f4488,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f234,f4486]) ).

fof(f234,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X5,X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

fof(f4484,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f233,f4482]) ).

fof(f233,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
      | ~ c_lessequals(X2,X5,X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

fof(f4480,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f232,f4478]) ).

fof(f232,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

fof(f4476,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f231,f4474]) ).

fof(f231,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X2,X5,X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X6,X2,X0),c_HOL_Oplus__class_Oplus(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

fof(f4472,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f230,f4470]) ).

fof(f230,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_lessequals(X2,X5,X0)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

fof(f4468,plain,
    ( spl0_268
    | ~ spl0_80
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1383,f1265,f1226,f4466]) ).

fof(f4466,plain,
    ( spl0_268
  <=> ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f1383,plain,
    ( ! [X0] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X0,tc_nat)
    | ~ spl0_80
    | ~ spl0_86 ),
    inference(superposition,[],[f1227,f1266]) ).

fof(f4464,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f229,f4462]) ).

fof(f229,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_lessequals(X2,X5,X0)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X2,X6,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

fof(f4460,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f143,f4458]) ).

fof(f143,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem0_0) ).

fof(f4456,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f33,f4454]) ).

fof(f33,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X4,X3,tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

fof(f4452,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f20,f4450]) ).

fof(f20,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X3,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(f4341,plain,
    ( spl0_263
    | ~ spl0_81
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1382,f1265,f1230,f4339]) ).

fof(f4339,plain,
    ( spl0_263
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f1382,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
    | ~ spl0_81
    | ~ spl0_86 ),
    inference(superposition,[],[f1231,f1266]) ).

fof(f3722,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f857,f3720]) ).

fof(f3720,plain,
    ( spl0_262
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Oone__class_Oone(tc_nat) = X4
        | c_HOL_Oone__class_Oone(tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f857,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X4
      | c_HOL_Oone__class_Oone(tc_nat) = X3 ),
    inference(forward_demodulation,[],[f856,f552]) ).

fof(f552,axiom,
    ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

fof(f856,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X4
      | c_HOL_Oone__class_Oone(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f855,f552]) ).

fof(f855,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f816,f552]) ).

fof(f816,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f446,f149,f149,f149]) ).

fof(f446,axiom,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

fof(f3718,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f850,f3716]) ).

fof(f850,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
    inference(forward_demodulation,[],[f849,f552]) ).

fof(f849,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f812,f552]) ).

fof(f812,plain,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f502,f149,f149]) ).

fof(f502,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

fof(f3714,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f848,f3712]) ).

fof(f848,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | c_HOL_Oone__class_Oone(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
    inference(forward_demodulation,[],[f847,f552]) ).

fof(f847,plain,
    ! [X3,X4] :
      ( c_HOL_Oone__class_Oone(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(forward_demodulation,[],[f811,f552]) ).

fof(f811,plain,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f501,f149,f149]) ).

fof(f501,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

fof(f3710,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f845,f3708]) ).

fof(f3708,plain,
    ( spl0_259
  <=> ! [X4,X3] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f845,plain,
    ! [X3,X4] :
      ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
    inference(forward_demodulation,[],[f809,f552]) ).

fof(f809,plain,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f447,f149]) ).

fof(f447,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

fof(f3706,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f830,f3704]) ).

fof(f830,plain,
    ! [X10,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(X19,c_HOL_Oplus__class_Oplus(X10,X18,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f597,f330]) ).

fof(f597,axiom,
    ! [X10,X18,X19] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X18,tc_nat),X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X19,X10,tc_nat),X18,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

fof(f3702,plain,
    ( spl0_257
    | ~ spl0_109
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1576,f1532,f1360,f3700]) ).

fof(f1532,plain,
    ( spl0_132
  <=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1576,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))),X1)
    | ~ spl0_109
    | ~ spl0_132 ),
    inference(resolution,[],[f1533,f1361]) ).

fof(f1533,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1532]) ).

fof(f3698,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f803,f3696]) ).

fof(f803,plain,
    ! [X3,X4] :
      ( X3 = X4
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f64,f149]) ).

fof(f64,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

fof(f3694,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f802,f3692]) ).

fof(f802,plain,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f424,f149]) ).

fof(f424,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

fof(f3690,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f749,f3688]) ).

fof(f749,plain,
    ! [X10,X9,X4] : c_Lambda_Olift(c_Lambda_Oliftn(X4,X9,X10),X10) = c_Lambda_Oliftn(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X9,X10),
    inference(definition_unfolding,[],[f18,f149]) ).

fof(f18,axiom,
    ! [X10,X9,X4] : c_Lambda_Oliftn(c_Suc(X4),X9,X10) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X9,X10),X10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).

fof(f3686,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f676,f3684]) ).

fof(f676,axiom,
    ! [X10,X19,X27] :
      ( X10 = X19
      | c_HOL_Oord__class_Oless(X10,X19,tc_nat)
      | c_Lambda_OdB_OVar(X19) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X19),X27,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

fof(f3682,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f631,f3680]) ).

fof(f631,axiom,
    ! [X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | c_List_Olast(c_List_Oupt(X19,X18),tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__upt_0) ).

fof(f3678,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f603,f3676]) ).

fof(f603,axiom,
    ! [X10,X19] :
      ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
      | c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).

fof(f3674,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f347,f3672]) ).

fof(f347,axiom,
    ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

fof(f3670,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f346,f3668]) ).

