TSTP Solution File: LCL800-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL800-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 Apr 30 13:49:29 EDT 2024

% Result   : Unsatisfiable 5.70s 1.21s
% Output   : Refutation 5.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  785
% Syntax   : Number of formulae    : 1803 ( 328 unt;   0 def)
%            Number of atoms       : 4691 ( 870 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 5248 (2360   ~;2345   |;   0   &)
%                                         ( 543 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :  570 ( 568 usr; 544 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;   8 con; 0-3 aty)
%            Number of variables   : 2989 (2989   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f23675,plain,
    $false,
    inference(avatar_sat_refutation,[],[f404,f409,f414,f419,f424,f429,f434,f439,f444,f449,f454,f459,f464,f469,f474,f479,f484,f489,f494,f499,f504,f509,f514,f519,f524,f528,f532,f536,f540,f544,f548,f552,f556,f560,f564,f568,f572,f576,f580,f584,f588,f593,f597,f602,f606,f610,f615,f619,f623,f627,f631,f635,f639,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f687,f691,f707,f711,f715,f719,f723,f727,f731,f735,f739,f743,f747,f751,f755,f759,f764,f768,f772,f776,f780,f811,f853,f875,f879,f883,f887,f891,f895,f899,f905,f909,f913,f917,f921,f925,f929,f933,f937,f941,f945,f949,f953,f957,f961,f1045,f1053,f1057,f1061,f1065,f1069,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1118,f1226,f1301,f1305,f1309,f1314,f1318,f1322,f1326,f1337,f1341,f1345,f1349,f1353,f1357,f1475,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1704,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1887,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2307,f2311,f2315,f2319,f2323,f2328,f2332,f2336,f2930,f2934,f2938,f2942,f2946,f2950,f2954,f2958,f2962,f2966,f2970,f2974,f2978,f2983,f3313,f3345,f3349,f3353,f3357,f3361,f3365,f3369,f3373,f3377,f3381,f3385,f3389,f3393,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3463,f3554,f3603,f3607,f3611,f3615,f3619,f3623,f3627,f3653,f3657,f3661,f4111,f4115,f4119,f4123,f4207,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4285,f4289,f4502,f4506,f4510,f4514,f4633,f4670,f4674,f4682,f4794,f4798,f4803,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4900,f4904,f4908,f4912,f5303,f5307,f5311,f5315,f5319,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5383,f5387,f5391,f5395,f5605,f5820,f5835,f5839,f5843,f5847,f5851,f5855,f5859,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5892,f5896,f6031,f6460,f6464,f6468,f6472,f6476,f6480,f6484,f6490,f6494,f6498,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6534,f6538,f6542,f6546,f6550,f6554,f6558,f6562,f6566,f6570,f7198,f7454,f7852,f7856,f7860,f7872,f7876,f7880,f7884,f7888,f7892,f7896,f7900,f7904,f7908,f7912,f7916,f7920,f7924,f7928,f7932,f7936,f7940,f7944,f7948,f7952,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8539,f9482,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9546,f9550,f9562,f9566,f9570,f9574,f9578,f9582,f9586,f9590,f9594,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9676,f9680,f9684,f9688,f10304,f11137,f12060,f12406,f12410,f12414,f12418,f12422,f12479,f12483,f12487,f12491,f12495,f12499,f12503,f12507,f12511,f12515,f12519,f12523,f12527,f12531,f12535,f12539,f12543,f12547,f12551,f12555,f12559,f12563,f12567,f12572,f12576,f12581,f12585,f12589,f12593,f12597,f12601,f12662,f12666,f12670,f12674,f12678,f12682,f12686,f12690,f12694,f12698,f12702,f12734,f12738,f12742,f12746,f12750,f12754,f12758,f12762,f12766,f12770,f12802,f12806,f12810,f16303,f16818,f16822,f16826,f16832,f16836,f16840,f16844,f16848,f16852,f16856,f16860,f16864,f16868,f16884,f16888,f16892,f16896,f16900,f16904,f16908,f16912,f16916,f16920,f16938,f16942,f16946,f16950,f16954,f17070,f17186,f17266,f17270,f17349,f17353,f17357,f17361,f17365,f17369,f17373,f17377,f17381,f17385,f17389,f17393,f17397,f17401,f17405,f17409,f17413,f17417,f17421,f17425,f17429,f17433,f17437,f17441,f17445,f17449,f17453,f17763,f19089,f20263,f22428,f23674]) ).

fof(f23674,plain,
    ( spl0_1
    | ~ spl0_52
    | ~ spl0_200
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f23640,f17407,f2980,f633,f401]) ).

fof(f401,plain,
    ( spl0_1
  <=> c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f633,plain,
    ( spl0_52
  <=> ! [X12,X15] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f2980,plain,
    ( spl0_200
  <=> c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f17407,plain,
    ( spl0_528
  <=> ! [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_528])]) ).

fof(f23640,plain,
    ( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____)))
    | ~ spl0_52
    | ~ spl0_200
    | ~ spl0_528 ),
    inference(forward_demodulation,[],[f23623,f634]) ).

fof(f634,plain,
    ( ! [X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f633]) ).

fof(f23623,plain,
    ( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))))
    | ~ spl0_200
    | ~ spl0_528 ),
    inference(superposition,[],[f2982,f17408]) ).

fof(f17408,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_528 ),
    inference(avatar_component_clause,[],[f17407]) ).

fof(f2982,plain,
    ( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f2980]) ).

fof(f22428,plain,
    ( spl0_543
    | ~ spl0_84
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f8982,f8000,f778,f22426]) ).

fof(f22426,plain,
    ( spl0_543
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f778,plain,
    ( spl0_84
  <=> ! [X28,X24] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
        | c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f8000,plain,
    ( spl0_376
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f8982,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)),X2)
    | ~ spl0_84
    | ~ spl0_376 ),
    inference(resolution,[],[f8001,f779]) ).

fof(f779,plain,
    ( ! [X28,X24] :
        ( c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28))
        | ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f778]) ).

fof(f8001,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1),X2)
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f8000]) ).

fof(f20263,plain,
    ( spl0_542
    | ~ spl0_329
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f7863,f7452,f6524,f20261]) ).

fof(f20261,plain,
    ( spl0_542
  <=> ! [X2,X0,X1,X3] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).

fof(f6524,plain,
    ( spl0_329
  <=> ! [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_329])]) ).

fof(f7452,plain,
    ( spl0_341
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f7863,plain,
    ( ! [X2,X3,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2),X3)
    | ~ spl0_329
    | ~ spl0_341 ),
    inference(resolution,[],[f7453,f6525]) ).

fof(f6525,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_329 ),
    inference(avatar_component_clause,[],[f6524]) ).

fof(f7453,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f7452]) ).

fof(f19089,plain,
    ( spl0_541
    | ~ spl0_125
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f7362,f6524,f1224,f19087]) ).

fof(f19087,plain,
    ( spl0_541
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f1224,plain,
    ( spl0_125
  <=> ! [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_125])]) ).

fof(f7362,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1),X2)
    | ~ spl0_125
    | ~ spl0_329 ),
    inference(resolution,[],[f6525,f1225]) ).

fof(f1225,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1224]) ).

fof(f17763,plain,
    ( spl0_540
    | ~ spl0_190
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f5503,f5309,f2940,f17761]) ).

fof(f17761,plain,
    ( spl0_540
  <=> ! [X0] :
        ( c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f2940,plain,
    ( spl0_190
  <=> ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f5309,plain,
    ( spl0_276
  <=> ! [X0] :
        ( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f5503,plain,
    ( ! [X0] :
        ( c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_190
    | ~ spl0_276 ),
    inference(superposition,[],[f2941,f5310]) ).

fof(f5310,plain,
    ( ! [X0] :
        ( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f5309]) ).

fof(f2941,plain,
    ( ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0))
    | ~ spl0_190 ),
    inference(avatar_component_clause,[],[f2940]) ).

fof(f17453,plain,
    ( spl0_539
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f4029,f3659,f3655,f17451]) ).

fof(f17451,plain,
    ( spl0_539
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f3655,plain,
    ( spl0_234
  <=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f3659,plain,
    ( spl0_235
  <=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f4029,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),tc_nat)
    | ~ spl0_234
    | ~ spl0_235 ),
    inference(superposition,[],[f3660,f3656]) ).

fof(f3656,plain,
    ( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
    | ~ spl0_234 ),
    inference(avatar_component_clause,[],[f3655]) ).

fof(f3660,plain,
    ( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f3659]) ).

fof(f17449,plain,
    ( spl0_538
    | ~ spl0_56
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f3570,f3427,f653,f17447]) ).

fof(f17447,plain,
    ( spl0_538
  <=> ! [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_Suc(c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f653,plain,
    ( spl0_56
  <=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f3427,plain,
    ( spl0_223
  <=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f3570,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_Suc(c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_223 ),
    inference(superposition,[],[f654,f3428]) ).

fof(f3428,plain,
    ( ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f3427]) ).

fof(f654,plain,
    ( ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat)
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f653]) ).

fof(f17445,plain,
    ( spl0_537
    | ~ spl0_13
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f3555,f3419,f461,f17443]) ).

fof(f17443,plain,
    ( spl0_537
  <=> ! [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_537])]) ).

fof(f461,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f3419,plain,
    ( spl0_221
  <=> ! [X20,X0,X23,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f3555,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_13
    | ~ spl0_221 ),
    inference(resolution,[],[f3420,f463]) ).

fof(f463,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f461]) ).

fof(f3420,plain,
    ( ! [X0,X22,X23,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) )
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f3419]) ).

fof(f17441,plain,
    ( spl0_536
    | ~ spl0_13
    | ~ spl0_181
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f3550,f3411,f2313,f461,f17439]) ).

fof(f17439,plain,
    ( spl0_536
  <=> ! [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_536])]) ).

fof(f2313,plain,
    ( spl0_181
  <=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f3411,plain,
    ( spl0_219
  <=> ! [X21,X20,X0,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f3550,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_13
    | ~ spl0_181
    | ~ spl0_219 ),
    inference(forward_demodulation,[],[f3549,f2314]) ).

fof(f2314,plain,
    ( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f2313]) ).

fof(f3549,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_13
    | ~ spl0_219 ),
    inference(resolution,[],[f3412,f463]) ).

fof(f3412,plain,
    ( ! [X21,X0,X22,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) )
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f3411]) ).

fof(f17437,plain,
    ( spl0_535
    | ~ spl0_18
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f3518,f3399,f486,f17435]) ).

fof(f17435,plain,
    ( spl0_535
  <=> ! [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_535])]) ).

fof(f486,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f3399,plain,
    ( spl0_216
  <=> ! [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_216])]) ).

fof(f3518,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_18
    | ~ spl0_216 ),
    inference(resolution,[],[f3400,f488]) ).

fof(f488,plain,
    ( class_Ring__and__Field_Osemiring__1(tc_nat)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f486]) ).

fof(f3400,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_216 ),
    inference(avatar_component_clause,[],[f3399]) ).

fof(f17433,plain,
    ( spl0_534
    | ~ spl0_18
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f3504,f3391,f486,f17431]) ).

fof(f17431,plain,
    ( spl0_534
  <=> ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(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_534])]) ).

fof(f3391,plain,
    ( spl0_214
  <=> ! [X4,X0,X3] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(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_214])]) ).

fof(f3504,plain,
    ( ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(X1,tc_nat),tc_nat)
    | ~ spl0_18
    | ~ spl0_214 ),
    inference(resolution,[],[f3392,f488]) ).

fof(f3392,plain,
    ( ! [X3,X0,X4] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) )
    | ~ spl0_214 ),
    inference(avatar_component_clause,[],[f3391]) ).

fof(f17429,plain,
    ( spl0_533
    | ~ spl0_48
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f3449,f3343,f617,f17427]) ).

fof(f17427,plain,
    ( spl0_533
  <=> ! [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_533])]) ).

fof(f617,plain,
    ( spl0_48
  <=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f3343,plain,
    ( spl0_202
  <=> ! [X4,X14,X12,X3] :
        ( ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X12,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f3449,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_48
    | ~ spl0_202 ),
    inference(superposition,[],[f3344,f618]) ).

fof(f618,plain,
    ( ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f3344,plain,
    ( ! [X3,X14,X4,X12] :
        ( c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X12,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f3343]) ).

fof(f17425,plain,
    ( spl0_532
    | ~ spl0_80
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f3646,f3311,f762,f17423]) ).

fof(f17423,plain,
    ( spl0_532
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(c_Suc(X0)))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f762,plain,
    ( spl0_80
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f3311,plain,
    ( spl0_201
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f3646,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(c_Suc(X0)))),tc_nat)
    | ~ spl0_80
    | ~ spl0_201 ),
    inference(resolution,[],[f3312,f763]) ).

fof(f763,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f762]) ).

fof(f3312,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f3311]) ).

fof(f17421,plain,
    ( spl0_531
    | ~ spl0_46
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f3445,f3343,f608,f17419]) ).

fof(f17419,plain,
    ( spl0_531
  <=> ! [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_531])]) ).

fof(f608,plain,
    ( spl0_46
  <=> ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f3445,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_46
    | ~ spl0_202 ),
    inference(superposition,[],[f3344,f609]) ).

fof(f609,plain,
    ( ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f608]) ).

fof(f17417,plain,
    ( spl0_530
    | ~ spl0_48
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f3438,f3343,f617,f17415]) ).

fof(f17415,plain,
    ( spl0_530
  <=> ! [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_530])]) ).

fof(f3438,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_48
    | ~ spl0_202 ),
    inference(superposition,[],[f3344,f618]) ).

fof(f17413,plain,
    ( spl0_529
    | ~ spl0_65
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3317,f2972,f689,f17411]) ).

fof(f17411,plain,
    ( spl0_529
  <=> ! [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_529])]) ).

fof(f689,plain,
    ( spl0_65
  <=> ! [X25,X12,X28] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f2972,plain,
    ( spl0_198
  <=> ! [X28,X15,X12,X25] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f3317,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_65
    | ~ spl0_198 ),
    inference(superposition,[],[f2973,f690]) ).

fof(f690,plain,
    ( ! [X28,X25,X12] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f689]) ).

fof(f2973,plain,
    ( ! [X28,X15,X25,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12))
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f2972]) ).

fof(f17409,plain,
    ( spl0_528
    | ~ spl0_65
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3315,f2972,f689,f17407]) ).

fof(f3315,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_65
    | ~ spl0_198 ),
    inference(superposition,[],[f2973,f690]) ).

fof(f17405,plain,
    ( spl0_527
    | ~ spl0_175
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2894,f2334,f2289,f17403]) ).

fof(f17403,plain,
    ( spl0_527
  <=> ! [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_527])]) ).

fof(f2289,plain,
    ( spl0_175
  <=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f2334,plain,
    ( spl0_186
  <=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f2894,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_175
    | ~ spl0_186 ),
    inference(superposition,[],[f2335,f2290]) ).

fof(f2290,plain,
    ( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat)
    | ~ spl0_175 ),
    inference(avatar_component_clause,[],[f2289]) ).

fof(f2335,plain,
    ( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat)
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f2334]) ).

fof(f17401,plain,
    ( spl0_526
    | ~ spl0_66
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2713,f2313,f705,f17399]) ).

fof(f17399,plain,
    ( spl0_526
  <=> ! [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(X2,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f705,plain,
    ( spl0_66
  <=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f2713,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(X2,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
    | ~ spl0_66
    | ~ spl0_181 ),
    inference(superposition,[],[f2314,f706]) ).

fof(f706,plain,
    ( ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f705]) ).

fof(f17397,plain,
    ( spl0_525
    | ~ spl0_66
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f2709,f2313,f705,f17395]) ).

fof(f17395,plain,
    ( spl0_525
  <=> ! [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(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X2,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f2709,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(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X2,tc_nat)
    | ~ spl0_66
    | ~ spl0_181 ),
    inference(superposition,[],[f2314,f706]) ).

fof(f17393,plain,
    ( spl0_524
    | ~ spl0_67
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f2583,f2301,f709,f17391]) ).

fof(f17391,plain,
    ( spl0_524
  <=> ! [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_524])]) ).

fof(f709,plain,
    ( spl0_67
  <=> ! [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_67])]) ).

fof(f2301,plain,
    ( spl0_178
  <=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f2583,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_67
    | ~ spl0_178 ),
    inference(superposition,[],[f2302,f710]) ).

fof(f710,plain,
    ( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f2302,plain,
    ( ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat)
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f2301]) ).

fof(f17389,plain,
    ( spl0_523
    | ~ spl0_66
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2564,f2293,f705,f17387]) ).

fof(f17387,plain,
    ( spl0_523
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f2293,plain,
    ( spl0_176
  <=> ! [X4,X12,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f2564,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_66
    | ~ spl0_176 ),
    inference(superposition,[],[f2294,f706]) ).

fof(f2294,plain,
    ( ! [X3,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat) )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f2293]) ).

fof(f17385,plain,
    ( spl0_522
    | ~ spl0_66
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f2560,f2293,f705,f17383]) ).

fof(f17383,plain,
    ( spl0_522
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f2560,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
    | ~ spl0_66
    | ~ spl0_176 ),
    inference(superposition,[],[f2294,f706]) ).

fof(f17381,plain,
    ( spl0_521
    | ~ spl0_124
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2692,f1824,f1116,f17379]) ).

fof(f17379,plain,
    ( spl0_521
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f1116,plain,
    ( spl0_124
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1824,plain,
    ( spl0_160
  <=> ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f2692,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_124
    | ~ spl0_160 ),
    inference(superposition,[],[f1117,f1825]) ).

fof(f1825,plain,
    ( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)))
    | ~ spl0_160 ),
    inference(avatar_component_clause,[],[f1824]) ).

fof(f1117,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1116]) ).

fof(f17377,plain,
    ( spl0_520
    | ~ spl0_77
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2527,f2289,f749,f17375]) ).

fof(f17375,plain,
    ( spl0_520
  <=> ! [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_520])]) ).

fof(f749,plain,
    ( spl0_77
  <=> ! [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_77])]) ).

fof(f2527,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_77
    | ~ spl0_175 ),
    inference(superposition,[],[f2290,f750]) ).

fof(f750,plain,
    ( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f749]) ).

fof(f17373,plain,
    ( spl0_519
    | ~ spl0_78
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2471,f2285,f753,f17371]) ).

fof(f17371,plain,
    ( spl0_519
  <=> ! [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_519])]) ).

fof(f753,plain,
    ( spl0_78
  <=> ! [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_78])]) ).

fof(f2285,plain,
    ( spl0_174
  <=> ! [X4,X12,X3] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f2471,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_78
    | ~ spl0_174 ),
    inference(superposition,[],[f754,f2286]) ).

fof(f2286,plain,
    ( ! [X3,X4,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat)
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f2285]) ).

fof(f754,plain,
    ( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f753]) ).

fof(f17369,plain,
    ( spl0_518
    | ~ spl0_77
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2470,f2285,f749,f17367]) ).

fof(f17367,plain,
    ( spl0_518
  <=> ! [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_518])]) ).

fof(f2470,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_77
    | ~ spl0_174 ),
    inference(superposition,[],[f750,f2286]) ).

fof(f17365,plain,
    ( spl0_517
    | ~ spl0_67
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2445,f2285,f709,f17363]) ).