fof(f346,axiom,
    ! [X3,X10,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),c_HOL_Oplus__class_Oplus(X4,X10,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

fof(f3666,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f330,f3664]) ).

fof(f3662,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f287,f3660]) ).

fof(f3657,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f286,f3655]) ).

fof(f286,axiom,
    ! [X21,X11,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X11,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

fof(f3653,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f204,f3651]) ).

fof(f204,axiom,
    ! [X10,X27,X4] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).

fof(f3649,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f194,f3647]) ).

fof(f194,axiom,
    ! [X10,X19,X4] :
      ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
      | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X19,X4,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).

fof(f3645,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f132,f3643]) ).

fof(f132,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

fof(f3641,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f128,f3639]) ).

fof(f128,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
      | c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

fof(f3637,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f54,f3635]) ).

fof(f54,axiom,
    ! [X2,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

fof(f3318,plain,
    ( spl0_240
    | ~ spl0_43
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f2740,f2510,f1066,f3316]) ).

fof(f2740,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != c_Lambda_Olift(c_Lambda_OdB_OAbs(X0),X1)
    | ~ spl0_43
    | ~ spl0_204 ),
    inference(superposition,[],[f1067,f2511]) ).

fof(f2888,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f648,f2886]) ).

fof(f648,axiom,
    ! [X10,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

fof(f2884,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f647,f2882]) ).

fof(f647,axiom,
    ! [X10,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),X18,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

fof(f2880,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f635,f2878]) ).

fof(f635,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

fof(f2876,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f634,f2874]) ).

fof(f634,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

fof(f2872,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f605,f2870]) ).

fof(f605,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
      | ~ c_HOL_Oord__class_Oless(X11,X21,X0)
      | c_HOL_Oord__class_Oless(X1,X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f2868,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f604,f2866]) ).

fof(f604,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X21,X11,X0)
      | c_HOL_Oord__class_Oless(X21,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f2864,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f491,f2862]) ).

fof(f491,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X10,X4,tc_nat)
      | c_lessequals(X3,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

fof(f2860,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f487,f2858]) ).

fof(f2858,plain,
    ( spl0_232
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X5 = X6
        | c_HOL_Oplus__class_Oplus(X5,X2,X0) != c_HOL_Oplus__class_Oplus(X6,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f487,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X5 = X6
      | c_HOL_Oplus__class_Oplus(X5,X2,X0) != c_HOL_Oplus__class_Oplus(X6,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f2856,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f486,f2854]) ).

fof(f2854,plain,
    ( spl0_231
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X5 = X6
        | c_HOL_Oplus__class_Oplus(X2,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f486,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X5 = X6
      | c_HOL_Oplus__class_Oplus(X2,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f2852,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f485,f2850]) ).

fof(f2850,plain,
    ( spl0_230
  <=> ! [X5,X0,X6,X2] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X5 = X6
        | c_HOL_Oplus__class_Oplus(X2,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f485,axiom,
    ! [X2,X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X5 = X6
      | c_HOL_Oplus__class_Oplus(X2,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f2848,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f417,f2846]) ).

fof(f417,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X11,X21,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
      | c_HOL_Oord__class_Oless(X1,X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

fof(f2844,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f416,f2842]) ).

fof(f416,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X11,X0)
      | ~ c_HOL_Oord__class_Oless(X11,X21,X0)
      | c_HOL_Oord__class_Oless(X1,X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

fof(f2840,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f410,f2838]) ).

fof(f410,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X11,X0)
      | ~ c_lessequals(X11,X21,X0)
      | c_lessequals(X1,X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

fof(f2836,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f408,f2834]) ).

fof(f408,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X11,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X21,X11,X0)
      | c_HOL_Oord__class_Oless(X21,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

fof(f2832,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f407,f2830]) ).

fof(f407,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X21,X11,X0)
      | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
      | c_HOL_Oord__class_Oless(X21,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

fof(f2828,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f406,f2826]) ).

fof(f406,axiom,
    ! [X21,X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_lessequals(X11,X1,X0)
      | ~ c_lessequals(X21,X11,X0)
      | c_lessequals(X21,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

fof(f2824,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f405,f2822]) ).

fof(f405,axiom,
    ! [X3,X10,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

fof(f2820,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f404,f2818]) ).

fof(f404,axiom,
    ! [X3,X10,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

fof(f2816,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f403,f2814]) ).

fof(f403,axiom,
    ! [X10,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

fof(f2812,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f326,f2810]) ).

fof(f326,axiom,
    ! [X3,X26,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X3,X26,tc_nat),c_HOL_Ominus__class_Ominus(X4,X26,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

fof(f2808,plain,
    ( spl0_219
    | ~ spl0_39
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1993,f1789,f1050,f2806]) ).

fof(f1993,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_39
    | ~ spl0_164 ),
    inference(resolution,[],[f1790,f1051]) ).

fof(f2804,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f325,f2802]) ).

fof(f325,axiom,
    ! [X3,X26,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X26,X4,tc_nat),c_HOL_Ominus__class_Ominus(X26,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

fof(f2800,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f264,f2798]) ).

fof(f264,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X2,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

fof(f2796,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f263,f2794]) ).

fof(f263,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

fof(f2792,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f249,f2790]) ).

fof(f249,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

fof(f2788,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f248,f2786]) ).

fof(f248,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

fof(f2784,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f237,f2782]) ).

fof(f237,axiom,
    ! [X3,X10,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

fof(f2780,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f236,f2778]) ).