fof(f17363,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f2445,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_67
    | ~ spl0_174 ),
    inference(superposition,[],[f2286,f710]) ).

fof(f17361,plain,
    ( spl0_516
    | ~ spl0_78
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2372,f2277,f753,f17359]) ).

fof(f17359,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f2277,plain,
    ( spl0_172
  <=> ! [X6,X5,X7] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f2372,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_78
    | ~ spl0_172 ),
    inference(superposition,[],[f754,f2278]) ).

fof(f2278,plain,
    ( ! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat)
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f2277]) ).

fof(f17357,plain,
    ( spl0_515
    | ~ spl0_77
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2371,f2277,f749,f17355]) ).

fof(f17355,plain,
    ( spl0_515
  <=> ! [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_515])]) ).

fof(f2371,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_77
    | ~ spl0_172 ),
    inference(superposition,[],[f750,f2278]) ).

fof(f17353,plain,
    ( spl0_514
    | ~ spl0_67
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2347,f2277,f709,f17351]) ).

fof(f17351,plain,
    ( spl0_514
  <=> ! [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_514])]) ).

fof(f2347,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_67
    | ~ spl0_172 ),
    inference(superposition,[],[f2278,f710]) ).

fof(f17349,plain,
    ( spl0_513
    | ~ spl0_67
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2337,f2277,f709,f17347]) ).

fof(f17347,plain,
    ( spl0_513
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f2337,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
    | ~ spl0_67
    | ~ spl0_172 ),
    inference(superposition,[],[f2278,f710]) ).

fof(f17270,plain,
    ( ~ spl0_25
    | spl0_512
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2271,f1885,f757,f17268,f521]) ).

fof(f521,plain,
    ( spl0_25
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f17268,plain,
    ( spl0_512
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f757,plain,
    ( spl0_79
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f1885,plain,
    ( spl0_171
  <=> ! [X6,X0,X5,X7] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X7,X6,X0)
        | c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f2271,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | ~ class_Orderings_Oorder(tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(resolution,[],[f1886,f758]) ).

fof(f758,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f757]) ).

fof(f1886,plain,
    ( ! [X0,X6,X7,X5] :
        ( ~ c_HOL_Oord__class_Oless(X7,X6,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
        | ~ class_Orderings_Oorder(X0)
        | c_HOL_Oord__class_Oless(X7,X5,X0) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1885]) ).

fof(f17266,plain,
    ( spl0_511
    | ~ spl0_124
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f2064,f1702,f1116,f17264]) ).

fof(f17264,plain,
    ( spl0_511
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f1702,plain,
    ( spl0_152
  <=> ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f2064,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_124
    | ~ spl0_152 ),
    inference(superposition,[],[f1117,f1703]) ).

fof(f1703,plain,
    ( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)))
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1702]) ).

fof(f17186,plain,
    ( ~ spl0_25
    | spl0_510
    | ~ spl0_83
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f2270,f1885,f774,f17184,f521]) ).

fof(f17184,plain,
    ( spl0_510
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),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_510])]) ).

fof(f774,plain,
    ( spl0_83
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f2270,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(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) )
    | ~ spl0_83
    | ~ spl0_171 ),
    inference(resolution,[],[f1886,f775]) ).

fof(f775,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f774]) ).

fof(f17070,plain,
    ( ~ spl0_23
    | spl0_509
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f2246,f1864,f757,f17068,f511]) ).

fof(f511,plain,
    ( spl0_23
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f17068,plain,
    ( spl0_509
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f1864,plain,
    ( spl0_170
  <=> ! [X5,X0,X6,X7] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X7,X0)
        | c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f2246,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_79
    | ~ spl0_170 ),
    inference(resolution,[],[f1865,f758]) ).

fof(f1865,plain,
    ( ! [X0,X6,X7,X5] :
        ( ~ c_HOL_Oord__class_Oless(X6,X7,X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | ~ class_Orderings_Opreorder(X0)
        | c_HOL_Oord__class_Oless(X5,X7,X0) )
    | ~ spl0_170 ),
    inference(avatar_component_clause,[],[f1864]) ).

fof(f16954,plain,
    ( ~ spl0_23
    | spl0_508
    | ~ spl0_83
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f2245,f1864,f774,f16952,f511]) ).

fof(f16952,plain,
    ( spl0_508
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X2),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f2245,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X2),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_83
    | ~ spl0_170 ),
    inference(resolution,[],[f1865,f775]) ).

fof(f16950,plain,
    ( spl0_507
    | ~ spl0_46
    | ~ spl0_111
    | ~ spl0_131
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f2197,f1852,f1320,f1055,f608,f16948]) ).

fof(f16948,plain,
    ( spl0_507
  <=> ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(X1),tc_nat))
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f1055,plain,
    ( spl0_111
  <=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1320,plain,
    ( spl0_131
  <=> ! [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_131])]) ).

fof(f1852,plain,
    ( spl0_167
  <=> ! [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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f2197,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(X1),tc_nat))
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_46
    | ~ spl0_111
    | ~ spl0_131
    | ~ spl0_167 ),
    inference(forward_demodulation,[],[f2196,f609]) ).

fof(f2196,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),tc_nat))
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_111
    | ~ spl0_131
    | ~ spl0_167 ),
    inference(forward_demodulation,[],[f2195,f1056]) ).

fof(f1056,plain,
    ( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat))
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1055]) ).

fof(f2195,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_nat))
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_131
    | ~ spl0_167 ),
    inference(forward_demodulation,[],[f2183,f73]) ).

fof(f73,axiom,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

fof(f2183,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_131
    | ~ spl0_167 ),
    inference(resolution,[],[f1853,f1321]) ).

fof(f1321,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_131 ),
    inference(avatar_component_clause,[],[f1320]) ).

fof(f1853,plain,
    ( ! [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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1852]) ).

fof(f16946,plain,
    ( spl0_506
    | ~ spl0_79
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2025,f1832,f757,f16944]) ).

fof(f16944,plain,
    ( spl0_506
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f1832,plain,
    ( spl0_162
  <=> ! [X13,X12,X11] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
        | c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f2025,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_79
    | ~ spl0_162 ),
    inference(resolution,[],[f1833,f758]) ).

fof(f1833,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
        | c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1832]) ).

fof(f16942,plain,
    ( spl0_505
    | ~ spl0_83
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2024,f1832,f774,f16940]) ).

fof(f16940,plain,
    ( spl0_505
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),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_505])]) ).

fof(f2024,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_83
    | ~ spl0_162 ),
    inference(resolution,[],[f1833,f775]) ).

fof(f16938,plain,
    ( spl0_504
    | ~ spl0_82
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1775,f1516,f770,f16936]) ).

fof(f16936,plain,
    ( spl0_504
  <=> ! [X0,X1] :
        ( c_Suc(X0) = c_Suc(X1)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f770,plain,
    ( spl0_82
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f1516,plain,
    ( spl0_149
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Suc(X3) = X4
        | c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1775,plain,
    ( ! [X0,X1] :
        ( c_Suc(X0) = c_Suc(X1)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_82
    | ~ spl0_149 ),
    inference(resolution,[],[f1517,f771]) ).

fof(f771,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f770]) ).

fof(f1517,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat)
        | c_Suc(X3) = X4
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1516]) ).

fof(f16920,plain,
    ( spl0_503
    | ~ spl0_99
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1697,f1508,f923,f16918]) ).

fof(f16918,plain,
    ( spl0_503
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f923,plain,
    ( spl0_99
  <=> ! [X4,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1508,plain,
    ( spl0_147
  <=> ! [X13,X12,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1697,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_99
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f924]) ).

fof(f924,plain,
    ( ! [X4,X5] :
        ( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f923]) ).

fof(f1509,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1508]) ).

fof(f16916,plain,
    ( spl0_502
    | ~ spl0_100
    | ~ spl0_112
    | ~ spl0_120
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1660,f1500,f1099,f1059,f927,f16914]) ).

fof(f16914,plain,
    ( spl0_502
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat))
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f927,plain,
    ( spl0_100
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1059,plain,
    ( spl0_112
  <=> ! [X4,X3] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1099,plain,
    ( spl0_120
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1500,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f1660,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat))
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_100
    | ~ spl0_112
    | ~ spl0_120
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1659,f1100]) ).

fof(f1100,plain,
    ( ! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat)
    | ~ spl0_120 ),
    inference(avatar_component_clause,[],[f1099]) ).

fof(f1659,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X0),tc_nat),tc_nat))
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_100
    | ~ spl0_112
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1640,f1060]) ).

fof(f1060,plain,
    ( ! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat)
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f1059]) ).

fof(f1640,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_HOL_Oplus__class_Oplus(c_Suc(X0),c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X0),tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_100
    | ~ spl0_145 ),
    inference(resolution,[],[f1501,f928]) ).

fof(f928,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f927]) ).

fof(f1501,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_145 ),
    inference(avatar_component_clause,[],[f1500]) ).

fof(f16912,plain,
    ( spl0_501
    | ~ spl0_82
    | ~ spl0_112
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1646,f1500,f1059,f770,f16910]) ).

fof(f16910,plain,
    ( spl0_501
  <=> ! [X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,c_Suc(X0),tc_nat),tc_nat)) = X1
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f1646,plain,
    ( ! [X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,c_Suc(X0),tc_nat),tc_nat)) = X1
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_82
    | ~ spl0_112
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1622,f1060]) ).

fof(f1622,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_Suc(X0),c_HOL_Ominus__class_Ominus(X1,c_Suc(X0),tc_nat),tc_nat) = X1
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_82
    | ~ spl0_145 ),
    inference(resolution,[],[f1501,f771]) ).

fof(f16908,plain,
    ( spl0_500
    | ~ spl0_80
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1638,f1500,f762,f16906]) ).

fof(f16906,plain,
    ( spl0_500
  <=> ! [X0,X1] :
        ( c_Suc(X1) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f1638,plain,
    ( ! [X0,X1] :
        ( c_Suc(X1) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_Suc(X1),X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_80
    | ~ spl0_145 ),
    inference(resolution,[],[f1501,f763]) ).

fof(f16904,plain,
    ( spl0_499
    | ~ spl0_119
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1605,f1496,f1095,f16902]) ).

fof(f16902,plain,
    ( spl0_499
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f1095,plain,
    ( spl0_119
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1496,plain,
    ( spl0_144
  <=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1605,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
    | ~ spl0_119
    | ~ spl0_144 ),
    inference(superposition,[],[f1096,f1497]) ).

fof(f1497,plain,
    ( ! [X3,X4] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1496]) ).

fof(f1096,plain,
    ( ! [X3,X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_119 ),
    inference(avatar_component_clause,[],[f1095]) ).

fof(f16900,plain,
    ( spl0_498
    | ~ spl0_115
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1603,f1496,f1079,f16898]) ).

fof(f16898,plain,
    ( spl0_498
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f1079,plain,
    ( spl0_115
  <=> ! [X13,X11,X3] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f1603,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) )
    | ~ spl0_115
    | ~ spl0_144 ),
    inference(superposition,[],[f1080,f1497]) ).

fof(f1080,plain,
    ( ! [X3,X11,X13] :
        ( c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f1079]) ).

fof(f16896,plain,
    ( spl0_497
    | ~ spl0_119
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1572,f1492,f1095,f16894]) ).

fof(f16894,plain,
    ( spl0_497
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f1492,plain,
    ( spl0_143
  <=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1572,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
    | ~ spl0_119
    | ~ spl0_143 ),
    inference(superposition,[],[f1096,f1493]) ).

fof(f1493,plain,
    ( ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1492]) ).

fof(f16892,plain,
    ( spl0_496
    | ~ spl0_115
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1570,f1492,f1079,f16890]) ).

fof(f16890,plain,
    ( spl0_496
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f1570,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_115
    | ~ spl0_143 ),
    inference(superposition,[],[f1080,f1493]) ).

fof(f16888,plain,
    ( spl0_495
    | ~ spl0_99
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1458,f1343,f923,f16886]) ).

fof(f16886,plain,
    ( spl0_495
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_Suc(X0)),X1,c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f1343,plain,
    ( spl0_135
  <=> ! [X13,X11,X15] :
        ( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
        | c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1458,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_Suc(X0)),X1,c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_99
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f924]) ).

fof(f1344,plain,
    ( ! [X11,X15,X13] :
        ( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
        | c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1343]) ).

fof(f16884,plain,
    ( spl0_494
    | ~ spl0_56
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1455,f1343,f653,f16882]) ).

fof(f16882,plain,
    ( spl0_494
  <=> ! [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_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f1455,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_Suc(X0))
    | ~ spl0_56
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f654]) ).

fof(f16868,plain,
    ( spl0_493
    | ~ spl0_113
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1451,f1343,f1063,f16866]) ).

fof(f16866,plain,
    ( spl0_493
  <=> ! [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_493])]) ).

fof(f1063,plain,
    ( spl0_113
  <=> ! [X6,X5,X7] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f1451,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_113
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f1064]) ).

fof(f1064,plain,
    ( ! [X6,X7,X5] :
        ( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f1063]) ).

fof(f16864,plain,
    ( spl0_492
    | ~ spl0_115
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1450,f1343,f1079,f16862]) ).

fof(f16862,plain,
    ( spl0_492
  <=> ! [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_492])]) ).

fof(f1450,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_115
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f1080]) ).

fof(f16860,plain,
    ( spl0_491
    | ~ spl0_102
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1442,f1339,f935,f16858]) ).

fof(f16858,plain,
    ( spl0_491
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(c_Suc(X0),X1,X2),c_Lambda_Olift(X3,X2))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f935,plain,
    ( spl0_102
  <=> ! [X11,X28,X24] :
        ( ~ c_Lambda_Obeta(X24,X28)
        | c_Lambda_Obeta(c_Lambda_Olift(X24,X11),c_Lambda_Olift(X28,X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1339,plain,
    ( spl0_134
  <=> ! [X25,X12,X4] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f1442,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Oliftn(c_Suc(X0),X1,X2),c_Lambda_Olift(X3,X2))
        | ~ c_Lambda_Obeta(c_Lambda_Oliftn(X0,X1,X2),X3) )
    | ~ spl0_102
    | ~ spl0_134 ),
    inference(superposition,[],[f936,f1340]) ).

fof(f1340,plain,
    ( ! [X4,X25,X12] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12)
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1339]) ).

fof(f936,plain,
    ( ! [X28,X11,X24] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X24,X11),c_Lambda_Olift(X28,X11))
        | ~ c_Lambda_Obeta(X24,X28) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f935]) ).

fof(f16856,plain,
    ( spl0_490
    | ~ spl0_102
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1441,f1339,f935,f16854]) ).

fof(f16854,plain,
    ( spl0_490
  <=> ! [X0,X3,X2,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Oliftn(c_Suc(X0),X1,X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f1441,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Olift(X3,X2),c_Lambda_Oliftn(c_Suc(X0),X1,X2))
        | ~ c_Lambda_Obeta(X3,c_Lambda_Oliftn(X0,X1,X2)) )
    | ~ spl0_102
    | ~ spl0_134 ),
    inference(superposition,[],[f936,f1340]) ).

fof(f16852,plain,
    ( spl0_489
    | ~ spl0_99
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1436,f1335,f923,f16850]) ).

fof(f16850,plain,
    ( spl0_489
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f1335,plain,
    ( spl0_133
  <=> ! [X11,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1436,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_99
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f924]) ).

fof(f1336,plain,
    ( ! [X11,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1335]) ).

fof(f16848,plain,
    ( spl0_488
    | ~ spl0_56
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1433,f1335,f653,f16846]) ).

fof(f16846,plain,
    ( spl0_488
  <=> ! [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_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1433,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_Suc(X0))
    | ~ spl0_56
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f654]) ).

fof(f16844,plain,
    ( spl0_487
    | ~ spl0_113
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1429,f1335,f1063,f16842]) ).

fof(f16842,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f1429,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_113
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f1064]) ).

fof(f16840,plain,
    ( spl0_486
    | ~ spl0_115
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1428,f1335,f1079,f16838]) ).

fof(f16838,plain,
    ( spl0_486
  <=> ! [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_486])]) ).

fof(f1428,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_115
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f1080]) ).

fof(f16836,plain,
    ( spl0_485
    | ~ spl0_122
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1425,f1335,f1107,f16834]) ).

fof(f16834,plain,
    ( spl0_485
  <=> ! [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_485])]) ).

fof(f1107,plain,
    ( spl0_122
  <=> ! [X6,X5] :
        ( X5 = X6
        | c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_HOL_Oord__class_Oless(X6,X5,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1425,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_122
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f1108]) ).

fof(f1108,plain,
    ( ! [X6,X5] :
        ( c_HOL_Oord__class_Oless(X6,X5,tc_nat)
        | c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | X5 = X6 )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f1107]) ).

fof(f16832,plain,
    ( spl0_484
    | ~ spl0_96
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1399,f1320,f911,f16830]) ).

fof(f16830,plain,
    ( spl0_484
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f911,plain,
    ( spl0_96
  <=> ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1399,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat))) )
    | ~ spl0_96
    | ~ spl0_131 ),
    inference(resolution,[],[f1321,f912]) ).

fof(f912,plain,
    ( ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f911]) ).

fof(f16826,plain,
    ( spl0_483
    | ~ spl0_98
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1398,f1320,f919,f16824]) ).

fof(f16824,plain,
    ( spl0_483
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f919,plain,
    ( spl0_98
  <=> ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1398,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat))) )
    | ~ spl0_98
    | ~ spl0_131 ),
    inference(resolution,[],[f1321,f920]) ).

fof(f920,plain,
    ( ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f919]) ).

fof(f16822,plain,
    ( spl0_482
    | ~ spl0_100
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1261,f1107,f927,f16820]) ).

fof(f16820,plain,
    ( spl0_482
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
        | c_Suc(X0) = c_Suc(X1)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f1261,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat)
        | c_Suc(X0) = c_Suc(X1)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_100
    | ~ spl0_122 ),
    inference(resolution,[],[f1108,f928]) ).

fof(f16818,plain,
    ( spl0_481
    | ~ spl0_97
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1247,f1107,f915,f16816]) ).

fof(f16816,plain,
    ( spl0_481
  <=> ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f915,plain,
    ( spl0_97
  <=> ! [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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1247,plain,
    ( ! [X0] :
        ( c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_97
    | ~ spl0_122 ),
    inference(resolution,[],[f1108,f916]) ).

fof(f916,plain,
    ( ! [X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f915]) ).

fof(f16303,plain,
    ( spl0_480
    | ~ spl0_308
    | ~ spl0_435 ),
    inference(avatar_split_clause,[],[f15493,f12517,f5882,f16301]) ).

fof(f16301,plain,
    ( spl0_480
  <=> ! [X0,X1] : c_Lambda_OdB_OAbs(X1) != c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f5882,plain,
    ( spl0_308
  <=> ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f12517,plain,
    ( spl0_435
  <=> ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0) != c_Lambda_OdB_OAbs(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f15493,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OAbs(X1) != c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_308
    | ~ spl0_435 ),
    inference(superposition,[],[f12518,f5883]) ).

fof(f5883,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
    | ~ spl0_308 ),
    inference(avatar_component_clause,[],[f5882]) ).