fof(f236,axiom,
    ! [X3,X10,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X3,tc_nat),c_HOL_Oplus__class_Oplus(X10,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

fof(f2776,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f235,f2774]) ).

fof(f235,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X19,X18,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),c_HOL_Oplus__class_Oplus(X18,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

fof(f2772,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f191,f2770]) ).

fof(f191,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X1,X11,X0)
      | c_lessequals(X11,X1,X0)
      | c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

fof(f2768,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f147,f2766]) ).

fof(f147,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

fof(f2764,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f146,f2762]) ).

fof(f146,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).

fof(f2760,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f145,f2758]) ).

fof(f145,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,X5,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X2,X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

fof(f2756,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f53,f2754]) ).

fof(f53,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat)
      | c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

fof(f2752,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f52,f2750]) ).

fof(f52,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X18,X10,tc_nat),X19,tc_nat)
      | c_lessequals(X18,c_HOL_Oplus__class_Oplus(X19,X10,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

fof(f2512,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f656,f2510]) ).

fof(f656,axiom,
    ! [X10,X27] : c_Lambda_Olift(c_Lambda_OdB_OAbs(X27),X10) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X27,c_HOL_Oplus__class_Oplus(X10,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).

fof(f2508,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f655,f2506]) ).

fof(f655,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

fof(f2504,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f625,f2502]) ).

fof(f2502,plain,
    ( spl0_202
  <=> ! [X0,X11,X1] :
        ( ~ class_Orderings_Olinorder(X0)
        | X1 = X11
        | c_HOL_Oord__class_Oless(X11,X1,X0)
        | c_HOL_Oord__class_Oless(X1,X11,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f625,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | X1 = X11
      | c_HOL_Oord__class_Oless(X11,X1,X0)
      | c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

fof(f2500,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f609,f2498]) ).

fof(f609,axiom,
    ! [X10,X9,X27] : c_Lambda_Olift(c_Lambda_OdB_OApp(X27,X9),X10) = c_Lambda_OdB_OApp(c_Lambda_Olift(X27,X10),c_Lambda_Olift(X9,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

fof(f2496,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f517,f2494]) ).

fof(f517,axiom,
    ! [X19,X4] :
      ( ~ c_lessequals(X19,X4,tc_nat)
      | c_HOL_Ominus__class_Ominus(X4,c_HOL_Ominus__class_Ominus(X4,X19,tc_nat),tc_nat) = X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

fof(f2492,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f458,f2490]) ).

fof(f458,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | X1 = X11
      | ~ c_lessequals(X1,X11,X0)
      | c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

fof(f2488,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f448,f2486]) ).

fof(f448,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | X2 = X5
      | ~ c_lessequals(X5,X2,X0)
      | c_HOL_Oord__class_Oless(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

fof(f2481,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f239,f2479]) ).

fof(f239,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X4,X3,tc_nat)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

fof(f2477,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f207,f2475]) ).

fof(f207,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | X1 = X11
      | ~ c_lessequals(X1,X11,X0)
      | ~ c_lessequals(X11,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

fof(f2228,plain,
    ( spl0_195
    | ~ spl0_24
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1444,f1356,f976,f2225]) ).

fof(f2225,plain,
    ( spl0_195
  <=> 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_195])]) ).

fof(f1356,plain,
    ( spl0_108
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1444,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_24
    | ~ spl0_108 ),
    inference(resolution,[],[f1357,f978]) ).

fof(f1357,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1356]) ).

fof(f2195,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f789,f2193]) ).

fof(f789,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f523,f149]) ).

fof(f523,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

fof(f2191,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f785,f2189]) ).

fof(f785,plain,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f111,f149]) ).

fof(f111,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

fof(f2187,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f783,f2185]) ).

fof(f783,plain,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
    inference(definition_unfolding,[],[f380,f149]) ).

fof(f380,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_Suc(X4),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

fof(f2183,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f782,f2181]) ).

fof(f782,plain,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f170,f149]) ).

fof(f170,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

fof(f2179,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f773,f2177]) ).

fof(f773,plain,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_lessequals(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) ),
    inference(definition_unfolding,[],[f112,f149]) ).

fof(f112,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_lessequals(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

fof(f2175,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f772,f2173]) ).

fof(f772,plain,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f522,f149]) ).

fof(f522,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

fof(f2171,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f767,f2169]) ).

fof(f767,plain,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f169,f149]) ).

fof(f169,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

fof(f2167,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f764,f2165]) ).

fof(f764,plain,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
    inference(definition_unfolding,[],[f379,f149]) ).

fof(f379,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

fof(f2163,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f675,f2161]) ).

fof(f675,axiom,
    ! [X19,X9,X27,X30] :
      ( ~ c_Lambda_Obeta(X30,X27)
      | c_Lambda_Obeta(c_Lambda_Osubst(X30,X9,X19),c_Lambda_Osubst(X27,X9,X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

fof(f2159,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f667,f2157]) ).

fof(f667,axiom,
    ! [X29,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X18,X19,tc_nat)
      | c_Lambda_OdB_OVar(X18) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X18),X29,X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

fof(f2155,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f651,f2153]) ).

fof(f651,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

fof(f2151,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f650,f2149]) ).

fof(f650,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

fof(f2147,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f589,f2145]) ).

fof(f589,axiom,
    ! [X10,X19,X4] :
      ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
      | c_Lambda_OdB_OVar(X19) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X19),X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

fof(f2143,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f543,f2141]) ).

fof(f543,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

fof(f2139,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f482,f2137]) ).

fof(f482,axiom,
    ! [X3,X10,X4] :
      ( X3 = X4
      | c_HOL_Oplus__class_Oplus(X4,X10,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

fof(f2135,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f422,f2133]) ).

fof(f422,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X2,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

fof(f2131,plain,
    ( spl0_178
    | ~ spl0_24
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1419,f1310,f976,f2128]) ).

fof(f2128,plain,
    ( spl0_178
  <=> 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_178])]) ).

fof(f1310,plain,
    ( spl0_97
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1419,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_24
    | ~ spl0_97 ),
    inference(resolution,[],[f1311,f978]) ).

fof(f1311,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1310]) ).

fof(f2126,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f421,f2124]) ).

fof(f421,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

fof(f2122,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f412,f2120]) ).

fof(f412,axiom,
    ! [X10,X18,X19] :
      ( ~ c_lessequals(X19,X18,tc_nat)
      | ~ c_lessequals(X18,X10,tc_nat)
      | c_lessequals(X19,X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

fof(f2118,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f381,f2116]) ).

fof(f381,axiom,
    ! [X21,X11,X1] :
      ( X11 = X21
      | c_HOL_Oplus__class_Oplus(X1,X21,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X11,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

fof(f2114,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f311,f2112]) ).

fof(f311,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

fof(f2110,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f87,f2108]) ).

fof(f87,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

fof(f2106,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f82,f2104]) ).

fof(f2104,plain,
    ( spl0_172
  <=> ! [X4,X0,X3] :
        ( ~ class_Nat_Osemiring__char__0(X0)
        | X3 = X4
        | c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f82,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Nat_Osemiring__char__0(X0)
      | X3 = X4
      | c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

fof(f2016,plain,
    ( spl0_171
    | ~ spl0_29
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f1402,f1285,f1001,f2014]) ).

fof(f2014,plain,
    ( spl0_171
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f1285,plain,
    ( spl0_91
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1402,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
    | ~ spl0_29
    | ~ spl0_91 ),
    inference(resolution,[],[f1286,f1003]) ).

fof(f1286,plain,
    ( ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f1285]) ).

fof(f1887,plain,
    ( spl0_170
    | ~ spl0_19
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f1400,f1277,f951,f1885]) ).

fof(f1885,plain,
    ( spl0_170
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f1277,plain,
    ( spl0_89
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f1400,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
    | ~ spl0_19
    | ~ spl0_89 ),
    inference(resolution,[],[f1278,f953]) ).

fof(f1278,plain,
    ( ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f1277]) ).

fof(f1811,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f824,f1809]) ).

fof(f824,plain,
    ! [X3,X19] : c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X19,tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f737,f733]) ).

fof(f733,plain,
    ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(definition_unfolding,[],[f148,f149]) ).

fof(f148,axiom,
    ! [X4] : c_Suc(X4) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

fof(f737,plain,
    ! [X3,X19] : c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X19,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f118,f149]) ).

fof(f118,axiom,
    ! [X3,X19] : c_HOL_Oord__class_Oless(X19,c_Suc(c_HOL_Oplus__class_Oplus(X3,X19,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

fof(f1807,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f822,f1805]) ).

fof(f822,plain,
    ! [X3,X1] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f735,f733]) ).

fof(f735,plain,
    ! [X3,X1] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f117,f149]) ).

fof(f117,axiom,
    ! [X3,X1] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X1,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

fof(f1803,plain,
    ( spl0_167
    | ~ spl0_32
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f1398,f1273,f1016,f1801]) ).

fof(f1801,plain,
    ( spl0_167
  <=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1273,plain,
    ( spl0_88
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f1398,plain,
    ( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
    | ~ spl0_32
    | ~ spl0_88 ),
    inference(resolution,[],[f1274,f1018]) ).

fof(f1274,plain,
    ( ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f1273]) ).

fof(f1799,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f738,f1797]) ).

fof(f738,plain,
    ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f606,f149]) ).

fof(f606,axiom,
    ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

fof(f1795,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f623,f1793]) ).

fof(f623,axiom,
    ! [X11,X1] :
      ( X1 = X11
      | c_HOL_Oord__class_Oless(X1,X11,tc_nat)
      | c_HOL_Oord__class_Oless(X11,X1,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

fof(f1791,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f613,f1789]) ).

fof(f613,axiom,
    ! [X10,X18,X4] :
      ( ~ c_HOL_Oord__class_Oless(X18,X10,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X18,X4,tc_nat),X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

fof(f1787,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f587,f1785]) ).

fof(f587,axiom,
    ! [X10,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X10,tc_nat)
      | c_Lambda_OdB_OVar(X19) = c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

fof(f1783,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f451,f1781]) ).

fof(f451,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

fof(f1779,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f306,f1777]) ).

fof(f306,axiom,
    ! [X21,X11,X1] :
      ( ~ c_lessequals(X1,X11,tc_nat)
      | c_lessequals(X1,c_HOL_Oplus__class_Oplus(X11,X21,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

fof(f1775,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f304,f1773]) ).

fof(f304,axiom,
    ! [X3,X10,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

fof(f1771,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f303,f1769]) ).

fof(f303,axiom,
    ! [X3,X10,X4] :
      ( c_lessequals(X10,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X10,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

fof(f1767,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f301,f1765]) ).