fof(f12518,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0) != c_Lambda_OdB_OAbs(X2)
    | ~ spl0_435 ),
    inference(avatar_component_clause,[],[f12517]) ).

fof(f12810,plain,
    ( spl0_479
    | ~ spl0_55
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f4038,f3659,f649,f12808]) ).

fof(f12808,plain,
    ( spl0_479
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f649,plain,
    ( spl0_55
  <=> ! [X11,X3] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f4038,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_235 ),
    inference(superposition,[],[f650,f3660]) ).

fof(f650,plain,
    ( ! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f649]) ).

fof(f12806,plain,
    ( spl0_478
    | ~ spl0_54
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f4037,f3659,f645,f12804]) ).

fof(f12804,plain,
    ( spl0_478
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f645,plain,
    ( spl0_54
  <=> ! [X11,X3] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X11,X3,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f4037,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_235 ),
    inference(superposition,[],[f646,f3660]) ).

fof(f646,plain,
    ( ! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X11,X3,tc_nat)),tc_nat)
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f645]) ).

fof(f12802,plain,
    ( spl0_477
    | ~ spl0_55
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3951,f3655,f649,f12800]) ).

fof(f12800,plain,
    ( spl0_477
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f3951,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_234 ),
    inference(superposition,[],[f650,f3656]) ).

fof(f12770,plain,
    ( spl0_476
    | ~ spl0_54
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3950,f3655,f645,f12768]) ).

fof(f12768,plain,
    ( spl0_476
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f3950,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_234 ),
    inference(superposition,[],[f646,f3656]) ).

fof(f12766,plain,
    ( spl0_475
    | ~ spl0_56
    | ~ spl0_229 ),
    inference(avatar_split_clause,[],[f3782,f3613,f653,f12764]) ).

fof(f12764,plain,
    ( spl0_475
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f3613,plain,
    ( spl0_229
  <=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f3782,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_229 ),
    inference(superposition,[],[f654,f3614]) ).

fof(f3614,plain,
    ( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f3613]) ).

fof(f12762,plain,
    ( spl0_474
    | ~ spl0_56
    | ~ spl0_228 ),
    inference(avatar_split_clause,[],[f3744,f3609,f653,f12760]) ).

fof(f12760,plain,
    ( spl0_474
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f3609,plain,
    ( spl0_228
  <=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f3744,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_228 ),
    inference(superposition,[],[f654,f3610]) ).

fof(f3610,plain,
    ( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f3609]) ).

fof(f12758,plain,
    ( spl0_473
    | ~ spl0_52
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3316,f2972,f633,f12756]) ).

fof(f12756,plain,
    ( spl0_473
  <=> ! [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_473])]) ).

fof(f3316,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_52
    | ~ spl0_198 ),
    inference(superposition,[],[f2973,f634]) ).

fof(f12754,plain,
    ( spl0_472
    | ~ spl0_52
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3314,f2972,f633,f12752]) ).

fof(f12752,plain,
    ( spl0_472
  <=> ! [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_472])]) ).

fof(f3314,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_52
    | ~ spl0_198 ),
    inference(superposition,[],[f2973,f634]) ).

fof(f12750,plain,
    ( spl0_471
    | ~ spl0_56
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f2900,f2334,f653,f12748]) ).

fof(f12748,plain,
    ( spl0_471
  <=> ! [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_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f2900,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_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_186 ),
    inference(superposition,[],[f654,f2335]) ).

fof(f12746,plain,
    ( spl0_470
    | ~ spl0_79
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2806,f2321,f757,f12744]) ).

fof(f12744,plain,
    ( spl0_470
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f2321,plain,
    ( spl0_183
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f2806,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_79
    | ~ spl0_183 ),
    inference(resolution,[],[f2322,f758]) ).

fof(f2322,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f2321]) ).

fof(f12742,plain,
    ( spl0_469
    | ~ spl0_83
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2805,f2321,f774,f12740]) ).

fof(f12740,plain,
    ( spl0_469
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f2805,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_83
    | ~ spl0_183 ),
    inference(resolution,[],[f2322,f775]) ).

fof(f12738,plain,
    ( spl0_468
    | ~ spl0_48
    | ~ spl0_96
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2787,f2317,f911,f617,f12736]) ).

fof(f12736,plain,
    ( spl0_468
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f2317,plain,
    ( spl0_182
  <=> ! [X11,X4,X12] :
        ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f2787,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 )
    | ~ spl0_48
    | ~ spl0_96
    | ~ spl0_182 ),
    inference(forward_demodulation,[],[f2769,f618]) ).

fof(f2769,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 )
    | ~ spl0_96
    | ~ spl0_182 ),
    inference(resolution,[],[f2318,f912]) ).

fof(f2318,plain,
    ( ! [X11,X4,X12] :
        ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) )
    | ~ spl0_182 ),
    inference(avatar_component_clause,[],[f2317]) ).

fof(f12734,plain,
    ( spl0_467
    | ~ spl0_48
    | ~ spl0_98
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2786,f2317,f919,f617,f12732]) ).

fof(f12732,plain,
    ( spl0_467
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f2786,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 )
    | ~ spl0_48
    | ~ spl0_98
    | ~ spl0_182 ),
    inference(forward_demodulation,[],[f2768,f618]) ).

fof(f2768,plain,
    ( ! [X0,X1] :
        ( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 )
    | ~ spl0_98
    | ~ spl0_182 ),
    inference(resolution,[],[f2318,f920]) ).

fof(f12702,plain,
    ( spl0_466
    | ~ spl0_121
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f2653,f2305,f1103,f12700]) ).

fof(f12700,plain,
    ( spl0_466
  <=> ! [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_466])]) ).

fof(f1103,plain,
    ( spl0_121
  <=> ! [X13,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f2305,plain,
    ( spl0_179
  <=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f2653,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_121
    | ~ spl0_179 ),
    inference(superposition,[],[f1104,f2306]) ).

fof(f2306,plain,
    ( ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
    | ~ spl0_179 ),
    inference(avatar_component_clause,[],[f2305]) ).

fof(f1104,plain,
    ( ! [X4,X12,X13] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1103]) ).

fof(f12698,plain,
    ( spl0_465
    | ~ spl0_121
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f2612,f2301,f1103,f12696]) ).

fof(f12696,plain,
    ( spl0_465
  <=> ! [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_465])]) ).

fof(f2612,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_121
    | ~ spl0_178 ),
    inference(superposition,[],[f1104,f2302]) ).

fof(f12694,plain,
    ( spl0_464
    | ~ spl0_56
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2535,f2289,f653,f12692]) ).

fof(f12692,plain,
    ( spl0_464
  <=> ! [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_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f2535,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_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_175 ),
    inference(superposition,[],[f654,f2290]) ).

fof(f12690,plain,
    ( spl0_463
    | ~ spl0_119
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2478,f2285,f1095,f12688]) ).

fof(f12688,plain,
    ( spl0_463
  <=> ! [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_463])]) ).

fof(f2478,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_119
    | ~ spl0_174 ),
    inference(superposition,[],[f1096,f2286]) ).

fof(f12686,plain,
    ( spl0_462
    | ~ spl0_115
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2476,f2285,f1079,f12684]) ).

fof(f12684,plain,
    ( spl0_462
  <=> ! [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_462])]) ).

fof(f2476,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_115
    | ~ spl0_174 ),
    inference(superposition,[],[f1080,f2286]) ).

fof(f12682,plain,
    ( spl0_461
    | ~ spl0_54
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2466,f2285,f645,f12680]) ).

fof(f12680,plain,
    ( spl0_461
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_Suc(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_461])]) ).

fof(f2466,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_174 ),
    inference(superposition,[],[f646,f2286]) ).

fof(f12678,plain,
    ( spl0_460
    | ~ spl0_118
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2378,f2277,f1091,f12676]) ).

fof(f12676,plain,
    ( spl0_460
  <=> ! [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_460])]) ).

fof(f1091,plain,
    ( spl0_118
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f2378,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_118
    | ~ spl0_172 ),
    inference(superposition,[],[f1092,f2278]) ).

fof(f1092,plain,
    ( ! [X3,X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f1091]) ).

fof(f12674,plain,
    ( spl0_459
    | ~ spl0_114
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2376,f2277,f1067,f12672]) ).

fof(f12672,plain,
    ( spl0_459
  <=> ! [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_459])]) ).

fof(f1067,plain,
    ( spl0_114
  <=> ! [X11,X12,X13] :
        ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f2376,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_114
    | ~ spl0_172 ),
    inference(superposition,[],[f1068,f2278]) ).

fof(f1068,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat)
        | c_HOL_Oord__class_Oless(X11,X12,tc_nat) )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f1067]) ).

fof(f12670,plain,
    ( spl0_458
    | ~ spl0_113
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2375,f2277,f1063,f12668]) ).

fof(f12668,plain,
    ( spl0_458
  <=> ! [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_458])]) ).

fof(f2375,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_113
    | ~ spl0_172 ),
    inference(superposition,[],[f1064,f2278]) ).

fof(f12666,plain,
    ( spl0_457
    | ~ spl0_55
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2368,f2277,f649,f12664]) ).

fof(f12664,plain,
    ( spl0_457
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Suc(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_457])]) ).

fof(f2368,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_172 ),
    inference(superposition,[],[f650,f2278]) ).

fof(f12662,plain,
    ( spl0_456
    | ~ spl0_46
    | ~ spl0_111
    | ~ spl0_308
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f7845,f6568,f5882,f1055,f608,f12660]) ).

fof(f12660,plain,
    ( spl0_456
  <=> ! [X0] : c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f6568,plain,
    ( spl0_339
  <=> ! [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_339])]) ).

fof(f7845,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_46
    | ~ spl0_111
    | ~ spl0_308
    | ~ spl0_339 ),
    inference(forward_demodulation,[],[f7844,f609]) ).

fof(f7844,plain,
    ( ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) = c_Lambda_OdB_OVar(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
    | ~ spl0_111
    | ~ spl0_308
    | ~ spl0_339 ),
    inference(forward_demodulation,[],[f7816,f1056]) ).

fof(f7816,plain,
    ( ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))
    | ~ spl0_308
    | ~ spl0_339 ),
    inference(superposition,[],[f6569,f5883]) ).

fof(f6569,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_339 ),
    inference(avatar_component_clause,[],[f6568]) ).

fof(f12601,plain,
    ( ~ spl0_23
    | spl0_455
    | ~ spl0_56
    | ~ spl0_170 ),
    inference(avatar_split_clause,[],[f2244,f1864,f653,f12599,f511]) ).

fof(f12599,plain,
    ( spl0_455
  <=> ! [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,c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f2244,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
        | ~ class_Orderings_Opreorder(tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
    | ~ spl0_56
    | ~ spl0_170 ),
    inference(resolution,[],[f1865,f654]) ).

fof(f12597,plain,
    ( spl0_454
    | ~ spl0_66
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f2170,f1848,f705,f12595]) ).

fof(f12595,plain,
    ( spl0_454
  <=> ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,c_Suc(X0),tc_nat)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).

fof(f1848,plain,
    ( spl0_166
  <=> ! [X4,X12,X3] :
        ( X3 = X4
        | c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f2170,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,c_Suc(X0),tc_nat)
        | X1 = X2 )
    | ~ spl0_66
    | ~ spl0_166 ),
    inference(superposition,[],[f1849,f706]) ).

fof(f1849,plain,
    ( ! [X3,X4,X12] :
        ( c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1848]) ).

fof(f12593,plain,
    ( spl0_453
    | ~ spl0_162
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2137,f1844,f1832,f12591]) ).

fof(f12591,plain,
    ( spl0_453
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f1844,plain,
    ( spl0_165
  <=> ! [X4,X12,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f2137,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat),tc_nat) )
    | ~ spl0_162
    | ~ spl0_165 ),
    inference(resolution,[],[f1845,f1833]) ).

fof(f1845,plain,
    ( ! [X3,X4,X12] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1844]) ).

fof(f12589,plain,
    ( spl0_452
    | ~ spl0_67
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f2122,f1840,f709,f12587]) ).

fof(f12587,plain,
    ( spl0_452
  <=> ! [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_452])]) ).

fof(f1840,plain,
    ( spl0_164
  <=> ! [X4,X12,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f2122,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_67
    | ~ spl0_164 ),
    inference(superposition,[],[f1841,f710]) ).

fof(f1841,plain,
    ( ! [X3,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1840]) ).

fof(f12585,plain,
    ( spl0_451
    | ~ spl0_67
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f2114,f1840,f709,f12583]) ).

fof(f12583,plain,
    ( spl0_451
  <=> ! [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_451])]) ).

fof(f2114,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_67
    | ~ spl0_164 ),
    inference(superposition,[],[f1841,f710]) ).

fof(f12581,plain,
    ( spl0_450
    | ~ spl0_67
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f2086,f1836,f709,f12579]) ).

fof(f12579,plain,
    ( spl0_450
  <=> ! [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_450])]) ).

fof(f1836,plain,
    ( spl0_163
  <=> ! [X13,X12,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f2086,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_67
    | ~ spl0_163 ),
    inference(superposition,[],[f1837,f710]) ).

fof(f1837,plain,
    ( ! [X11,X12,X13] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1836]) ).

fof(f12576,plain,
    ( spl0_449
    | ~ spl0_54
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2040,f1832,f645,f12574]) ).

fof(f12574,plain,
    ( spl0_449
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f2040,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X1,tc_nat),tc_nat)
    | ~ spl0_54
    | ~ spl0_162 ),
    inference(forward_demodulation,[],[f2026,f61]) ).

fof(f61,axiom,
    ! [X3,X4,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

fof(f2026,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)),X1,tc_nat),tc_nat)
    | ~ spl0_54
    | ~ spl0_162 ),
    inference(resolution,[],[f1833,f646]) ).

fof(f12572,plain,
    ( spl0_448
    | ~ spl0_67
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2031,f1832,f709,f12570]) ).

fof(f12570,plain,
    ( spl0_448
  <=> ! [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_448])]) ).

fof(f2031,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_67
    | ~ spl0_162 ),
    inference(superposition,[],[f1833,f710]) ).

fof(f12567,plain,
    ( spl0_447
    | ~ spl0_55
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f2027,f1832,f649,f12565]) ).

fof(f12565,plain,
    ( spl0_447
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f2027,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X2,tc_nat),tc_nat)
    | ~ spl0_55
    | ~ spl0_162 ),
    inference(resolution,[],[f1833,f650]) ).

fof(f12563,plain,
    ( spl0_446
    | ~ spl0_104
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f7826,f6568,f943,f12561]) ).

fof(f12561,plain,
    ( spl0_446
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f943,plain,
    ( spl0_104
  <=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f7826,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)),X2)
    | ~ spl0_104
    | ~ spl0_339 ),
    inference(superposition,[],[f944,f6569]) ).

fof(f944,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f943]) ).

fof(f12559,plain,
    ( spl0_445
    | ~ spl0_78
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f2008,f1828,f753,f12557]) ).

fof(f12557,plain,
    ( spl0_445
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f1828,plain,
    ( spl0_161
  <=> ! [X13,X12,X11] :
        ( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f2008,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
    | ~ spl0_78
    | ~ spl0_161 ),
    inference(superposition,[],[f1829,f754]) ).

fof(f1829,plain,
    ( ! [X11,X12,X13] :
        ( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1828]) ).

fof(f12555,plain,
    ( spl0_444
    | ~ spl0_66
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1972,f1816,f705,f12553]) ).

fof(f12553,plain,
    ( spl0_444
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f1816,plain,
    ( spl0_158
  <=> ! [X4,X12,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1972,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_66
    | ~ spl0_158 ),
    inference(superposition,[],[f1817,f706]) ).

fof(f1817,plain,
    ( ! [X3,X4,X12] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1816]) ).

fof(f12551,plain,
    ( spl0_443
    | ~ spl0_66
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1968,f1816,f705,f12549]) ).

fof(f12549,plain,
    ( spl0_443
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f1968,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_66
    | ~ spl0_158 ),
    inference(superposition,[],[f1817,f706]) ).

fof(f12547,plain,
    ( spl0_442
    | ~ spl0_106
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1789,f1524,f951,f12545]) ).

fof(f12545,plain,
    ( spl0_442
  <=> ! [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_442])]) ).

fof(f951,plain,
    ( spl0_106
  <=> ! [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_106])]) ).

fof(f1524,plain,
    ( spl0_151
  <=> ! [X25,X12,X28] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1789,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_106
    | ~ spl0_151 ),
    inference(superposition,[],[f952,f1525]) ).

fof(f1525,plain,
    ( ! [X28,X25,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12))
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1524]) ).

fof(f952,plain,
    ( ! [X38,X36,X37,X35] :
        ( c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38)
        | X36 = X38 )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f951]) ).

fof(f12543,plain,
    ( spl0_441
    | ~ spl0_105
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1787,f1524,f947,f12541]) ).

fof(f12541,plain,
    ( spl0_441
  <=> ! [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_441])]) ).

fof(f947,plain,
    ( spl0_105
  <=> ! [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_105])]) ).

fof(f1787,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_105
    | ~ spl0_151 ),
    inference(superposition,[],[f948,f1525]) ).

fof(f948,plain,
    ( ! [X38,X36,X37,X35] :
        ( c_Lambda_OdB_OApp(X35,X36) != c_Lambda_OdB_OApp(X37,X38)
        | X35 = X37 )
    | ~ spl0_105 ),
    inference(avatar_component_clause,[],[f947]) ).

fof(f12539,plain,
    ( spl0_440
    | ~ spl0_100
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1766,f1516,f927,f12537]) ).

fof(f12537,plain,
    ( spl0_440
  <=> ! [X0,X1] :
        ( c_Suc(X0) = c_Suc(X1)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f1766,plain,
    ( ! [X0,X1] :
        ( c_Suc(X0) = c_Suc(X1)
        | ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_100
    | ~ spl0_149 ),
    inference(resolution,[],[f1517,f928]) ).

fof(f12535,plain,
    ( spl0_439
    | ~ spl0_79
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1696,f1508,f757,f12533]) ).

fof(f12533,plain,
    ( spl0_439
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f1696,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
    | ~ spl0_79
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f758]) ).

fof(f12531,plain,
    ( spl0_438
    | ~ spl0_83
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1695,f1508,f774,f12529]) ).

fof(f12529,plain,
    ( spl0_438
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f1695,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
        | c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_83
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f775]) ).

fof(f12527,plain,
    ( spl0_437
    | ~ spl0_87
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1599,f1496,f873,f12525]) ).

fof(f12525,plain,
    ( spl0_437
  <=> ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f873,plain,
    ( spl0_87
  <=> ! [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_87])]) ).

fof(f1599,plain,
    ( ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
    | ~ spl0_87
    | ~ spl0_144 ),
    inference(superposition,[],[f874,f1497]) ).

fof(f874,plain,
    ( ! [X3,X4] :
        ( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f873]) ).

fof(f12523,plain,
    ( spl0_436
    | ~ spl0_87
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1566,f1492,f873,f12521]) ).

fof(f12521,plain,
    ( spl0_436
  <=> ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1566,plain,
    ( ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
    | ~ spl0_87
    | ~ spl0_143 ),
    inference(superposition,[],[f874,f1493]) ).

fof(f12519,plain,
    ( spl0_435
    | ~ spl0_33
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f7819,f6568,f554,f12517]) ).