fof(f301,axiom,
    ! [X3,X18,X19] :
      ( ~ c_lessequals(X19,X18,tc_nat)
      | c_lessequals(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

fof(f1763,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f205,f1761]) ).

fof(f205,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

fof(f1759,plain,
    ( spl0_156
    | ~ spl0_32
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f1397,f1269,f1016,f1757]) ).

fof(f1757,plain,
    ( spl0_156
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1269,plain,
    ( spl0_87
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f1397,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
    | ~ spl0_32
    | ~ spl0_87 ),
    inference(resolution,[],[f1270,f1018]) ).

fof(f1270,plain,
    ( ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f1269]) ).

fof(f1755,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f176,f1753]) ).

fof(f176,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X2,X5,X0) = c_HOL_Otimes__class_Otimes(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f1751,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f134,f1749]) ).

fof(f134,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

fof(f1747,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f133,f1745]) ).

fof(f133,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

fof(f1743,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f106,f1741]) ).

fof(f106,axiom,
    ! [X10,X18,X19] :
      ( c_HOL_Oord__class_Oless(X19,X10,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X10,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

fof(f1739,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f105,f1737]) ).

fof(f105,axiom,
    ! [X3,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X18,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

fof(f1735,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f104,f1733]) ).

fof(f104,axiom,
    ! [X3,X18,X19] :
      ( ~ c_HOL_Oord__class_Oless(X19,X18,tc_nat)
      | c_HOL_Oord__class_Oless(X19,c_HOL_Oplus__class_Oplus(X3,X18,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

fof(f1731,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f91,f1729]) ).

fof(f1729,plain,
    ( spl0_149
  <=> ! [X5,X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,X5,X0) = c_HOL_Oplus__class_Oplus(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f91,axiom,
    ! [X2,X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,X5,X0) = c_HOL_Oplus__class_Oplus(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f1727,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f88,f1725]) ).

fof(f1725,plain,
    ( spl0_148
  <=> ! [X11,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X1,X11,X0) = c_HOL_Oplus__class_Oplus(X11,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f88,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X1,X11,X0) = c_HOL_Oplus__class_Oplus(X11,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f1723,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f24,f1721]) ).

fof(f24,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

fof(f1719,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f23,f1717]) ).

fof(f23,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

fof(f1678,plain,
    ( spl0_145
    | ~ spl0_48
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1627,f1512,f1086,f1676]) ).

fof(f1676,plain,
    ( spl0_145
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1627,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_48
    | ~ spl0_127 ),
    inference(duplicate_literal_removal,[],[f1619]) ).

fof(f1619,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_48
    | ~ spl0_127 ),
    inference(resolution,[],[f1513,f1087]) ).

fof(f1604,plain,
    ( spl0_144
    | ~ spl0_66
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f1385,f1265,f1158,f1602]) ).

fof(f1602,plain,
    ( spl0_144
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1385,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != X0
    | ~ spl0_66
    | ~ spl0_86 ),
    inference(superposition,[],[f1159,f1266]) ).

fof(f1580,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f659,f1578]) ).

fof(f659,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
      | ~ c_HOL_Oord__class_Oless(X11,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

fof(f1574,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f658,f1572]) ).

fof(f658,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X11,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f1570,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f657,f1568]) ).

fof(f657,axiom,
    ! [X2,X0,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f1566,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f637,f1564]) ).

fof(f637,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f1562,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f630,f1560]) ).

fof(f630,axiom,
    ! [X38,X36,X37,X35] :
      ( X35 = X37
      | c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

fof(f1558,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f629,f1556]) ).

fof(f629,axiom,
    ! [X38,X36,X37,X35] :
      ( X36 = X38
      | c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

fof(f1554,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f619,f1552]) ).

fof(f619,axiom,
    ! [X9,X27] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X27),X9),c_Lambda_Osubst(X27,X9,c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

fof(f1550,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f592,f1548]) ).

fof(f592,axiom,
    ! [X29,X9,X27] :
      ( ~ c_Lambda_Obeta(X27,X9)
      | c_Lambda_Obeta(c_Lambda_OdB_OApp(X29,X27),c_Lambda_OdB_OApp(X29,X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

fof(f1546,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f591,f1544]) ).

fof(f591,axiom,
    ! [X29,X9,X27] :
      ( ~ c_Lambda_Obeta(X27,X9)
      | c_Lambda_Obeta(c_Lambda_OdB_OApp(X27,X29),c_Lambda_OdB_OApp(X9,X29)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

fof(f1542,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f586,f1540]) ).

fof(f586,axiom,
    ! [X19,X27,X30] :
      ( ~ c_Lambda_Obeta(X30,X27)
      | c_Lambda_Obeta(c_Lambda_Olift(X30,X19),c_Lambda_Olift(X27,X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

fof(f1538,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f583,f1536]) ).

fof(f583,axiom,
    ! [X27,X30] :
      ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27)
      | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27)) = X27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).

fof(f1534,plain,
    ( spl0_132
    | ~ spl0_109
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1490,f1447,f1360,f1532]) ).

fof(f1447,plain,
    ( spl0_113
  <=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1490,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
    | ~ spl0_109
    | ~ spl0_113 ),
    inference(resolution,[],[f1448,f1361]) ).

fof(f1448,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f1447]) ).

fof(f1530,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f481,f1528]) ).

fof(f481,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X1,X11,X0)
      | c_lessequals(X11,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f1526,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f329,f1524]) ).