fof(f554,plain,
    ( spl0_33
  <=> ! [X27,X30] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X30) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f7819,plain,
    ( ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0) != c_Lambda_OdB_OAbs(X2)
    | ~ spl0_33
    | ~ spl0_339 ),
    inference(superposition,[],[f555,f6569]) ).

fof(f555,plain,
    ( ! [X27,X30] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X30)
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f554]) ).

fof(f12515,plain,
    ( spl0_434
    | ~ spl0_81
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1446,f1343,f766,f12513]) ).

fof(f12513,plain,
    ( spl0_434
  <=> ! [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_434])]) ).

fof(f766,plain,
    ( spl0_81
  <=> ! [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_81])]) ).

fof(f1446,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_81
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f767]) ).

fof(f767,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_81 ),
    inference(avatar_component_clause,[],[f766]) ).

fof(f12511,plain,
    ( spl0_433
    | ~ spl0_81
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1424,f1335,f766,f12509]) ).

fof(f12509,plain,
    ( spl0_433
  <=> ! [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_433])]) ).

fof(f1424,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_81
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f767]) ).

fof(f12507,plain,
    ( spl0_432
    | ~ spl0_120
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1410,f1320,f1099,f12505]) ).

fof(f12505,plain,
    ( spl0_432
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f1410,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) )
    | ~ spl0_120
    | ~ spl0_131 ),
    inference(superposition,[],[f1321,f1100]) ).

fof(f12503,plain,
    ( spl0_431
    | ~ spl0_120
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1396,f1316,f1099,f12501]) ).

fof(f12501,plain,
    ( spl0_431
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f1316,plain,
    ( spl0_130
  <=> ! [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_130])]) ).

fof(f1396,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) )
    | ~ spl0_120
    | ~ spl0_130 ),
    inference(superposition,[],[f1317,f1100]) ).

fof(f1317,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_130 ),
    inference(avatar_component_clause,[],[f1316]) ).

fof(f12499,plain,
    ( spl0_430
    | ~ spl0_112
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1377,f1307,f1059,f12497]) ).

fof(f12497,plain,
    ( spl0_430
  <=> ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
        | c_Suc(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f1307,plain,
    ( spl0_128
  <=> ! [X4,X12,X3] :
        ( X3 = X4
        | c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1377,plain,
    ( ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
        | c_Suc(X0) = X2 )
    | ~ spl0_112
    | ~ spl0_128 ),
    inference(superposition,[],[f1308,f1060]) ).

fof(f1308,plain,
    ( ! [X3,X4,X12] :
        ( c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat)
        | X3 = X4 )
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1307]) ).

fof(f12495,plain,
    ( spl0_429
    | ~ spl0_111
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1375,f1307,f1055,f12493]) ).

fof(f12493,plain,
    ( spl0_429
  <=> ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat)
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f1375,plain,
    ( ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat)
        | X0 = X2 )
    | ~ spl0_111
    | ~ spl0_128 ),
    inference(superposition,[],[f1308,f1056]) ).

fof(f12491,plain,
    ( spl0_428
    | ~ spl0_112
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1364,f1303,f1059,f12489]) ).

fof(f12489,plain,
    ( spl0_428
  <=> ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(c_Suc(X0),X2,tc_nat)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f1303,plain,
    ( spl0_127
  <=> ! [X6,X5,X7] :
        ( X6 = X7
        | c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1364,plain,
    ( ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(c_Suc(X0),X2,tc_nat)
        | X1 = X2 )
    | ~ spl0_112
    | ~ spl0_127 ),
    inference(superposition,[],[f1304,f1060]) ).

fof(f1304,plain,
    ( ! [X6,X7,X5] :
        ( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
        | X6 = X7 )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1303]) ).

fof(f12487,plain,
    ( spl0_427
    | ~ spl0_111
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1362,f1303,f1055,f12485]) ).

fof(f12485,plain,
    ( spl0_427
  <=> ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
        | c_Suc(X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f1362,plain,
    ( ! [X2,X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
        | c_Suc(X1) = X2 )
    | ~ spl0_111
    | ~ spl0_127 ),
    inference(superposition,[],[f1304,f1056]) ).

fof(f12483,plain,
    ( spl0_426
    | ~ spl0_99
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1294,f1111,f923,f12481]) ).

fof(f12481,plain,
    ( spl0_426
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X1))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f1111,plain,
    ( spl0_123
  <=> ! [X11,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1294,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X1))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_99
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f924]) ).

fof(f1112,plain,
    ( ! [X11,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1111]) ).

fof(f12479,plain,
    ( spl0_425
    | ~ spl0_56
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1291,f1111,f653,f12477]) ).

fof(f12477,plain,
    ( spl0_425
  <=> ! [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_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f1291,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_Suc(X0))
    | ~ spl0_56
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f654]) ).

fof(f12422,plain,
    ( spl0_424
    | ~ spl0_113
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1288,f1111,f1063,f12420]) ).

fof(f12420,plain,
    ( spl0_424
  <=> ! [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_424])]) ).

fof(f1288,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_113
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f1064]) ).

fof(f12418,plain,
    ( spl0_423
    | ~ spl0_115
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1287,f1111,f1079,f12416]) ).

fof(f12416,plain,
    ( spl0_423
  <=> ! [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_423])]) ).

fof(f1287,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_115
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f1080]) ).

fof(f12414,plain,
    ( spl0_422
    | ~ spl0_122
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1284,f1111,f1107,f12412]) ).

fof(f12412,plain,
    ( spl0_422
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f1284,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat)
        | X0 = X1 )
    | ~ spl0_122
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f1108]) ).

fof(f12410,plain,
    ( spl0_421
    | ~ spl0_114
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1196,f1079,f1067,f12408]) ).

fof(f12408,plain,
    ( spl0_421
  <=> ! [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(X0,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f1196,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) )
    | ~ spl0_114
    | ~ spl0_115 ),
    inference(resolution,[],[f1080,f1068]) ).

fof(f12406,plain,
    ( spl0_420
    | ~ spl0_113
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1177,f1067,f1063,f12404]) ).

fof(f12404,plain,
    ( spl0_420
  <=> ! [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_420])]) ).

fof(f1177,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_113
    | ~ spl0_114 ),
    inference(resolution,[],[f1068,f1064]) ).

fof(f12060,plain,
    ( spl0_419
    | ~ spl0_46
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f6812,f6474,f608,f12058]) ).

fof(f12058,plain,
    ( spl0_419
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f6474,plain,
    ( spl0_317
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f6812,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat)
    | ~ spl0_46
    | ~ spl0_317 ),
    inference(superposition,[],[f6475,f609]) ).

fof(f6475,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f6474]) ).

fof(f11137,plain,
    ( spl0_418
    | ~ spl0_271
    | ~ spl0_288 ),
    inference(avatar_split_clause,[],[f5781,f5357,f4902,f11135]) ).

fof(f11135,plain,
    ( spl0_418
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f4902,plain,
    ( spl0_271
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f5357,plain,
    ( spl0_288
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f5781,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_271
    | ~ spl0_288 ),
    inference(superposition,[],[f5358,f4903]) ).

fof(f4903,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f4902]) ).

fof(f5358,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
    | ~ spl0_288 ),
    inference(avatar_component_clause,[],[f5357]) ).

fof(f10304,plain,
    ( spl0_417
    | ~ spl0_27
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f5472,f5309,f530,f10302]) ).

fof(f10302,plain,
    ( spl0_417
  <=> ! [X0] :
        ( c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f530,plain,
    ( spl0_27
  <=> ! [X4] : c_Suc(X4) != X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f5472,plain,
    ( ! [X0] :
        ( c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_27
    | ~ spl0_276 ),
    inference(superposition,[],[f531,f5310]) ).

fof(f531,plain,
    ( ! [X4] : c_Suc(X4) != X4
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f530]) ).

fof(f9688,plain,
    ( spl0_416
    | ~ spl0_109
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2687,f1824,f1043,f9686]) ).

fof(f9686,plain,
    ( spl0_416
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f1043,plain,
    ( spl0_109
  <=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f2687,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_109
    | ~ spl0_160 ),
    inference(superposition,[],[f1044,f1825]) ).

fof(f1044,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1043]) ).

fof(f9684,plain,
    ( spl0_415
    | ~ spl0_50
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f4036,f3659,f625,f9682]) ).

fof(f9682,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f625,plain,
    ( spl0_50
  <=> ! [X13,X11] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f4036,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
    | ~ spl0_50
    | ~ spl0_235 ),
    inference(superposition,[],[f626,f3660]) ).

fof(f626,plain,
    ( ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f625]) ).

fof(f9680,plain,
    ( spl0_414
    | ~ spl0_49
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f4035,f3659,f621,f9678]) ).

fof(f9678,plain,
    ( spl0_414
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f621,plain,
    ( spl0_49
  <=> ! [X13,X11] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f4035,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
    | ~ spl0_49
    | ~ spl0_235 ),
    inference(superposition,[],[f622,f3660]) ).

fof(f622,plain,
    ( ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat)
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f621]) ).

fof(f9676,plain,
    ( spl0_413
    | ~ spl0_50
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3949,f3655,f625,f9674]) ).

fof(f9674,plain,
    ( spl0_413
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f3949,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
    | ~ spl0_50
    | ~ spl0_234 ),
    inference(superposition,[],[f626,f3656]) ).

fof(f9672,plain,
    ( spl0_412
    | ~ spl0_49
    | ~ spl0_234 ),
    inference(avatar_split_clause,[],[f3948,f3655,f621,f9670]) ).

fof(f9670,plain,
    ( spl0_412
  <=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f3948,plain,
    ( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
    | ~ spl0_49
    | ~ spl0_234 ),
    inference(superposition,[],[f622,f3656]) ).

fof(f9668,plain,
    ( spl0_411
    | ~ spl0_55
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2809,f2321,f649,f9666]) ).

fof(f9666,plain,
    ( spl0_411
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f2809,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) = X0 )
    | ~ spl0_55
    | ~ spl0_183 ),
    inference(resolution,[],[f2322,f650]) ).

fof(f9664,plain,
    ( spl0_410
    | ~ spl0_54
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2808,f2321,f645,f9662]) ).

fof(f9662,plain,
    ( spl0_410
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f2808,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = X0 )
    | ~ spl0_54
    | ~ spl0_183 ),
    inference(resolution,[],[f2322,f646]) ).

fof(f9660,plain,
    ( spl0_409
    | ~ spl0_44
    | ~ spl0_175 ),
    inference(avatar_split_clause,[],[f2531,f2289,f600,f9658]) ).

fof(f9658,plain,
    ( spl0_409
  <=> ! [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_409])]) ).

fof(f600,plain,
    ( spl0_44
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f2531,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_44
    | ~ spl0_175 ),
    inference(superposition,[],[f2290,f601]) ).

fof(f601,plain,
    ( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f600]) ).

fof(f9656,plain,
    ( spl0_408
    | ~ spl0_49
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2464,f2285,f621,f9654]) ).

fof(f9654,plain,
    ( spl0_408
  <=> ! [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_408])]) ).

fof(f2464,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_49
    | ~ spl0_174 ),
    inference(superposition,[],[f622,f2286]) ).

fof(f9652,plain,
    ( spl0_407
    | ~ spl0_88
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2374,f2277,f877,f9650]) ).

fof(f9650,plain,
    ( spl0_407
  <=> ! [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_407])]) ).

fof(f877,plain,
    ( spl0_88
  <=> ! [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_88])]) ).

fof(f2374,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_88
    | ~ spl0_172 ),
    inference(superposition,[],[f878,f2278]) ).

fof(f878,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_88 ),
    inference(avatar_component_clause,[],[f877]) ).

fof(f9648,plain,
    ( spl0_406
    | ~ spl0_50
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f2366,f2277,f625,f9646]) ).

fof(f9646,plain,
    ( spl0_406
  <=> ! [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_406])]) ).

fof(f2366,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_50
    | ~ spl0_172 ),
    inference(superposition,[],[f626,f2278]) ).

fof(f9644,plain,
    ( spl0_405
    | ~ spl0_109
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f2059,f1702,f1043,f9642]) ).

fof(f9642,plain,
    ( spl0_405
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f2059,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_109
    | ~ spl0_152 ),
    inference(superposition,[],[f1044,f1703]) ).

fof(f9594,plain,
    ( ~ spl0_12
    | spl0_404
    | ~ spl0_81
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f2204,f1856,f766,f9592,f456]) ).

fof(f456,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f9592,plain,
    ( spl0_404
  <=> ! [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_404])]) ).

fof(f1856,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

fof(f2204,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_81
    | ~ spl0_168 ),
    inference(resolution,[],[f1857,f767]) ).

fof(f1857,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_168 ),
    inference(avatar_component_clause,[],[f1856]) ).

fof(f9590,plain,
    ( spl0_403
    | ~ spl0_81
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f2177,f1852,f766,f9588]) ).

fof(f9588,plain,
    ( spl0_403
  <=> ! [X0] :
        ( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f2177,plain,
    ( ! [X0] :
        ( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_81
    | ~ spl0_167 ),
    inference(resolution,[],[f1853,f767]) ).

fof(f9586,plain,
    ( spl0_402
    | ~ spl0_55
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1699,f1508,f649,f9584]) ).

fof(f9584,plain,
    ( spl0_402
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f1699,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) )
    | ~ spl0_55
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f650]) ).

fof(f9582,plain,
    ( spl0_401
    | ~ spl0_54
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1698,f1508,f645,f9580]) ).

fof(f9580,plain,
    ( spl0_401
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f1698,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) )
    | ~ spl0_54
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f646]) ).

fof(f9578,plain,
    ( spl0_400
    | ~ spl0_56
    | ~ spl0_147 ),
    inference(avatar_split_clause,[],[f1694,f1508,f653,f9576]) ).

fof(f9576,plain,
    ( spl0_400
  <=> ! [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(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f1694,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(c_Suc(X0),c_Suc(X1),tc_nat) )
    | ~ spl0_56
    | ~ spl0_147 ),
    inference(resolution,[],[f1509,f654]) ).

fof(f9574,plain,
    ( spl0_399
    | ~ spl0_57
    | ~ spl0_96
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1651,f1500,f911,f657,f9572]) ).

fof(f9572,plain,
    ( spl0_399
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f657,plain,
    ( spl0_57
  <=> ! [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_57])]) ).

fof(f1651,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 )
    | ~ spl0_57
    | ~ spl0_96
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1631,f658]) ).

fof(f658,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_57 ),
    inference(avatar_component_clause,[],[f657]) ).

fof(f1631,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 )
    | ~ spl0_96
    | ~ spl0_145 ),
    inference(resolution,[],[f1501,f912]) ).

fof(f9570,plain,
    ( spl0_398
    | ~ spl0_57
    | ~ spl0_98
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1650,f1500,f919,f657,f9568]) ).

fof(f9568,plain,
    ( spl0_398
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f1650,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 )
    | ~ spl0_57
    | ~ spl0_98
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1630,f658]) ).

fof(f1630,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 )
    | ~ spl0_98
    | ~ spl0_145 ),
    inference(resolution,[],[f1501,f920]) ).

fof(f9566,plain,
    ( spl0_397
    | ~ spl0_78
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1598,f1496,f753,f9564]) ).

fof(f9564,plain,
    ( spl0_397
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1598,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
    | ~ spl0_78
    | ~ spl0_144 ),
    inference(superposition,[],[f754,f1497]) ).

fof(f9562,plain,
    ( spl0_396
    | ~ spl0_77
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1597,f1496,f749,f9560]) ).

fof(f9560,plain,
    ( spl0_396
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1597,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0
    | ~ spl0_77
    | ~ spl0_144 ),
    inference(superposition,[],[f750,f1497]) ).

fof(f9550,plain,
    ( spl0_395
    | ~ spl0_66
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1587,f1496,f705,f9548]) ).

fof(f9548,plain,
    ( spl0_395
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f1587,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
    | ~ spl0_66
    | ~ spl0_144 ),
    inference(superposition,[],[f1497,f706]) ).

fof(f9546,plain,
    ( spl0_394
    | ~ spl0_78
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1565,f1492,f753,f9544]) ).

fof(f9544,plain,
    ( spl0_394
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f1565,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
    | ~ spl0_78
    | ~ spl0_143 ),
    inference(superposition,[],[f754,f1493]) ).

fof(f9542,plain,
    ( spl0_393
    | ~ spl0_77
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1564,f1492,f749,f9540]) ).

fof(f9540,plain,
    ( spl0_393
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f1564,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0
    | ~ spl0_77
    | ~ spl0_143 ),
    inference(superposition,[],[f750,f1493]) ).

fof(f9538,plain,
    ( spl0_392
    | ~ spl0_66
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1555,f1492,f705,f9536]) ).

fof(f9536,plain,
    ( spl0_392
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f1555,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
    | ~ spl0_66
    | ~ spl0_143 ),
    inference(superposition,[],[f1493,f706]) ).

fof(f9534,plain,
    ( spl0_391
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1457,f1343,f757,f9532]) ).

fof(f9532,plain,
    ( spl0_391
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f1457,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f758]) ).

fof(f9530,plain,
    ( spl0_390
    | ~ spl0_83
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1456,f1343,f774,f9528]) ).

fof(f9528,plain,
    ( spl0_390
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f1456,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_83
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f775]) ).

fof(f9526,plain,
    ( spl0_389
    | ~ spl0_65
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1444,f1339,f689,f9524]) ).

fof(f9524,plain,
    ( spl0_389
  <=> ! [X0,X3,X2,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_Suc(X0),X1,X2),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f1444,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_Suc(X0),X1,X2),X3,X2)
    | ~ spl0_65
    | ~ spl0_134 ),
    inference(superposition,[],[f690,f1340]) ).

fof(f9522,plain,
    ( spl0_388
    | ~ spl0_79
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1435,f1335,f757,f9520]) ).

fof(f9520,plain,
    ( spl0_388
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f1435,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
        | ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_79
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f758]) ).

fof(f9518,plain,
    ( spl0_387
    | ~ spl0_83
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1434,f1335,f774,f9516]) ).

fof(f9516,plain,
    ( spl0_387
  <=> ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f1434,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
        | c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_83
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f775]) ).

fof(f9514,plain,
    ( spl0_386
    | ~ spl0_56
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1413,f1324,f653,f9512]) ).

fof(f9512,plain,
    ( spl0_386
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f1324,plain,
    ( spl0_132
  <=> ! [X4,X3] :
        ( X3 = X4
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1413,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
        | c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 )
    | ~ spl0_56
    | ~ spl0_132 ),
    inference(resolution,[],[f1325,f654]) ).

fof(f1325,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | X3 = X4 )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1324]) ).

fof(f9510,plain,
    ( spl0_385
    | ~ spl0_84
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f7862,f7452,f778,f9508]) ).

fof(f9508,plain,
    ( spl0_385
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f7862,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)),X2)
    | ~ spl0_84
    | ~ spl0_341 ),
    inference(resolution,[],[f7453,f779]) ).

fof(f9506,plain,
    ( spl0_384
    | ~ spl0_81
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1283,f1111,f766,f9504]) ).

fof(f9504,plain,
    ( spl0_384
  <=> ! [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_384])]) ).

fof(f1283,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_81
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f767]) ).

fof(f9502,plain,
    ( spl0_383
    | ~ spl0_50
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1257,f1107,f625,f9500]) ).

fof(f9500,plain,
    ( spl0_383
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f1257,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 )
    | ~ spl0_50
    | ~ spl0_122 ),
    inference(resolution,[],[f1108,f626]) ).

fof(f9498,plain,
    ( spl0_382
    | ~ spl0_49
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1256,f1107,f621,f9496]) ).

fof(f9496,plain,
    ( spl0_382
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1256,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
    | ~ spl0_49
    | ~ spl0_122 ),
    inference(resolution,[],[f1108,f622]) ).

fof(f9494,plain,
    ( spl0_381
    | ~ spl0_97
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1230,f1103,f915,f9492]) ).

fof(f9492,plain,
    ( spl0_381
  <=> ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(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_381])]) ).

fof(f1230,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
    | ~ spl0_97
    | ~ spl0_121 ),
    inference(resolution,[],[f1104,f916]) ).

fof(f9490,plain,
    ( spl0_380
    | ~ spl0_111
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1202,f1079,f1055,f9488]) ).

fof(f9488,plain,
    ( spl0_380
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f1202,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) )
    | ~ spl0_111
    | ~ spl0_115 ),
    inference(superposition,[],[f1080,f1056]) ).

fof(f9486,plain,
    ( spl0_379
    | ~ spl0_112
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1183,f1067,f1059,f9484]) ).

fof(f9484,plain,
    ( spl0_379
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f1183,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) )
    | ~ spl0_112
    | ~ spl0_114 ),
    inference(superposition,[],[f1068,f1060]) ).

fof(f9482,plain,
    ( spl0_378
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1169,f1063,f1059,f9480]) ).

fof(f9480,plain,
    ( spl0_378
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f1169,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) )
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(superposition,[],[f1064,f1060]) ).

fof(f8539,plain,
    ( spl0_377
    | ~ spl0_29
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f7818,f6568,f538,f8537]) ).

fof(f8537,plain,
    ( spl0_377
  <=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f538,plain,
    ( spl0_29
  <=> ! [X25,X11] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f7818,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2)
    | ~ spl0_29
    | ~ spl0_339 ),
    inference(superposition,[],[f539,f6569]) ).

fof(f539,plain,
    ( ! [X11,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f538]) ).

fof(f8002,plain,
    ( spl0_376
    | ~ spl0_104
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f7360,f6524,f943,f8000]) ).

fof(f7360,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1),X2)
    | ~ spl0_104
    | ~ spl0_329 ),
    inference(resolution,[],[f6525,f944]) ).

fof(f7998,plain,
    ( spl0_375
    | ~ spl0_57
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f3516,f3395,f657,f7996]) ).

fof(f7996,plain,
    ( spl0_375
  <=> ! [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_375])]) ).

fof(f3395,plain,
    ( spl0_215
  <=> ! [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_215])]) ).

fof(f3516,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_57
    | ~ spl0_215 ),
    inference(trivial_inequality_removal,[],[f3508]) ).

fof(f3508,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_57
    | ~ spl0_215 ),
    inference(superposition,[],[f3396,f658]) ).

fof(f3396,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_215 ),
    inference(avatar_component_clause,[],[f3395]) ).

fof(f7994,plain,
    ( spl0_374
    | ~ spl0_32
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2749,f2317,f550,f7992]) ).

fof(f7992,plain,
    ( spl0_374
  <=> ! [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_374])]) ).

fof(f550,plain,
    ( spl0_32
  <=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f2749,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_32
    | ~ spl0_182 ),
    inference(resolution,[],[f2318,f551]) ).

fof(f551,plain,
    ( ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f550]) ).

fof(f7990,plain,
    ( spl0_373
    | ~ spl0_118
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1604,f1496,f1091,f7988]) ).

fof(f7988,plain,
    ( spl0_373
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1604,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_118
    | ~ spl0_144 ),
    inference(superposition,[],[f1092,f1497]) ).

fof(f7986,plain,
    ( spl0_372
    | ~ spl0_114
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1602,f1496,f1067,f7984]) ).

fof(f7984,plain,
    ( spl0_372
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f1602,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_114
    | ~ spl0_144 ),
    inference(superposition,[],[f1068,f1497]) ).

fof(f7982,plain,
    ( spl0_371
    | ~ spl0_113
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1601,f1496,f1063,f7980]) ).

fof(f7980,plain,
    ( spl0_371
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f1601,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_113
    | ~ spl0_144 ),
    inference(superposition,[],[f1064,f1497]) ).

fof(f7978,plain,
    ( spl0_370
    | ~ spl0_55
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1596,f1496,f649,f7976]) ).

fof(f7976,plain,
    ( spl0_370
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f1596,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_144 ),
    inference(superposition,[],[f650,f1497]) ).

fof(f7974,plain,
    ( spl0_369
    | ~ spl0_118
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1571,f1492,f1091,f7972]) ).

fof(f7972,plain,
    ( spl0_369
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f1571,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_118
    | ~ spl0_143 ),
    inference(superposition,[],[f1092,f1493]) ).

fof(f7970,plain,
    ( spl0_368
    | ~ spl0_114
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1569,f1492,f1067,f7968]) ).

fof(f7968,plain,
    ( spl0_368
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f1569,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_114
    | ~ spl0_143 ),
    inference(superposition,[],[f1068,f1493]) ).

fof(f7966,plain,
    ( spl0_367
    | ~ spl0_113
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1568,f1492,f1063,f7964]) ).

fof(f7964,plain,
    ( spl0_367
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f1568,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_113
    | ~ spl0_143 ),
    inference(superposition,[],[f1064,f1493]) ).

fof(f7962,plain,
    ( spl0_366
    | ~ spl0_55
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1563,f1492,f649,f7960]) ).

fof(f7960,plain,
    ( spl0_366
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f1563,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_143 ),
    inference(superposition,[],[f650,f1493]) ).

fof(f7952,plain,
    ( spl0_365
    | ~ spl0_81
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1545,f1488,f766,f7950]) ).

fof(f7950,plain,
    ( spl0_365
  <=> ! [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_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f1488,plain,
    ( spl0_142
  <=> ! [X4,X3] :
        ( 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_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1545,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_Otimes__class_Otimes(X0,X1,tc_nat) )
    | ~ spl0_81
    | ~ spl0_142 ),
    inference(resolution,[],[f1489,f767]) ).

fof(f1489,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1488]) ).

fof(f7948,plain,
    ( spl0_364
    | ~ spl0_81
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1537,f1484,f766,f7946]) ).

fof(f7946,plain,
    ( spl0_364
  <=> ! [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_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f1484,plain,
    ( spl0_141
  <=> ! [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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1537,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_Otimes__class_Otimes(X1,X0,tc_nat) )
    | ~ spl0_81
    | ~ spl0_141 ),
    inference(resolution,[],[f1485,f767]) ).

fof(f1485,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1484]) ).

fof(f7944,plain,
    ( spl0_363
    | ~ spl0_55
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1460,f1343,f649,f7942]) ).

fof(f7942,plain,
    ( spl0_363
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f1460,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)))
    | ~ spl0_55
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f650]) ).

fof(f7940,plain,
    ( spl0_362
    | ~ spl0_54
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1459,f1343,f645,f7938]) ).

fof(f7938,plain,
    ( spl0_362
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f1459,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)))
    | ~ spl0_54
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f646]) ).

fof(f7936,plain,
    ( spl0_361
    | ~ spl0_55
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1438,f1335,f649,f7934]) ).

fof(f7934,plain,
    ( spl0_361
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f1438,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)))
    | ~ spl0_55
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f650]) ).

fof(f7932,plain,
    ( spl0_360
    | ~ spl0_54
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1437,f1335,f645,f7930]) ).

fof(f7930,plain,
    ( spl0_360
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f1437,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)))
    | ~ spl0_54
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f646]) ).

fof(f7928,plain,
    ( spl0_359
    | ~ spl0_78
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1409,f1320,f753,f7926]) ).

fof(f7926,plain,
    ( spl0_359
  <=> ! [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_359])]) ).

fof(f1409,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_78
    | ~ spl0_131 ),
    inference(superposition,[],[f1321,f754]) ).

fof(f7924,plain,
    ( spl0_358
    | ~ spl0_77
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1408,f1320,f749,f7922]) ).

fof(f7922,plain,
    ( spl0_358
  <=> ! [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_358])]) ).

fof(f1408,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_77
    | ~ spl0_131 ),
    inference(superposition,[],[f1321,f750]) ).

fof(f7920,plain,
    ( spl0_357
    | ~ spl0_67
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1360,f1303,f709,f7918]) ).

fof(f7918,plain,
    ( spl0_357
  <=> ! [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_357])]) ).

fof(f1360,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_67
    | ~ spl0_127 ),
    inference(superposition,[],[f1304,f710]) ).

fof(f7916,plain,
    ( spl0_356
    | ~ spl0_79
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1293,f1111,f757,f7914]) ).

fof(f7914,plain,
    ( spl0_356
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f1293,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
        | ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
    | ~ spl0_79
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f758]) ).

fof(f7912,plain,
    ( spl0_355
    | ~ spl0_26
    | ~ spl0_339 ),
    inference(avatar_split_clause,[],[f7817,f6568,f526,f7910]) ).

fof(f7910,plain,
    ( spl0_355
  <=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f526,plain,
    ( spl0_26
  <=> ! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f7817,plain,
    ( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0))
    | ~ spl0_26
    | ~ spl0_339 ),
    inference(superposition,[],[f527,f6569]) ).

fof(f527,plain,
    ( ! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f526]) ).

fof(f7908,plain,
    ( spl0_354
    | ~ spl0_83
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1292,f1111,f774,f7906]) ).

fof(f7906,plain,
    ( spl0_354
  <=> ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f1292,plain,
    ( ! [X0,X1] :
        ( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
        | c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_83
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f775]) ).

fof(f7904,plain,
    ( spl0_353
    | ~ spl0_120
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1243,f1103,f1099,f7902]) ).

fof(f7902,plain,
    ( spl0_353
  <=> ! [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_Suc(X0),X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f1243,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_Suc(X0),X2,tc_nat) )
    | ~ spl0_120
    | ~ spl0_121 ),
    inference(superposition,[],[f1104,f1100]) ).

fof(f7900,plain,
    ( spl0_352
    | ~ spl0_82
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1229,f1103,f770,f7898]) ).

fof(f7898,plain,
    ( spl0_352
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f1229,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_82
    | ~ spl0_121 ),
    inference(resolution,[],[f1104,f771]) ).

fof(f7896,plain,
    ( spl0_351
    | ~ spl0_112
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1204,f1079,f1059,f7894]) ).

fof(f7894,plain,
    ( spl0_351
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f1204,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
    | ~ spl0_112
    | ~ spl0_115 ),
    inference(superposition,[],[f1080,f1060]) ).

fof(f7892,plain,
    ( spl0_350
    | ~ spl0_80
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1197,f1079,f762,f7890]) ).

fof(f7890,plain,
    ( spl0_350
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,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_350])]) ).

fof(f1197,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
    | ~ spl0_80
    | ~ spl0_115 ),
    inference(resolution,[],[f1080,f763]) ).

fof(f7888,plain,
    ( spl0_349
    | ~ spl0_111
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1181,f1067,f1055,f7886]) ).

fof(f7886,plain,
    ( spl0_349
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f1181,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
        | c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
    | ~ spl0_111
    | ~ spl0_114 ),
    inference(superposition,[],[f1068,f1056]) ).

fof(f7884,plain,
    ( spl0_348
    | ~ spl0_79
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1173,f1067,f757,f7882]) ).

fof(f7882,plain,
    ( spl0_348
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1173,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
    | ~ spl0_79
    | ~ spl0_114 ),
    inference(resolution,[],[f1068,f758]) ).

fof(f7880,plain,
    ( spl0_347
    | ~ spl0_83
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1172,f1067,f774,f7878]) ).

fof(f7878,plain,
    ( spl0_347
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),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_347])]) ).

fof(f1172,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
    | ~ spl0_83
    | ~ spl0_114 ),
    inference(resolution,[],[f1068,f775]) ).

fof(f7876,plain,
    ( spl0_346
    | ~ spl0_111
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1167,f1063,f1055,f7874]) ).

fof(f7874,plain,
    ( spl0_346
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f1167,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
    | ~ spl0_111
    | ~ spl0_113 ),
    inference(superposition,[],[f1064,f1056]) ).

fof(f7872,plain,
    ( spl0_345
    | ~ spl0_80
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1162,f1063,f762,f7870]) ).

fof(f7870,plain,
    ( spl0_345
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f1162,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
        | c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
    | ~ spl0_80
    | ~ spl0_113 ),
    inference(resolution,[],[f1064,f763]) ).

fof(f7860,plain,
    ( spl0_344
    | ~ spl0_88
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1147,f1059,f877,f7858]) ).

fof(f7858,plain,
    ( spl0_344
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f1147,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_88
    | ~ spl0_112 ),
    inference(superposition,[],[f878,f1060]) ).

fof(f7856,plain,
    ( spl0_343
    | ~ spl0_87
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1146,f1059,f873,f7854]) ).

fof(f7854,plain,
    ( spl0_343
  <=> ! [X0,X1] :
        ( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f1146,plain,
    ( ! [X0,X1] :
        ( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_87
    | ~ spl0_112 ),
    inference(superposition,[],[f874,f1060]) ).

fof(f7852,plain,
    ( spl0_342
    | ~ spl0_87
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1130,f1055,f873,f7850]) ).

fof(f7850,plain,
    ( spl0_342
  <=> ! [X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f1130,plain,
    ( ! [X0,X1] :
        ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) )
    | ~ spl0_87
    | ~ spl0_111 ),
    inference(superposition,[],[f874,f1056]) ).

fof(f7454,plain,
    ( spl0_341
    | ~ spl0_29
    | ~ spl0_329 ),
    inference(avatar_split_clause,[],[f7359,f6524,f538,f7452]) ).

fof(f7359,plain,
    ( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
    | ~ spl0_29
    | ~ spl0_329 ),
    inference(resolution,[],[f6525,f539]) ).

fof(f7198,plain,
    ( spl0_340
    | ~ spl0_120
    | ~ spl0_150 ),
    inference(avatar_split_clause,[],[f1882,f1520,f1099,f7196]) ).

fof(f7196,plain,
    ( spl0_340
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f1520,plain,
    ( spl0_150
  <=> ! [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_150])]) ).

fof(f1882,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_120
    | ~ spl0_150 ),
    inference(superposition,[],[f1521,f1100]) ).

fof(f1521,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_150 ),
    inference(avatar_component_clause,[],[f1520]) ).

fof(f6570,plain,
    ( spl0_339
    | ~ spl0_28
    | ~ spl0_182 ),
    inference(avatar_split_clause,[],[f2744,f2317,f534,f6568]) ).

fof(f534,plain,
    ( spl0_28
  <=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f2744,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_28
    | ~ spl0_182 ),
    inference(resolution,[],[f2318,f535]) ).

fof(f535,plain,
    ( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f6566,plain,
    ( spl0_338
    | ~ spl0_56
    | ~ spl0_179 ),
    inference(avatar_split_clause,[],[f2652,f2305,f653,f6564]) ).

fof(f6564,plain,
    ( spl0_338
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f2652,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_179 ),
    inference(superposition,[],[f654,f2306]) ).

fof(f6562,plain,
    ( spl0_337
    | ~ spl0_56
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f2611,f2301,f653,f6560]) ).

fof(f6560,plain,
    ( spl0_337
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f2611,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_56
    | ~ spl0_178 ),
    inference(superposition,[],[f654,f2302]) ).

fof(f6558,plain,
    ( spl0_336
    | ~ spl0_55
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f2467,f2285,f649,f6556]) ).

fof(f6556,plain,
    ( spl0_336
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(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_336])]) ).

fof(f2467,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_174 ),
    inference(superposition,[],[f650,f2286]) ).

fof(f6554,plain,
    ( spl0_335
    | ~ spl0_114
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f2138,f1844,f1067,f6552]) ).

fof(f6552,plain,
    ( spl0_335
  <=> ! [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_335])]) ).

fof(f2138,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_114
    | ~ spl0_165 ),
    inference(resolution,[],[f1845,f1068]) ).

fof(f6550,plain,
    ( spl0_334
    | ~ spl0_88
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1600,f1496,f877,f6548]) ).

fof(f6548,plain,
    ( spl0_334
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f1600,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
    | ~ spl0_88
    | ~ spl0_144 ),
    inference(superposition,[],[f878,f1497]) ).

fof(f6546,plain,
    ( spl0_333
    | ~ spl0_50
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1594,f1496,f625,f6544]) ).

fof(f6544,plain,
    ( spl0_333
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f1594,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
    | ~ spl0_50
    | ~ spl0_144 ),
    inference(superposition,[],[f626,f1497]) ).

fof(f6542,plain,
    ( spl0_332
    | ~ spl0_88
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1567,f1492,f877,f6540]) ).

fof(f6540,plain,
    ( spl0_332
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1567,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
    | ~ spl0_88
    | ~ spl0_143 ),
    inference(superposition,[],[f878,f1493]) ).

fof(f6538,plain,
    ( spl0_331
    | ~ spl0_50
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1561,f1492,f625,f6536]) ).

fof(f6536,plain,
    ( spl0_331
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f1561,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
    | ~ spl0_50
    | ~ spl0_143 ),
    inference(superposition,[],[f626,f1493]) ).

fof(f6534,plain,
    ( spl0_330
    | ~ spl0_65
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1471,f1355,f689,f6532]) ).

fof(f6532,plain,
    ( spl0_330
  <=> ! [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_330])]) ).

fof(f1355,plain,
    ( spl0_138
  <=> ! [X28,X24,X11,X25] :
        ( ~ c_Lambda_Obeta(X24,X28)
        | c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1471,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_65
    | ~ spl0_138 ),
    inference(superposition,[],[f1356,f690]) ).

fof(f1356,plain,
    ( ! [X28,X11,X24,X25] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11))
        | ~ c_Lambda_Obeta(X24,X28) )
    | ~ spl0_138 ),
    inference(avatar_component_clause,[],[f1355]) ).

fof(f6526,plain,
    ( spl0_329
    | ~ spl0_65
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1469,f1355,f689,f6524]) ).

fof(f1469,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_65
    | ~ spl0_138 ),
    inference(superposition,[],[f1356,f690]) ).

fof(f6522,plain,
    ( spl0_328
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1454,f1343,f574,f6520]) ).

fof(f6520,plain,
    ( spl0_328
  <=> ! [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_Suc(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f574,plain,
    ( spl0_38
  <=> ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1454,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_Suc(X1))
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f575]) ).

fof(f575,plain,
    ( ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat)
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f574]) ).

fof(f6518,plain,
    ( spl0_327
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1445,f1339,f586,f6516]) ).

fof(f6516,plain,
    ( spl0_327
  <=> ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(c_Suc(X0),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f586,plain,
    ( spl0_41
  <=> ! [X25,X11] :
        ( ~ c_InductTermi_OIT(X25)
        | c_InductTermi_OIT(c_Lambda_Olift(X25,X11)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1445,plain,
    ( ! [X2,X0,X1] :
        ( c_InductTermi_OIT(c_Lambda_Oliftn(c_Suc(X0),X1,X2))
        | ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) )
    | ~ spl0_41
    | ~ spl0_134 ),
    inference(superposition,[],[f587,f1340]) ).