fof(f329,axiom,
    ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

fof(f1522,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f319,f1520]) ).

fof(f319,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X11,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f1518,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f315,f1516]) ).

fof(f315,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X11,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

fof(f1514,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f312,f1512]) ).

fof(f312,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X11,X1,X0)
      | c_HOL_Oord__class_Oless(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

fof(f1510,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f310,f1508]) ).

fof(f310,axiom,
    ! [X0,X4] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

fof(f1506,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f255,f1504]) ).

fof(f1504,plain,
    ( spl0_125
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f255,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

fof(f1502,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f254,f1500]) ).

fof(f254,axiom,
    ! [X2,X0] :
      ( ~ class_Power_Opower(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

fof(f1498,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f218,f1496]) ).

fof(f218,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
      | c_lessequals(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

fof(f1494,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f217,f1492]) ).

fof(f217,axiom,
    ! [X0,X11,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X11,X0)
      | c_lessequals(X1,X11,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

fof(f1488,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f189,f1486]) ).

fof(f189,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

fof(f1484,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f187,f1482]) ).

fof(f1482,plain,
    ( spl0_120
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f187,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

fof(f1480,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f150,f1478]) ).

fof(f1478,plain,
    ( spl0_119
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f150,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

fof(f1476,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f79,f1474]) ).

fof(f1474,plain,
    ( spl0_118
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f79,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f1472,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f78,f1470]) ).

fof(f1470,plain,
    ( spl0_117
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f78,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f1468,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f75,f1466]) ).

fof(f75,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f1464,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f74,f1462]) ).

fof(f74,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(f1460,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f2,f1458]) ).

fof(f2,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

fof(f1449,plain,
    ( spl0_113
    | ~ spl0_40
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f1445,f1360,f1054,f1447]) ).

fof(f1445,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
    | ~ spl0_40
    | ~ spl0_109 ),
    inference(resolution,[],[f1361,f1055]) ).

fof(f1423,plain,
    ( spl0_112
    | ~ spl0_17
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f1371,f1252,f941,f1421]) ).

fof(f1421,plain,
    ( spl0_112
  <=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1252,plain,
    ( spl0_83
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f1371,plain,
    ( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
    | ~ spl0_17
    | ~ spl0_83 ),
    inference(resolution,[],[f1253,f943]) ).

fof(f1253,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f1252]) ).

fof(f1370,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f838,f1368]) ).

fof(f838,plain,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
    inference(forward_demodulation,[],[f837,f551]) ).

fof(f551,axiom,
    ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

fof(f837,plain,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
    inference(forward_demodulation,[],[f779,f90]) ).

fof(f779,plain,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
    inference(definition_unfolding,[],[f154,f149]) ).

fof(f154,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

fof(f1366,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f729,f1364]) ).

fof(f729,plain,
    ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f349,f149]) ).

fof(f349,axiom,
    ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

fof(f1362,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f638,f1360]) ).

fof(f638,axiom,
    ! [X27,X30] :
      ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X30),X27)
      | c_Lambda_Obeta(X30,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X30,X27)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).

fof(f1358,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f602,f1356]) ).

fof(f602,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

fof(f1354,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f567,f1352]) ).

fof(f567,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

fof(f1348,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f566,f1346]) ).

fof(f566,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

fof(f1344,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f558,f1342]) ).

fof(f1342,plain,
    ( spl0_105
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f558,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f1340,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f557,f1338]) ).

fof(f1338,plain,
    ( spl0_104
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f557,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f1336,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f556,f1334]) ).

fof(f1334,plain,
    ( spl0_103
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f556,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f1332,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f555,f1330]) ).

fof(f1330,plain,
    ( spl0_102
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f555,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f1328,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f550,f1326]) ).

fof(f1326,plain,
    ( spl0_101
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f550,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f1324,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f549,f1322]) ).

fof(f1322,plain,
    ( spl0_100
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f549,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f1320,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f548,f1318]) ).

fof(f548,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

fof(f1316,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f507,f1314]) ).

fof(f1314,plain,
    ( spl0_98
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f507,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

fof(f1312,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f352,f1310]) ).

fof(f352,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

fof(f1308,plain,
    ( spl0_96
    | ~ spl0_64
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f1249,f1230,f1150,f1305]) ).

fof(f1305,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(f1249,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
    | ~ spl0_64
    | ~ spl0_81 ),
    inference(superposition,[],[f1231,f1151]) ).

fof(f1303,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f258,f1301]) ).

fof(f258,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f1299,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f193,f1297]) ).

fof(f193,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

fof(f1295,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f141,f1293]) ).

fof(f1293,plain,
    ( spl0_93
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f141,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

fof(f1291,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f140,f1289]) ).

fof(f1289,plain,
    ( spl0_92
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f140,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f1287,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f139,f1285]) ).

fof(f139,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f1283,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f138,f1281]) ).

fof(f1281,plain,
    ( spl0_90
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f138,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f1279,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f137,f1277]) ).

fof(f137,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f1275,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f95,f1273]) ).

fof(f95,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

fof(f1271,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f94,f1269]) ).

fof(f94,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

fof(f1267,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f90,f1265]) ).

fof(f1263,plain,
    ( ~ spl0_85
    | ~ spl0_64
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f1247,f1226,f1150,f1260]) ).

fof(f1260,plain,
    ( spl0_85
  <=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1247,plain,
    ( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_64
    | ~ spl0_80 ),
    inference(superposition,[],[f1227,f1151]) ).