fof(f587,plain,
    ( ! [X11,X25] :
        ( c_InductTermi_OIT(c_Lambda_Olift(X25,X11))
        | ~ c_InductTermi_OIT(X25) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f586]) ).

fof(f6514,plain,
    ( spl0_326
    | ~ spl0_38
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1432,f1335,f574,f6512]) ).

fof(f6512,plain,
    ( spl0_326
  <=> ! [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_Suc(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f1432,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_Suc(X1))
    | ~ spl0_38
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f575]) ).

fof(f6510,plain,
    ( spl0_325
    | ~ spl0_81
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1387,f1316,f766,f6508]) ).

fof(f6508,plain,
    ( spl0_325
  <=> ! [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_325])]) ).

fof(f1387,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_81
    | ~ spl0_130 ),
    inference(resolution,[],[f1317,f767]) ).

fof(f6506,plain,
    ( spl0_324
    | ~ spl0_55
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1296,f1111,f649,f6504]) ).

fof(f6504,plain,
    ( spl0_324
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1296,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)))
    | ~ spl0_55
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f650]) ).

fof(f6502,plain,
    ( spl0_323
    | ~ spl0_54
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1295,f1111,f645,f6500]) ).

fof(f6500,plain,
    ( spl0_323
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f1295,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)))
    | ~ spl0_54
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f646]) ).

fof(f6498,plain,
    ( spl0_322
    | ~ spl0_67
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1179,f1067,f709,f6496]) ).

fof(f6496,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f1179,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_67
    | ~ spl0_114 ),
    inference(superposition,[],[f1068,f710]) ).

fof(f6494,plain,
    ( spl0_321
    | ~ spl0_55
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1175,f1067,f649,f6492]) ).

fof(f6492,plain,
    ( spl0_321
  <=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(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_321])]) ).

fof(f1175,plain,
    ( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_114 ),
    inference(resolution,[],[f1068,f650]) ).

fof(f6490,plain,
    ( spl0_320
    | ~ spl0_78
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1145,f1059,f753,f6488]) ).

fof(f6488,plain,
    ( spl0_320
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f1145,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1
    | ~ spl0_78
    | ~ spl0_112 ),
    inference(superposition,[],[f754,f1060]) ).

fof(f6484,plain,
    ( spl0_319
    | ~ spl0_77
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1144,f1059,f749,f6482]) ).

fof(f6482,plain,
    ( spl0_319
  <=> ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f1144,plain,
    ( ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
    | ~ spl0_77
    | ~ spl0_112 ),
    inference(superposition,[],[f750,f1060]) ).

fof(f6480,plain,
    ( spl0_318
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1134,f1059,f709,f6478]) ).

fof(f6478,plain,
    ( spl0_318
  <=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f1134,plain,
    ( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(superposition,[],[f1060,f710]) ).

fof(f6476,plain,
    ( spl0_317
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1131,f1055,f877,f6474]) ).

fof(f1131,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
    | ~ spl0_88
    | ~ spl0_111 ),
    inference(superposition,[],[f878,f1056]) ).

fof(f6472,plain,
    ( spl0_316
    | ~ spl0_78
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1129,f1055,f753,f6470]) ).

fof(f6470,plain,
    ( spl0_316
  <=> ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f1129,plain,
    ( ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
    | ~ spl0_78
    | ~ spl0_111 ),
    inference(superposition,[],[f754,f1056]) ).

fof(f6468,plain,
    ( spl0_315
    | ~ spl0_77
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1128,f1055,f749,f6466]) ).

fof(f6466,plain,
    ( spl0_315
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f1128,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0
    | ~ spl0_77
    | ~ spl0_111 ),
    inference(superposition,[],[f750,f1056]) ).

fof(f6464,plain,
    ( spl0_314
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1119,f1055,f709,f6462]) ).

fof(f6462,plain,
    ( spl0_314
  <=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f1119,plain,
    ( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat)
    | ~ spl0_67
    | ~ spl0_111 ),
    inference(superposition,[],[f1056,f710]) ).

fof(f6460,plain,
    ( spl0_313
    | ~ spl0_61
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f1040,f931,f673,f6458]) ).

fof(f6458,plain,
    ( spl0_313
  <=> ! [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_313])]) ).

fof(f673,plain,
    ( spl0_61
  <=> ! [X25,X28] :
        ( ~ c_Lambda_Obeta(X28,X25)
        | c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f931,plain,
    ( spl0_101
  <=> ! [X28,X24] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1040,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_61
    | ~ spl0_101 ),
    inference(resolution,[],[f932,f674]) ).

fof(f674,plain,
    ( ! [X28,X25] :
        ( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25))
        | ~ c_Lambda_Obeta(X28,X25) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f673]) ).

fof(f932,plain,
    ( ! [X28,X24] :
        ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
        | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f931]) ).

fof(f6031,plain,
    ( spl0_312
    | ~ spl0_97
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f4603,f3461,f915,f6028]) ).

fof(f6028,plain,
    ( spl0_312
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f3461,plain,
    ( spl0_224
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f4603,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_97
    | ~ spl0_224 ),
    inference(resolution,[],[f3462,f916]) ).

fof(f3462,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
    | ~ spl0_224 ),
    inference(avatar_component_clause,[],[f3461]) ).

fof(f5896,plain,
    ( spl0_311
    | ~ spl0_193
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f3246,f2960,f2952,f5894]) ).

fof(f5894,plain,
    ( spl0_311
  <=> ! [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_311])]) ).

fof(f2952,plain,
    ( spl0_193
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f2960,plain,
    ( spl0_195
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f3246,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_193
    | ~ spl0_195 ),
    inference(duplicate_literal_removal,[],[f3210]) ).

fof(f3210,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_193
    | ~ spl0_195 ),
    inference(resolution,[],[f2961,f2953]) ).

fof(f2953,plain,
    ( ! [X2,X0,X1,X8] :
        ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f2952]) ).

fof(f2961,plain,
    ( ! [X2,X0,X1,X8] :
        ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f2960]) ).

fof(f5892,plain,
    ( spl0_310
    | ~ spl0_30
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2802,f2321,f542,f5890]) ).

fof(f5890,plain,
    ( spl0_310
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f542,plain,
    ( spl0_30
  <=> ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f2802,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X0)) = X0 )
    | ~ spl0_30
    | ~ spl0_183 ),
    inference(resolution,[],[f2322,f543]) ).

fof(f543,plain,
    ( ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f542]) ).

fof(f5888,plain,
    ( spl0_309
    | ~ spl0_52
    | ~ spl0_138 ),
    inference(avatar_split_clause,[],[f1470,f1355,f633,f5886]) ).

fof(f5886,plain,
    ( spl0_309
  <=> ! [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_309])]) ).

fof(f1470,plain,
    ( ! [X2,X0,X1] :
        ( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
        | ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) )
    | ~ spl0_52
    | ~ spl0_138 ),
    inference(superposition,[],[f1356,f634]) ).

fof(f5884,plain,
    ( spl0_308
    | ~ spl0_51
    | ~ spl0_134 ),
    inference(avatar_split_clause,[],[f1440,f1339,f629,f5882]) ).

fof(f629,plain,
    ( spl0_51
  <=> ! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f1440,plain,
    ( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
    | ~ spl0_51
    | ~ spl0_134 ),
    inference(superposition,[],[f1340,f630]) ).

fof(f630,plain,
    ( ! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f629]) ).

fof(f5880,plain,
    ( spl0_307
    | ~ spl0_46
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1372,f1307,f608,f5878]) ).

fof(f5878,plain,
    ( spl0_307
  <=> ! [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_307])]) ).

fof(f1372,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
        | X0 = X1 )
    | ~ spl0_46
    | ~ spl0_128 ),
    inference(superposition,[],[f1308,f609]) ).

fof(f5876,plain,
    ( spl0_306
    | ~ spl0_48
    | ~ spl0_127 ),
    inference(avatar_split_clause,[],[f1363,f1303,f617,f5874]) ).

fof(f5874,plain,
    ( spl0_306
  <=> ! [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_306])]) ).

fof(f1363,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
        | X0 = X1 )
    | ~ spl0_48
    | ~ spl0_127 ),
    inference(superposition,[],[f1304,f618]) ).

fof(f5872,plain,
    ( spl0_305
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1290,f1111,f574,f5870]) ).

fof(f5870,plain,
    ( spl0_305
  <=> ! [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_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f1290,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_Suc(X0))
    | ~ spl0_38
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f575]) ).

fof(f5868,plain,
    ( spl0_304
    | ~ spl0_50
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f1195,f1079,f625,f5866]) ).

fof(f5866,plain,
    ( spl0_304
  <=> ! [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_304])]) ).

fof(f1195,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_50
    | ~ spl0_115 ),
    inference(resolution,[],[f1080,f626]) ).

fof(f5864,plain,
    ( spl0_303
    | ~ spl0_97
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f3883,f3371,f915,f5861]) ).

fof(f5861,plain,
    ( spl0_303
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3371,plain,
    ( spl0_209
  <=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f3883,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_97
    | ~ spl0_209 ),
    inference(resolution,[],[f3372,f916]) ).

fof(f3372,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f3371]) ).

fof(f5859,plain,
    ( spl0_302
    | ~ spl0_50
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f1161,f1063,f625,f5857]) ).

fof(f5857,plain,
    ( spl0_302
  <=> ! [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_302])]) ).

fof(f1161,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_50
    | ~ spl0_113 ),
    inference(resolution,[],[f1064,f626]) ).

fof(f5855,plain,
    ( spl0_301
    | ~ spl0_54
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1140,f1059,f645,f5853]) ).

fof(f5853,plain,
    ( spl0_301
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f1140,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
    | ~ spl0_54
    | ~ spl0_112 ),
    inference(superposition,[],[f646,f1060]) ).

fof(f5851,plain,
    ( spl0_300
    | ~ spl0_55
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1125,f1055,f649,f5849]) ).

fof(f5849,plain,
    ( spl0_300
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f1125,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
    | ~ spl0_55
    | ~ spl0_111 ),
    inference(superposition,[],[f650,f1056]) ).

fof(f5847,plain,
    ( spl0_299
    | ~ spl0_67
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f967,f877,f709,f5845]) ).

fof(f5845,plain,
    ( spl0_299
  <=> ! [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_299])]) ).

fof(f967,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_67
    | ~ spl0_88 ),
    inference(superposition,[],[f878,f710]) ).

fof(f5843,plain,
    ( spl0_298
    | ~ spl0_67
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f963,f873,f709,f5841]) ).

fof(f5841,plain,
    ( spl0_298
  <=> ! [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_298])]) ).

fof(f963,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
    | ~ spl0_67
    | ~ spl0_87 ),
    inference(superposition,[],[f874,f710]) ).

fof(f5839,plain,
    ( spl0_297
    | ~ spl0_80
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f868,f774,f762,f5837]) ).

fof(f5837,plain,
    ( spl0_297
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f868,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
    | ~ spl0_80
    | ~ spl0_83 ),
    inference(resolution,[],[f775,f763]) ).

fof(f5835,plain,
    ( spl0_296
    | ~ spl0_79
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f842,f762,f757,f5833]) ).

fof(f5833,plain,
    ( spl0_296
  <=> ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f842,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) )
    | ~ spl0_79
    | ~ spl0_80 ),
    inference(resolution,[],[f763,f758]) ).

fof(f5820,plain,
    ( spl0_295
    | ~ spl0_84
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1386,f1224,f778,f5818]) ).

fof(f5818,plain,
    ( spl0_295
  <=> ! [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_295])]) ).

fof(f1386,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_84
    | ~ spl0_125 ),
    inference(resolution,[],[f1225,f779]) ).

fof(f5605,plain,
    ( spl0_294
    | ~ spl0_79
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f1333,f1116,f757,f5603]) ).

fof(f5603,plain,
    ( spl0_294
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f1333,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
    | ~ spl0_79
    | ~ spl0_124 ),
    inference(resolution,[],[f1117,f758]) ).

fof(f5395,plain,
    ( spl0_293
    | ~ spl0_43
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f3331,f2976,f595,f5393]) ).

fof(f5393,plain,
    ( spl0_293
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f595,plain,
    ( spl0_43
  <=> ! [X38,X37,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X37,X38) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f2976,plain,
    ( spl0_199
  <=> ! [X28,X4,X12,X25] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f3331,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2)
    | ~ spl0_43
    | ~ spl0_199 ),
    inference(superposition,[],[f596,f2977]) ).

fof(f2977,plain,
    ( ! [X28,X4,X25,X12] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12))
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f2976]) ).

fof(f596,plain,
    ( ! [X38,X37,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X37,X38)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f5391,plain,
    ( spl0_292
    | ~ spl0_40
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f3330,f2976,f582,f5389]) ).

fof(f5389,plain,
    ( spl0_292
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f582,plain,
    ( spl0_40
  <=> ! [X30,X36,X35] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OApp(X35,X36) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f3330,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2)
    | ~ spl0_40
    | ~ spl0_199 ),
    inference(superposition,[],[f583,f2977]) ).

fof(f583,plain,
    ( ! [X36,X35,X30] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OApp(X35,X36)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f582]) ).

fof(f5387,plain,
    ( spl0_291
    | ~ spl0_43
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3319,f2972,f595,f5385]) ).

fof(f5385,plain,
    ( spl0_291
  <=> ! [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_291])]) ).

fof(f3319,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
    | ~ spl0_43
    | ~ spl0_198 ),
    inference(superposition,[],[f596,f2973]) ).

fof(f5383,plain,
    ( spl0_290
    | ~ spl0_40
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f3318,f2972,f582,f5381]) ).

fof(f5381,plain,
    ( spl0_290
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) != c_Lambda_OdB_OAbs(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f3318,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) != c_Lambda_OdB_OAbs(X4)
    | ~ spl0_40
    | ~ spl0_198 ),
    inference(superposition,[],[f583,f2973]) ).

fof(f5363,plain,
    ( spl0_289
    | ~ spl0_54
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1595,f1496,f645,f5361]) ).

fof(f5361,plain,
    ( spl0_289
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f1595,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_144 ),
    inference(superposition,[],[f646,f1497]) ).

fof(f5359,plain,
    ( spl0_288
    | ~ spl0_54
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1562,f1492,f645,f5357]) ).

fof(f1562,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_143 ),
    inference(superposition,[],[f646,f1493]) ).

fof(f5355,plain,
    ( spl0_287
    | ~ spl0_42
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1465,f1351,f590,f5353]) ).

fof(f5353,plain,
    ( spl0_287
  <=> ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_as____ = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f590,plain,
    ( spl0_42
  <=> v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f1351,plain,
    ( spl0_137
  <=> ! [X34,X0,X33,X32,X1] :
        ( X32 = X34
        | c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1465,plain,
    ( ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_as____ = X1 )
    | ~ spl0_42
    | ~ spl0_137 ),
    inference(superposition,[],[f1352,f592]) ).

fof(f592,plain,
    ( v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f590]) ).

fof(f1352,plain,
    ( ! [X0,X1,X34,X32,X33] :
        ( c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0)
        | X32 = X34 )
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1351]) ).

fof(f5351,plain,
    ( spl0_286
    | ~ spl0_42
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1462,f1347,f590,f5349]) ).

fof(f5349,plain,
    ( spl0_286
  <=> ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_a____ = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f1347,plain,
    ( spl0_136
  <=> ! [X34,X0,X33,X32,X1] :
        ( X1 = X33
        | c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f1462,plain,
    ( ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_a____ = X0 )
    | ~ spl0_42
    | ~ spl0_136 ),
    inference(superposition,[],[f1348,f592]) ).

fof(f1348,plain,
    ( ! [X0,X1,X34,X32,X33] :
        ( c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0)
        | X1 = X33 )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1347]) ).

fof(f5347,plain,
    ( spl0_285
    | ~ spl0_30
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1453,f1343,f542,f5345]) ).

fof(f5345,plain,
    ( spl0_285
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f1453,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X0))
    | ~ spl0_30
    | ~ spl0_135 ),
    inference(resolution,[],[f1344,f543]) ).

fof(f5343,plain,
    ( spl0_284
    | ~ spl0_30
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1431,f1335,f542,f5341]) ).

fof(f5341,plain,
    ( spl0_284
  <=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f1431,plain,
    ( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X0))
    | ~ spl0_30
    | ~ spl0_133 ),
    inference(resolution,[],[f1336,f543]) ).

fof(f5339,plain,
    ( spl0_283
    | ~ spl0_56
    | ~ spl0_120 ),
    inference(avatar_split_clause,[],[f1222,f1099,f653,f5337]) ).

fof(f5337,plain,
    ( spl0_283
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f1222,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_56
    | ~ spl0_120 ),
    inference(superposition,[],[f654,f1100]) ).

fof(f5335,plain,
    ( spl0_282
    | ~ spl0_48
    | ~ spl0_114 ),
    inference(avatar_split_clause,[],[f1182,f1067,f617,f5333]) ).

fof(f5333,plain,
    ( spl0_282
  <=> ! [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_282])]) ).

fof(f1182,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_48
    | ~ spl0_114 ),
    inference(superposition,[],[f1068,f618]) ).

fof(f5331,plain,
    ( spl0_281
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f1138,f1059,f621,f5329]) ).

fof(f5329,plain,
    ( spl0_281
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f1138,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat)
    | ~ spl0_49
    | ~ spl0_112 ),
    inference(superposition,[],[f622,f1060]) ).

fof(f5327,plain,
    ( spl0_280
    | ~ spl0_50
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1123,f1055,f625,f5325]) ).

fof(f5325,plain,
    ( spl0_280
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f1123,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat)
    | ~ spl0_50
    | ~ spl0_111 ),
    inference(superposition,[],[f626,f1056]) ).

fof(f5323,plain,
    ( spl0_279
    | ~ spl0_269
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f5199,f4898,f4880,f5321]) ).

fof(f5321,plain,
    ( spl0_279
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f4880,plain,
    ( spl0_269
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f4898,plain,
    ( spl0_270
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f5199,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | ~ spl0_269
    | ~ spl0_270 ),
    inference(superposition,[],[f4899,f4881]) ).

fof(f4881,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f4880]) ).

fof(f4899,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f4898]) ).

fof(f5319,plain,
    ( spl0_278
    | ~ spl0_65
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f1047,f939,f689,f5317]) ).

fof(f5317,plain,
    ( spl0_278
  <=> ! [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_278])]) ).

fof(f939,plain,
    ( spl0_103
  <=> ! [X25,X28] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1047,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_65
    | ~ spl0_103 ),
    inference(superposition,[],[f940,f690]) ).

fof(f940,plain,
    ( ! [X28,X25] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat)))
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f939]) ).

fof(f5315,plain,
    ( spl0_277
    | ~ spl0_81
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1020,f919,f766,f5313]) ).

fof(f5313,plain,
    ( spl0_277
  <=> ! [X0] :
        ( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1020,plain,
    ( ! [X0] :
        ( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_81
    | ~ spl0_98 ),
    inference(resolution,[],[f920,f767]) ).

fof(f5311,plain,
    ( spl0_276
    | ~ spl0_81
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1007,f911,f766,f5309]) ).