fof(f1258,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f35,f1256]) ).

fof(f1256,plain,
    ( spl0_84
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f35,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).

fof(f1254,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f34,f1252]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).

fof(f1236,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f826,f1234]) ).

fof(f1234,plain,
    ( spl0_82
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f826,plain,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(forward_demodulation,[],[f825,f551]) ).

fof(f825,plain,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
    inference(forward_demodulation,[],[f739,f733]) ).

fof(f739,plain,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f184,f149]) ).

fof(f184,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

fof(f1232,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f726,f1230]) ).

fof(f726,plain,
    ! [X4] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
    inference(definition_unfolding,[],[f226,f149]) ).

fof(f226,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

fof(f1228,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f725,f1226]) ).

fof(f725,plain,
    ! [X4] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
    inference(definition_unfolding,[],[f274,f149]) ).

fof(f274,axiom,
    ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

fof(f1224,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f721,f1222]) ).

fof(f721,plain,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
    inference(definition_unfolding,[],[f223,f149]) ).

fof(f223,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

fof(f1220,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f680,f1218]) ).

fof(f680,axiom,
    ! [X9,X27] :
      ( ~ c_Lambda_Obeta(X27,X9)
      | c_Lambda_Obeta(c_Lambda_OdB_OAbs(X27),c_Lambda_OdB_OAbs(X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

fof(f1216,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f679,f1214]) ).

fof(f679,axiom,
    ! [X10,X9,X27] : c_Lambda_Osubst(c_Lambda_Olift(X9,X10),X27,X10) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

fof(f1212,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f672,f1210]) ).

fof(f672,axiom,
    ! [X40,X39] :
      ( X39 = X40
      | c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OAbs(X40) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

fof(f1208,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f664,f1206]) ).

fof(f1206,plain,
    ( spl0_75
  <=> ! [X13,X12] :
        ( X12 = X13
        | c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f664,axiom,
    ! [X12,X13] :
      ( X12 = X13
      | c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

fof(f1204,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f636,f1202]) ).

fof(f1202,plain,
    ( spl0_74
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f636,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

fof(f1200,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f612,f1198]) ).

fof(f1198,plain,
    ( spl0_73
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f612,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

fof(f1196,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f480,f1194]) ).

fof(f480,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

fof(f1192,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f345,f1190]) ).

fof(f345,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

fof(f1188,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f216,f1186]) ).

fof(f216,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_lessequals(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

fof(f1184,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f199,f1182]) ).

fof(f1182,plain,
    ( spl0_69
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f199,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

fof(f1180,plain,
    ( ~ spl0_68
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1171,f1158,f1150,f1177]) ).

fof(f1177,plain,
    ( spl0_68
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f1171,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(superposition,[],[f1159,f1151]) ).

fof(f1175,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f73,f1173]) ).

fof(f73,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

fof(f1160,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f719,f1158]) ).

fof(f719,plain,
    ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X4,
    inference(definition_unfolding,[],[f394,f149]) ).

fof(f394,axiom,
    ! [X4] : c_Suc(X4) != X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f1156,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f666,f1154]) ).

fof(f666,axiom,
    ! [X10,X29] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X10),X29,X10) = X29,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

fof(f1152,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f552,f1150]) ).

fof(f1148,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f551,f1146]) ).

fof(f1144,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f490,f1142]) ).

fof(f490,axiom,
    ! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

fof(f1140,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f353,f1138]) ).

fof(f353,axiom,
    ! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

fof(f1136,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f333,f1134]) ).

fof(f1134,plain,
    ( spl0_60
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f333,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

fof(f1132,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f280,f1130]) ).

fof(f280,axiom,
    ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat),X19,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

fof(f1128,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f279,f1126]) ).

fof(f279,axiom,
    ! [X18,X19] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X19,X18,tc_nat),X19,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

fof(f1124,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f259,f1122]) ).

fof(f259,axiom,
    ! [X10,X9] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X9,X10) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).

fof(f1120,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f197,f1118]) ).

fof(f197,axiom,
    ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

fof(f1116,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f196,f1114]) ).

fof(f196,axiom,
    ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

fof(f1112,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f14,f1110]) ).

fof(f14,axiom,
    ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

fof(f1108,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f13,f1106]) ).

fof(f13,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

fof(f1104,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f681,f1102]) ).

fof(f681,axiom,
    ! [X38,X37,X12] : c_Lambda_OdB_OApp(X37,X38) != c_Lambda_OdB_OVar(X12),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

fof(f1100,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f673,f1098]) ).

fof(f673,axiom,
    ! [X19,X9] :
      ( ~ c_InductTermi_OIT(X9)
      | c_InductTermi_OIT(c_Lambda_Olift(X9,X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

fof(f1096,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f663,f1094]) ).

fof(f663,axiom,
    ! [X39,X36,X35] : c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OAbs(X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

fof(f1092,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f618,f1090]) ).

fof(f618,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1088,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f617,f1086]) ).

fof(f617,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1084,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f616,f1082]) ).

fof(f616,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1080,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f415,f1078]) ).

fof(f415,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | c_lessequals(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f1076,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f414,f1074]) ).

fof(f414,axiom,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f1072,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f678,f1070]) ).

fof(f678,axiom,
    ! [X30] :
      ( ~ c_InductTermi_OIT(X30)
      | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X30)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

fof(f1068,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f674,f1066]) ).

fof(f674,axiom,
    ! [X39,X12] : c_Lambda_OdB_OAbs(X39) != c_Lambda_OdB_OVar(X12),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

fof(f1064,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f363,f1062]) ).

fof(f363,axiom,
    ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

fof(f1060,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f298,f1058]) ).

fof(f298,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

fof(f1056,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f670,f1054]) ).

fof(f670,axiom,
    ! [X19,X9] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X19),X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

fof(f1052,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f614,f1050]) ).

fof(f614,axiom,
    ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f1048,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f411,f1046]) ).

fof(f411,axiom,
    ! [X4] : c_lessequals(X4,X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

fof(f1044,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f718,f1041]) ).

fof(f718,axiom,
    class_Power_Opower(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

fof(f1039,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f717,f1036]) ).

fof(f717,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f1034,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f716,f1031]) ).

fof(f1031,plain,
    ( spl0_35
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f716,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f1029,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f715,f1026]) ).

fof(f715,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f1024,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f714,f1021]) ).

fof(f1021,plain,
    ( spl0_33
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f714,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f1019,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f713,f1016]) ).

fof(f713,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

fof(f1014,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f712,f1011]) ).

fof(f1011,plain,
    ( spl0_31
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f712,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f1009,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f711,f1006]) ).

fof(f1006,plain,
    ( spl0_30
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f711,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f1004,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f710,f1001]) ).

fof(f710,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f999,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f709,f996]) ).

fof(f996,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Omult__mono(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f709,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(f994,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f708,f991]) ).

fof(f991,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f708,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f989,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f707,f986]) ).

fof(f986,plain,
    ( spl0_26
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f707,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(f984,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f706,f981]) ).

fof(f706,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

fof(f979,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f705,f976]) ).

fof(f705,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f974,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f704,f971]) ).

fof(f971,plain,
    ( spl0_23
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f704,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(f969,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f703,f966]) ).

fof(f966,plain,
    ( spl0_22
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f703,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f964,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f702,f961]) ).

fof(f961,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f702,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f959,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f701,f956]) ).

fof(f956,plain,
    ( spl0_20
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f701,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f954,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f700,f951]) ).

fof(f700,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f949,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f699,f946]) ).

fof(f699,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f944,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f698,f941]) ).

fof(f698,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(f939,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f697,f936]) ).

fof(f697,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f934,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f696,f931]) ).

fof(f931,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f696,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(f929,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f695,f926]) ).

fof(f926,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f695,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(f924,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f694,f921]) ).

fof(f921,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f694,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(f919,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f693,f916]) ).

fof(f916,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f693,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f914,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f692,f911]) ).

fof(f911,plain,
    ( spl0_11
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f692,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f909,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f691,f906]) ).

fof(f906,plain,
    ( spl0_10
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f691,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f904,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f690,f901]) ).

fof(f901,plain,
    ( spl0_9
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f690,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f899,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f689,f896]) ).

fof(f896,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f689,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(f894,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f688,f891]) ).

fof(f891,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f688,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f889,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f687,f886]) ).

fof(f886,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f687,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f884,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f686,f881]) ).

fof(f881,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f686,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(f879,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f685,f876]) ).

fof(f685,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(f874,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f684,f871]) ).

fof(f684,axiom,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OAbs(v_ra),c_Lambda_OdB_OVar(v_ia),v_ja)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f869,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f683,f867]) ).

fof(f683,axiom,
    ! [X18,X19] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X19),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f865,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f682,f862]) ).

fof(f862,plain,
    ( spl0_1
  <=> c_InductTermi_OIT(v_ra) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f682,axiom,
    c_InductTermi_OIT(v_ra),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11  % Problem    : LCL753-1 : TPTP v8.2.0. Released v4.1.0.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 03:00:22 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (351)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39  % (356)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)
% 0.13/0.40  % (358)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)
% 0.13/0.40  % (354)WARNING: value z3 for option sas not known
% 0.13/0.41  % (355)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.41  % (354)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)
% 0.13/0.41  % (357)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.42  % (353)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.42  % (352)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.48  TRYING [1]
% 0.19/0.49  TRYING [2]
% 1.45/0.60  TRYING [3]
% 1.45/0.61  TRYING [1]
% 1.69/0.63  TRYING [2]
% 5.90/1.24  TRYING [4]
% 6.58/1.32  TRYING [3]
% 7.98/1.55  TRYING [1]
% 7.98/1.56  TRYING [2]
% 8.65/1.65  TRYING [3]
% 12.78/2.22  TRYING [4]
% 19.14/3.18  TRYING [5]
% 25.18/3.99  TRYING [4]
% 26.47/4.19  TRYING [5]
% 31.69/4.95  % (356)First to succeed.
% 31.69/4.98  % (356)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-351"
% 31.69/4.99  % (356)Refutation found. Thanks to Tanya!
% 31.69/4.99  % SZS status Unsatisfiable for theBenchmark
% 31.69/4.99  % SZS output start Proof for theBenchmark
% See solution above
% 31.69/5.01  % (356)------------------------------
% 31.69/5.01  % (356)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 31.69/5.01  % (356)Termination reason: Refutation
% 31.69/5.01  
% 31.69/5.01  % (356)Memory used [KB]: 36825
% 31.69/5.01  % (356)Time elapsed: 4.587 s
% 31.69/5.01  % (356)Instructions burned: 13921 (million)
% 31.69/5.01  % (351)Success in time 4.628 s
%------------------------------------------------------------------------------