fof(f1007,plain,
    ( ! [X0] :
        ( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
    | ~ spl0_81
    | ~ spl0_96 ),
    inference(resolution,[],[f912,f767]) ).

fof(f5307,plain,
    ( spl0_275
    | ~ spl0_55
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f844,f762,f649,f5305]) ).

fof(f5305,plain,
    ( spl0_275
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f844,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat)
    | ~ spl0_55
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f841,f13]) ).

fof(f13,axiom,
    ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

fof(f841,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)),tc_nat)
    | ~ spl0_55
    | ~ spl0_80 ),
    inference(resolution,[],[f763,f650]) ).

fof(f5303,plain,
    ( spl0_274
    | ~ spl0_54
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f843,f762,f645,f5301]) ).

fof(f5301,plain,
    ( spl0_274
  <=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f843,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
    | ~ spl0_54
    | ~ spl0_80 ),
    inference(forward_demodulation,[],[f840,f14]) ).

fof(f14,axiom,
    ! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

fof(f840,plain,
    ( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)),tc_nat)
    | ~ spl0_54
    | ~ spl0_80 ),
    inference(resolution,[],[f763,f646]) ).

fof(f4912,plain,
    ( spl0_273
    | ~ spl0_43
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1786,f1524,f595,f4910]) ).

fof(f4910,plain,
    ( spl0_273
  <=> ! [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_273])]) ).

fof(f1786,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_43
    | ~ spl0_151 ),
    inference(superposition,[],[f596,f1525]) ).

fof(f4908,plain,
    ( spl0_272
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(avatar_split_clause,[],[f1785,f1524,f582,f4906]) ).

fof(f4906,plain,
    ( spl0_272
  <=> ! [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_272])]) ).

fof(f1785,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OAbs(X3)
    | ~ spl0_40
    | ~ spl0_151 ),
    inference(superposition,[],[f583,f1525]) ).

fof(f4904,plain,
    ( spl0_271
    | ~ spl0_46
    | ~ spl0_58
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1612,f1496,f661,f608,f4902]) ).

fof(f661,plain,
    ( spl0_58
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f1612,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
    | ~ spl0_46
    | ~ spl0_58
    | ~ spl0_144 ),
    inference(forward_demodulation,[],[f1585,f609]) ).

fof(f1585,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
    | ~ spl0_58
    | ~ spl0_144 ),
    inference(superposition,[],[f1497,f662]) ).

fof(f662,plain,
    ( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f661]) ).

fof(f4900,plain,
    ( spl0_270
    | ~ spl0_49
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1593,f1496,f621,f4898]) ).

fof(f1593,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
    | ~ spl0_49
    | ~ spl0_144 ),
    inference(superposition,[],[f622,f1497]) ).

fof(f4882,plain,
    ( spl0_269
    | ~ spl0_46
    | ~ spl0_59
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1580,f1492,f665,f608,f4880]) ).

fof(f665,plain,
    ( spl0_59
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1580,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
    | ~ spl0_46
    | ~ spl0_59
    | ~ spl0_143 ),
    inference(forward_demodulation,[],[f1554,f609]) ).

fof(f1554,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | ~ spl0_59
    | ~ spl0_143 ),
    inference(superposition,[],[f1493,f666]) ).

fof(f666,plain,
    ( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f665]) ).

fof(f4878,plain,
    ( spl0_268
    | ~ spl0_49
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1560,f1492,f621,f4876]) ).

fof(f4876,plain,
    ( spl0_268
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f1560,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
    | ~ spl0_49
    | ~ spl0_143 ),
    inference(superposition,[],[f622,f1493]) ).

fof(f4874,plain,
    ( spl0_267
    | ~ spl0_30
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f1289,f1111,f542,f4872]) ).

fof(f4872,plain,
    ( spl0_267
  <=> ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f1289,plain,
    ( ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X0))
    | ~ spl0_30
    | ~ spl0_123 ),
    inference(resolution,[],[f1112,f543]) ).

fof(f4870,plain,
    ( spl0_266
    | ~ spl0_52
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f1046,f939,f633,f4868]) ).

fof(f4868,plain,
    ( spl0_266
  <=> ! [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_266])]) ).

fof(f1046,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_52
    | ~ spl0_103 ),
    inference(superposition,[],[f940,f634]) ).

fof(f4866,plain,
    ( spl0_265
    | ~ spl0_79
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f859,f770,f757,f4864]) ).

fof(f4864,plain,
    ( spl0_265
  <=> ! [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_265])]) ).

fof(f859,plain,
    ( ! [X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
    | ~ spl0_79
    | ~ spl0_82 ),
    inference(resolution,[],[f771,f758]) ).

fof(f4862,plain,
    ( spl0_264
    | ~ spl0_50
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f838,f757,f625,f4860]) ).

fof(f4860,plain,
    ( spl0_264
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f838,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
    | ~ spl0_50
    | ~ spl0_79 ),
    inference(forward_demodulation,[],[f836,f13]) ).

fof(f836,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),X1,tc_nat)
    | ~ spl0_50
    | ~ spl0_79 ),
    inference(resolution,[],[f758,f626]) ).

fof(f4858,plain,
    ( spl0_263
    | ~ spl0_49
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f837,f757,f621,f4856]) ).

fof(f4856,plain,
    ( spl0_263
  <=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f837,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
    | ~ spl0_49
    | ~ spl0_79 ),
    inference(forward_demodulation,[],[f835,f14]) ).

fof(f835,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),X0,tc_nat)
    | ~ spl0_49
    | ~ spl0_79 ),
    inference(resolution,[],[f758,f622]) ).

fof(f4803,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f177,f4801]) ).

fof(f4801,plain,
    ( spl0_262
  <=> ! [X5,X7,X6,X19] :
        ( X5 = X19
        | X6 = X7
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f177,axiom,
    ! [X19,X6,X7,X5] :
      ( X5 = X19
      | X6 = X7
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X6,tc_nat),c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X19,X7,tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

fof(f4798,plain,
    ( spl0_261
    | ~ spl0_82
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f4602,f3461,f770,f4796]) ).

fof(f4796,plain,
    ( spl0_261
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f4602,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_82
    | ~ spl0_224 ),
    inference(resolution,[],[f3462,f771]) ).

fof(f4794,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f86,f4792]) ).

fof(f4792,plain,
    ( spl0_260
  <=> ! [X0,X8,X10,X2,X1] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X10,X0),X8,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f86,axiom,
    ! [X2,X10,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X10,X0),X8,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f4682,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f85,f4680]) ).

fof(f4680,plain,
    ( spl0_259
  <=> ! [X11,X13,X12,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X15,tc_nat),X12,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X15,tc_nat),X12,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f85,axiom,
    ! [X11,X15,X12,X13] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X15,tc_nat),X12,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X15,tc_nat),X12,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

fof(f4674,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f180,f4672]) ).

fof(f4672,plain,
    ( spl0_258
  <=> ! [X0,X21,X23,X22,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f180,axiom,
    ! [X21,X0,X22,X23,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f4670,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f112,f4668]) ).

fof(f4668,plain,
    ( spl0_257
  <=> ! [X0,X8,X9,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f112,axiom,
    ! [X2,X0,X1,X8,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f4633,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f214,f4631]) ).

fof(f4631,plain,
    ( spl0_256
  <=> ! [X5,X24,X9,X8] :
        ( X8 = X9
        | c_HOL_Ozero__class_Ozero(tc_nat) = X24
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X9,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f214,axiom,
    ! [X8,X9,X24,X5] :
      ( X8 = X9
      | c_HOL_Ozero__class_Ozero(tc_nat) = X24
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X9,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

fof(f4514,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f309,f4512]) ).

fof(f4512,plain,
    ( spl0_255
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f309,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

fof(f4510,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f136,f4508]) ).

fof(f4508,plain,
    ( spl0_254
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f136,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

fof(f4506,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f133,f4504]) ).

fof(f4504,plain,
    ( spl0_253
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f133,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

fof(f4502,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f129,f4500]) ).

fof(f4500,plain,
    ( spl0_252
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f129,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

fof(f4289,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f256,f4287]) ).

fof(f4287,plain,
    ( spl0_251
  <=> ! [X5,X0,X6,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f256,axiom,
    ! [X0,X6,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f4285,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f253,f4283]) ).

fof(f4283,plain,
    ( spl0_250
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f253,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f4267,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f252,f4265]) ).

fof(f4265,plain,
    ( spl0_249
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f252,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f4263,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f206,f4261]) ).

fof(f4261,plain,
    ( spl0_248
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f206,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

fof(f4259,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f205,f4257]) ).

fof(f4257,plain,
    ( spl0_247
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f205,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

fof(f4255,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f196,f4253]) ).

fof(f4253,plain,
    ( spl0_246
  <=> ! [X0,X8,X9,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X8,X9,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f196,axiom,
    ! [X2,X0,X1,X8,X9] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X8,X9,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f4251,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f194,f4249]) ).

fof(f4249,plain,
    ( spl0_245
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f194,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f4247,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f167,f4245]) ).

fof(f4245,plain,
    ( spl0_244
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f167,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

fof(f4243,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f166,f4241]) ).

fof(f4241,plain,
    ( spl0_243
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f166,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

fof(f4239,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f165,f4237]) ).

fof(f4237,plain,
    ( spl0_242
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f165,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,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_Otimes__class_Otimes(X2,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

fof(f4235,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f90,f4233]) ).

fof(f4233,plain,
    ( spl0_241
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,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(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f90,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,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(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f4207,plain,
    ( spl0_240
    | ~ spl0_82
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f3882,f3371,f770,f4205]) ).

fof(f4205,plain,
    ( spl0_240
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f3882,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_82
    | ~ spl0_209 ),
    inference(resolution,[],[f3372,f771]) ).

fof(f4123,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f268,f4121]) ).

fof(f4121,plain,
    ( spl0_239
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f268,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

fof(f4119,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f267,f4117]) ).

fof(f4117,plain,
    ( spl0_238
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f267,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

fof(f4115,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f119,f4113]) ).

fof(f4113,plain,
    ( spl0_237
  <=> ! [X4,X12,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f119,axiom,
    ! [X3,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

fof(f4111,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f118,f4109]) ).

fof(f4109,plain,
    ( spl0_236
  <=> ! [X4,X12,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f118,axiom,
    ! [X3,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

fof(f3661,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f255,f3659]) ).

fof(f255,axiom,
    ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

fof(f3657,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f254,f3655]) ).

fof(f254,axiom,
    ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

fof(f3653,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f208,f3651]) ).

fof(f3651,plain,
    ( spl0_233
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X8,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f208,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X8,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
      | c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f3627,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f197,f3625]) ).

fof(f3625,plain,
    ( spl0_232
  <=> ! [X11,X13,X14,X12] :
        ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f197,axiom,
    ! [X11,X14,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

fof(f3623,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f169,f3621]) ).

fof(f3621,plain,
    ( spl0_231
  <=> ! [X4,X3] :
        ( ~ 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)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f169,axiom,
    ! [X3,X4] :
      ( ~ 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)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

fof(f3619,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f163,f3617]) ).

fof(f3617,plain,
    ( spl0_230
  <=> ! [X4,X3] :
        ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f163,axiom,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

fof(f3615,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f95,f3613]) ).

fof(f95,axiom,
    ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

fof(f3611,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f94,f3609]) ).

fof(f94,axiom,
    ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

fof(f3607,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f69,f3605]) ).

fof(f3605,plain,
    ( spl0_227
  <=> ! [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_227])]) ).

fof(f69,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(f3603,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f33,f3601]) ).

fof(f3601,plain,
    ( spl0_226
  <=> ! [X4,X3,X14] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X14,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),c_HOL_Ominus__class_Ominus(X14,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f33,axiom,
    ! [X3,X14,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,X14,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),c_HOL_Ominus__class_Ominus(X14,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

fof(f3554,plain,
    ( spl0_225
    | ~ spl0_86
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2682,f1824,f851,f3552]) ).

fof(f3552,plain,
    ( spl0_225
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f851,plain,
    ( spl0_86
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f2682,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_86
    | ~ spl0_160 ),
    inference(superposition,[],[f852,f1825]) ).

fof(f852,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f851]) ).

fof(f3463,plain,
    ( spl0_224
    | ~ spl0_30
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2672,f1824,f542,f3461]) ).

fof(f2672,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
    | ~ spl0_30
    | ~ spl0_160 ),
    inference(superposition,[],[f543,f1825]) ).

fof(f3429,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f399,f3427]) ).

fof(f399,plain,
    ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f109,f73]) ).

fof(f109,axiom,
    ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

fof(f3425,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f251,f3423]) ).

fof(f3423,plain,
    ( spl0_222
  <=> ! [X5,X0,X6,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f251,axiom,
    ! [X0,X6,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

fof(f3421,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f249,f3419]) ).

fof(f249,axiom,
    ! [X0,X22,X23,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f3417,plain,
    ( spl0_220
    | ~ spl0_86
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f2054,f1702,f851,f3415]) ).

fof(f3415,plain,
    ( spl0_220
  <=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f2054,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat)
    | ~ spl0_86
    | ~ spl0_152 ),
    inference(superposition,[],[f852,f1703]) ).

fof(f3413,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f246,f3411]) ).

fof(f246,axiom,
    ! [X21,X0,X22,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f3409,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f245,f3407]) ).

fof(f3407,plain,
    ( spl0_218
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f245,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f3405,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f239,f3403]) ).

fof(f3403,plain,
    ( spl0_217
  <=> ! [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_217])]) ).

fof(f239,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(f3401,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f238,f3399]) ).

fof(f238,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(f3397,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f195,f3395]) ).

fof(f195,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(f3393,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f173,f3391]) ).

fof(f173,axiom,
    ! [X3,X0,X4] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(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__mult_0) ).

fof(f3389,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f157,f3387]) ).

fof(f3387,plain,
    ( spl0_213
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f157,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

fof(f3385,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f108,f3383]) ).

fof(f3383,plain,
    ( spl0_212
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f108,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

fof(f3381,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f77,f3379]) ).

fof(f3379,plain,
    ( spl0_211
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f77,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

fof(f3377,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f76,f3375]) ).

fof(f3375,plain,
    ( spl0_210
  <=> ! [X4,X12,X3] :
        ( X3 = X4
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
        | c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f76,axiom,
    ! [X3,X4,X12] :
      ( X3 = X4
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
      | c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

fof(f3373,plain,
    ( spl0_209
    | ~ spl0_30
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f2044,f1702,f542,f3371]) ).

fof(f2044,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
    | ~ spl0_30
    | ~ spl0_152 ),
    inference(superposition,[],[f543,f1703]) ).

fof(f3369,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f67,f3367]) ).

fof(f3367,plain,
    ( spl0_208
  <=> ! [X0,X8,X9,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f67,axiom,
    ! [X0,X1,X8,X9] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f3365,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f66,f3363]) ).

fof(f3363,plain,
    ( spl0_207
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f66,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f3361,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f64,f3359]) ).

fof(f3359,plain,
    ( spl0_206
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f64,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f3357,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f63,f3355]) ).

fof(f3355,plain,
    ( spl0_205
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f63,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f3353,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f62,f3351]) ).

fof(f3351,plain,
    ( spl0_204
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f62,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f3349,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f58,f3347]) ).

fof(f3347,plain,
    ( spl0_203
  <=> ! [X5,X0,X6,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f58,axiom,
    ! [X0,X6,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f3345,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f29,f3343]) ).

fof(f29,axiom,
    ! [X3,X14,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X12,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

fof(f3313,plain,
    ( spl0_201
    | ~ spl0_80
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f1077,f1043,f762,f3311]) ).

fof(f1077,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
    | ~ spl0_80
    | ~ spl0_109 ),
    inference(resolution,[],[f1044,f763]) ).

fof(f2983,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f367,f2980]) ).

fof(f367,axiom,
    c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

fof(f2978,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f361,f2976]) ).

fof(f361,axiom,
    ! [X28,X4,X25,X12] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).

fof(f2974,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f343,f2972]) ).

fof(f343,axiom,
    ! [X28,X15,X25,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

fof(f2970,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f244,f2968]) ).

fof(f2968,plain,
    ( spl0_197
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f244,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

fof(f2966,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f224,f2964]) ).

fof(f2964,plain,
    ( spl0_196
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f224,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f2962,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f223,f2960]) ).

fof(f223,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f2958,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f222,f2956]) ).

fof(f2956,plain,
    ( spl0_194
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f222,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f2954,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f221,f2952]) ).

fof(f221,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f2950,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f220,f2948]) ).

fof(f2948,plain,
    ( spl0_192
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f220,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f2946,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f219,f2944]) ).

fof(f2944,plain,
    ( spl0_191
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f219,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f2942,plain,
    ( spl0_190
    | ~ spl0_27
    | ~ spl0_160 ),
    inference(avatar_split_clause,[],[f2671,f1824,f530,f2940]) ).

fof(f2671,plain,
    ( ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0))
    | ~ spl0_27
    | ~ spl0_160 ),
    inference(superposition,[],[f531,f1825]) ).

fof(f2938,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f98,f2936]) ).

fof(f2936,plain,
    ( spl0_189
  <=> ! [X4,X12,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f98,axiom,
    ! [X3,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

fof(f2934,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f47,f2932]) ).

fof(f2932,plain,
    ( spl0_188
  <=> ! [X4,X12,X3] :
        ( X3 = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X12
        | c_HOL_Otimes__class_Otimes(X3,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X12,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f47,axiom,
    ! [X3,X4,X12] :
      ( X3 = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X12
      | c_HOL_Otimes__class_Otimes(X3,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

fof(f2930,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f45,f2928]) ).

fof(f2928,plain,
    ( spl0_187
  <=> ! [X4,X12,X3] :
        ( X3 = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) = X12
        | c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f45,axiom,
    ! [X3,X4,X12] :
      ( X3 = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) = X12
      | c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

fof(f2336,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f398,f2334]) ).

fof(f398,plain,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat),
    inference(forward_demodulation,[],[f96,f73]) ).

fof(f96,axiom,
    ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

fof(f2332,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f329,f2330]) ).

fof(f2330,plain,
    ( spl0_185
  <=> ! [X11,X12,X28] :
        ( X11 = X12
        | c_HOL_Oord__class_Oless(X12,X11,tc_nat)
        | c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X28,X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f329,axiom,
    ! [X28,X11,X12] :
      ( X11 = X12
      | c_HOL_Oord__class_Oless(X12,X11,tc_nat)
      | c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X28,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

fof(f2328,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f304,f2326]) ).

fof(f2326,plain,
    ( spl0_184
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
        | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f304,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_1) ).

fof(f2323,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f292,f2321]) ).

fof(f292,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
      | c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_0) ).

fof(f2319,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f286,f2317]) ).

fof(f286,axiom,
    ! [X11,X4,X12] :
      ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).

fof(f2315,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f250,f2313]) ).

fof(f250,axiom,
    ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

fof(f2311,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f158,f2309]) ).

fof(f2309,plain,
    ( spl0_180
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f158,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

fof(f2307,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f84,f2305]) ).

fof(f84,axiom,
    ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

fof(f2303,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f83,f2301]) ).

fof(f83,axiom,
    ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

fof(f2299,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f80,f2297]) ).

fof(f2297,plain,
    ( spl0_177
  <=> ! [X4,X12,X3] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f80,axiom,
    ! [X3,X4,X12] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

fof(f2295,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f79,f2293]) ).

fof(f79,axiom,
    ! [X3,X4,X12] :
      ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

fof(f2291,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f73,f2289]) ).

fof(f2287,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f61,f2285]) ).

fof(f2283,plain,
    ( spl0_173
    | ~ spl0_27
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f2043,f1702,f530,f2281]) ).

fof(f2281,plain,
    ( spl0_173
  <=> ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f2043,plain,
    ( ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0))
    | ~ spl0_27
    | ~ spl0_152 ),
    inference(superposition,[],[f531,f1703]) ).

fof(f2279,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f60,f2277]) ).

fof(f60,axiom,
    ! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

fof(f1887,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f306,f1885]) ).

fof(f306,axiom,
    ! [X0,X6,X7,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X7,X6,X0)
      | c_HOL_Oord__class_Oless(X7,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f1866,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f305,f1864]) ).

fof(f305,axiom,
    ! [X0,X6,X7,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X7,X0)
      | c_HOL_Oord__class_Oless(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f1862,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f273,f1860]) ).

fof(f1860,plain,
    ( spl0_169
  <=> ! [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_169])]) ).

fof(f273,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(f1858,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f272,f1856]) ).

fof(f272,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(f1854,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f262,f1852]) ).

fof(f262,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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

fof(f1850,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f237,f1848]) ).

fof(f237,axiom,
    ! [X3,X4,X12] :
      ( X3 = X4
      | c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

fof(f1846,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f227,f1844]) ).

fof(f227,axiom,
    ! [X3,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

fof(f1842,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f226,f1840]) ).

fof(f226,axiom,
    ! [X3,X4,X12] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

fof(f1838,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f225,f1836]) ).

fof(f225,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

fof(f1834,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f218,f1832]) ).

fof(f218,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
      | c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

fof(f1830,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f217,f1828]) ).

fof(f217,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

fof(f1826,plain,
    ( spl0_160
    | ~ spl0_38
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1014,f919,f574,f1824]) ).

fof(f1014,plain,
    ( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)))
    | ~ spl0_38
    | ~ spl0_98 ),
    inference(resolution,[],[f920,f575]) ).

fof(f1822,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f203,f1820]) ).

fof(f1820,plain,
    ( spl0_159
  <=> ! [X4,X12,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f203,axiom,
    ! [X3,X4,X12] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

fof(f1818,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f202,f1816]) ).

fof(f202,axiom,
    ! [X3,X4,X12] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

fof(f1814,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f201,f1812]) ).

fof(f1812,plain,
    ( spl0_157
  <=> ! [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_157])]) ).

fof(f201,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(f1810,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f200,f1808]) ).

fof(f1808,plain,
    ( spl0_156
  <=> ! [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_156])]) ).

fof(f200,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(f1806,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f106,f1804]) ).

fof(f1804,plain,
    ( spl0_155
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X8
        | c_HOL_Oplus__class_Oplus(X8,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f106,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X8
      | c_HOL_Oplus__class_Oplus(X8,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f1802,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f105,f1800]) ).

fof(f1800,plain,
    ( spl0_154
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X8
        | c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f105,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X8
      | c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f1798,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f104,f1796]) ).

fof(f1796,plain,
    ( spl0_153
  <=> ! [X0,X8,X2,X1] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X2 = X8
        | c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f104,axiom,
    ! [X2,X0,X1,X8] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X2 = X8
      | c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f1704,plain,
    ( spl0_152
    | ~ spl0_38
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1001,f911,f574,f1702]) ).

fof(f1001,plain,
    ( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)))
    | ~ spl0_38
    | ~ spl0_96 ),
    inference(resolution,[],[f912,f575]) ).

fof(f1526,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f354,f1524]) ).

fof(f354,axiom,
    ! [X28,X25,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

fof(f1522,plain,
    ( spl0_150
    | ~ spl0_56
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f856,f770,f653,f1520]) ).

fof(f856,plain,
    ( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
    | ~ spl0_56
    | ~ spl0_82 ),
    inference(resolution,[],[f771,f654]) ).

fof(f1518,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f312,f1516]) ).

fof(f312,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(f1514,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f279,f1512]) ).

fof(f1512,plain,
    ( spl0_148
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | X5 = X6
        | c_HOL_Oord__class_Oless(X6,X5,X0)
        | c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f279,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | X5 = X6
      | c_HOL_Oord__class_Oless(X6,X5,X0)
      | c_HOL_Oord__class_Oless(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

fof(f1510,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f274,f1508]) ).

fof(f274,axiom,
    ! [X11,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

fof(f1506,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f261,f1504]) ).

fof(f1504,plain,
    ( spl0_146
  <=> ! [X4,X11] :
        ( ~ 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(X11),tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f261,axiom,
    ! [X11,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(X11),tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

fof(f1502,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f242,f1500]) ).

fof(f242,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(f1498,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f171,f1496]) ).

fof(f171,axiom,
    ! [X3,X4] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

fof(f1494,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f170,f1492]) ).

fof(f170,axiom,
    ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

fof(f1490,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f89,f1488]) ).

fof(f89,axiom,
    ! [X3,X4] :
      ( 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_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

fof(f1486,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f88,f1484]) ).

fof(f88,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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

fof(f1482,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f32,f1480]) ).

fof(f1480,plain,
    ( spl0_140
  <=> ! [X4,X3] :
        ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
        | c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f32,axiom,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
      | c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

fof(f1475,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f31,f1473]) ).

fof(f1473,plain,
    ( spl0_139
  <=> ! [X4,X3] :
        ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
        | c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f31,axiom,
    ! [X3,X4] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

fof(f1357,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f355,f1355]) ).

fof(f355,axiom,
    ! [X28,X11,X24,X25] :
      ( ~ c_Lambda_Obeta(X24,X28)
      | c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

fof(f1353,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f340,f1351]) ).

fof(f340,axiom,
    ! [X0,X1,X34,X32,X33] :
      ( X32 = X34
      | c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

fof(f1349,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f339,f1347]) ).

fof(f339,axiom,
    ! [X0,X1,X34,X32,X33] :
      ( X1 = X33
      | c_List_Olist_OCons(X1,X32,X0) != c_List_Olist_OCons(X33,X34,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

fof(f1345,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f338,f1343]) ).

fof(f338,axiom,
    ! [X11,X15,X13] :
      ( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
      | c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

fof(f1341,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f330,f1339]) ).

fof(f330,axiom,
    ! [X4,X25,X12] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).

fof(f1337,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f326,f1335]) ).

fof(f326,axiom,
    ! [X11,X4,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).

fof(f1326,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f294,f1324]) ).

fof(f294,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(f1322,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f231,f1320]) ).

fof(f231,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(f1318,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f230,f1316]) ).

fof(f230,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(f1314,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f179,f1311]) ).

fof(f1311,plain,
    ( spl0_129
  <=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f179,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

fof(f1309,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f101,f1307]) ).

fof(f101,axiom,
    ! [X3,X4,X12] :
      ( X3 = X4
      | c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

fof(f1305,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f100,f1303]) ).

fof(f100,axiom,
    ! [X6,X7,X5] :
      ( X6 = X7
      | c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

fof(f1301,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f34,f1299]) ).

fof(f1299,plain,
    ( spl0_126
  <=> ! [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_126])]) ).

fof(f34,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(f1226,plain,
    ( spl0_125
    | ~ spl0_84
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f976,f943,f778,f1224]) ).

fof(f976,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
    | ~ spl0_84
    | ~ spl0_104 ),
    inference(resolution,[],[f944,f779]) ).

fof(f1118,plain,
    ( spl0_124
    | ~ spl0_79
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f901,f851,f757,f1116]) ).

fof(f901,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
    | ~ spl0_79
    | ~ spl0_86 ),
    inference(resolution,[],[f852,f758]) ).

fof(f1113,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f325,f1111]) ).

fof(f325,axiom,
    ! [X11,X12] :
      ( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

fof(f1109,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f282,f1107]) ).

fof(f282,axiom,
    ! [X6,X5] :
      ( X5 = X6
      | c_HOL_Oord__class_Oless(X5,X6,tc_nat)
      | c_HOL_Oord__class_Oless(X6,X5,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

fof(f1105,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f192,f1103]) ).

fof(f192,axiom,
    ! [X4,X12,X13] :
      ( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

fof(f1101,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f178,f1099]) ).

fof(f178,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

fof(f1097,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f49,f1095]) ).

fof(f49,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

fof(f1093,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f48,f1091]) ).

fof(f48,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

fof(f1089,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f30,f1087]) ).

fof(f1087,plain,
    ( spl0_117
  <=> ! [X5,X0,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f30,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f1085,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f27,f1083]) ).

fof(f1083,plain,
    ( spl0_116
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f27,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f1081,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f25,f1079]) ).

fof(f25,axiom,
    ! [X3,X11,X13] :
      ( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
      | c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

fof(f1069,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f23,f1067]) ).

fof(f23,axiom,
    ! [X11,X12,X13] :
      ( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

fof(f1065,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f21,f1063]) ).

fof(f21,axiom,
    ! [X6,X7,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

fof(f1061,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f14,f1059]) ).

fof(f1057,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f13,f1055]) ).

fof(f1053,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f1,f1051]) ).

fof(f1051,plain,
    ( spl0_110
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f1045,plain,
    ( spl0_109
    | ~ spl0_30
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f839,f762,f542,f1043]) ).

fof(f839,plain,
    ( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
    | ~ spl0_30
    | ~ spl0_80 ),
    inference(resolution,[],[f763,f543]) ).

fof(f961,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f359,f959]) ).

fof(f959,plain,
    ( spl0_108
  <=> ! [X25,X28,X15] :
        ( ~ c_Lambda_Obeta(X28,X25)
        | c_Lambda_Obeta(c_Lambda_OdB_OApp(X28,X15),c_Lambda_OdB_OApp(X25,X15)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f359,axiom,
    ! [X28,X15,X25] :
      ( ~ c_Lambda_Obeta(X28,X25)
      | c_Lambda_Obeta(c_Lambda_OdB_OApp(X28,X15),c_Lambda_OdB_OApp(X25,X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

fof(f957,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f358,f955]) ).

fof(f955,plain,
    ( spl0_107
  <=> ! [X25,X28,X15] :
        ( ~ c_Lambda_Obeta(X28,X25)
        | c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X28),c_Lambda_OdB_OApp(X15,X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f358,axiom,
    ! [X28,X15,X25] :
      ( ~ c_Lambda_Obeta(X28,X25)
      | c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X28),c_Lambda_OdB_OApp(X15,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

fof(f953,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f349,f951]) ).

fof(f349,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(f949,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f348,f947]) ).

fof(f348,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(f945,plain,
    ( spl0_104
    | ~ spl0_29
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f871,f778,f538,f943]) ).

fof(f871,plain,
    ( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
    | ~ spl0_29
    | ~ spl0_84 ),
    inference(resolution,[],[f779,f539]) ).

fof(f941,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f334,f939]) ).

fof(f334,axiom,
    ! [X28,X25] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

fof(f937,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f324,f935]) ).

fof(f324,axiom,
    ! [X28,X11,X24] :
      ( ~ c_Lambda_Obeta(X24,X28)
      | c_Lambda_Obeta(c_Lambda_Olift(X24,X11),c_Lambda_Olift(X28,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

fof(f933,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f320,f931]) ).

fof(f320,axiom,
    ! [X28,X24] :
      ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
      | c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).

fof(f929,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f317,f927]) ).

fof(f317,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(f925,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f316,f923]) ).

fof(f316,axiom,
    ! [X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

fof(f921,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f303,f919]) ).

fof(f303,axiom,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_0) ).

fof(f917,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f302,f915]) ).

fof(f302,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(f913,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f301,f911]) ).

fof(f301,axiom,
    ! [X4] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
      | c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__implies__Suc_0) ).

fof(f909,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f260,f907]) ).

fof(f907,plain,
    ( spl0_95
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f260,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f905,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f259,f903]) ).

fof(f903,plain,
    ( spl0_94
  <=> ! [X5,X0,X6] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f259,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f899,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f257,f897]) ).

fof(f897,plain,
    ( spl0_93
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f257,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

fof(f895,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f191,f893]) ).

fof(f893,plain,
    ( spl0_92
  <=> ! [X5,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),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f191,axiom,
    ! [X0,X5] :
      ( ~ 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),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

fof(f891,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f188,f889]) ).

fof(f889,plain,
    ( spl0_91
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f188,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f887,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f187,f885]) ).

fof(f885,plain,
    ( spl0_90
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f187,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f883,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f184,f881]) ).

fof(f881,plain,
    ( spl0_89
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f184,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f879,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f72,f877]) ).

fof(f72,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(f875,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f36,f873]) ).

fof(f36,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(f853,plain,
    ( spl0_86
    | ~ spl0_28
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f831,f757,f534,f851]) ).

fof(f831,plain,
    ( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
    | ~ spl0_28
    | ~ spl0_79 ),
    inference(resolution,[],[f758,f535]) ).

fof(f811,plain,
    ( spl0_85
    | ~ spl0_18
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f805,f713,f486,f808]) ).

fof(f808,plain,
    ( spl0_85
  <=> 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_85])]) ).

fof(f713,plain,
    ( spl0_68
  <=> ! [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_68])]) ).

fof(f805,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_18
    | ~ spl0_68 ),
    inference(resolution,[],[f714,f488]) ).

fof(f714,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_68 ),
    inference(avatar_component_clause,[],[f713]) ).

fof(f780,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f336,f778]) ).

fof(f336,axiom,
    ! [X28,X24] :
      ( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
      | c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).

fof(f776,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f315,f774]) ).

fof(f315,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(f772,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f314,f770]) ).

fof(f314,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(f768,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f271,f766]) ).

fof(f271,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(f764,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f264,f762]) ).

fof(f264,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

fof(f759,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f263,f757]) ).

fof(f263,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

fof(f755,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f151,f753]) ).

fof(f151,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(f751,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f150,f749]) ).

fof(f150,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(f747,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f147,f745]) ).

fof(f745,plain,
    ( spl0_76
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f147,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f743,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f146,f741]) ).

fof(f741,plain,
    ( spl0_75
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f146,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f739,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f145,f737]) ).

fof(f737,plain,
    ( spl0_74
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f145,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f735,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f144,f733]) ).

fof(f733,plain,
    ( spl0_73
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f144,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f731,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f139,f729]) ).

fof(f729,plain,
    ( spl0_72
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f139,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f727,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f138,f725]) ).

fof(f725,plain,
    ( spl0_71
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f138,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f723,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f113,f721]) ).

fof(f721,plain,
    ( spl0_70
  <=> ! [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_70])]) ).

fof(f113,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(f719,plain,
    ( spl0_69
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f703,f689,f685,f717]) ).

fof(f717,plain,
    ( spl0_69
  <=> ! [X0,X1] :
        ( c_InductTermi_OIT(X0)
        | ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f685,plain,
    ( spl0_64
  <=> ! [X13,X11,X24] :
        ( ~ c_InductTermi_OIT(X24)
        | c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f703,plain,
    ( ! [X0,X1] :
        ( c_InductTermi_OIT(X0)
        | ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) )
    | ~ spl0_64
    | ~ spl0_65 ),
    inference(superposition,[],[f686,f690]) ).

fof(f686,plain,
    ( ! [X11,X24,X13] :
        ( c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13))
        | ~ c_InductTermi_OIT(X24) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f685]) ).

fof(f715,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f87,f713]) ).

fof(f87,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(f711,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f28,f709]) ).

fof(f28,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(f707,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f4,f705]) ).

fof(f4,axiom,
    ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

fof(f691,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f362,f689]) ).

fof(f362,axiom,
    ! [X28,X25,X12] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

fof(f687,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f347,f685]) ).

fof(f347,axiom,
    ! [X11,X24,X13] :
      ( ~ c_InductTermi_OIT(X24)
      | c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

fof(f683,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f341,f681]) ).

fof(f681,plain,
    ( spl0_63
  <=> ! [X27,X26] :
        ( X26 = X27
        | c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OVar(X26) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f341,axiom,
    ! [X26,X27] :
      ( X26 = X27
      | c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OVar(X26) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

fof(f679,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f333,f677]) ).

fof(f677,plain,
    ( spl0_62
  <=> ! [X30,X31] :
        ( X30 = X31
        | c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OAbs(X31) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f333,axiom,
    ! [X31,X30] :
      ( X30 = X31
      | c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OAbs(X31) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

fof(f675,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f319,f673]) ).

fof(f319,axiom,
    ! [X28,X25] :
      ( ~ c_Lambda_Obeta(X28,X25)
      | c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

fof(f671,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f298,f669]) ).

fof(f669,plain,
    ( spl0_60
  <=> ! [X6,X5] :
        ( X5 = X6
        | c_Suc(X5) != c_Suc(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f298,axiom,
    ! [X6,X5] :
      ( X5 = X6
      | c_Suc(X5) != c_Suc(X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

fof(f667,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f190,f665]) ).

fof(f190,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

fof(f663,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f189,f661]) ).

fof(f189,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

fof(f659,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f82,f657]) ).

fof(f82,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(f655,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f57,f653]) ).

fof(f57,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(f651,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f19,f649]) ).

fof(f19,axiom,
    ! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

fof(f647,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f18,f645]) ).

fof(f18,axiom,
    ! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X11,X3,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

fof(f639,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f364,f637]) ).

fof(f637,plain,
    ( spl0_53
  <=> ! [X25,X11] :
        ( ~ c_InductTermi_OIT(X25)
        | c_InductTermi_OIT(c_Lambda_OdB_OApp(X25,c_Lambda_OdB_OVar(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f364,axiom,
    ! [X11,X25] :
      ( ~ c_InductTermi_OIT(X25)
      | c_InductTermi_OIT(c_Lambda_OdB_OApp(X25,c_Lambda_OdB_OVar(X11))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

fof(f635,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f346,f633]) ).

fof(f346,axiom,
    ! [X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

fof(f631,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f270,f629]) ).

fof(f270,axiom,
    ! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).

fof(f627,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f212,f625]) ).

fof(f212,axiom,
    ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

fof(f623,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f211,f621]) ).

fof(f211,axiom,
    ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

fof(f619,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f141,f617]) ).

fof(f141,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(f615,plain,
    ( ~ spl0_47
    | ~ spl0_39
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f598,f590,f578,f612]) ).

fof(f612,plain,
    ( spl0_47
  <=> v_rs____ = v_as____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f578,plain,
    ( spl0_39
  <=> ! [X5,X25,X0] : c_List_Olist_OCons(X5,X25,X0) != X25 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f598,plain,
    ( v_rs____ != v_as____
    | ~ spl0_39
    | ~ spl0_42 ),
    inference(superposition,[],[f579,f592]) ).

fof(f579,plain,
    ( ! [X0,X5,X25] : c_List_Olist_OCons(X5,X25,X0) != X25
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f578]) ).

fof(f610,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f140,f608]) ).

fof(f140,axiom,
    ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

fof(f606,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f44,f604]) ).

fof(f604,plain,
    ( spl0_45
  <=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f44,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(f602,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f43,f600]) ).

fof(f43,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(f597,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f366,f595]) ).

fof(f366,axiom,
    ! [X38,X37,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X37,X38),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

fof(f593,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f363,f590]) ).

fof(f363,axiom,
    v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).

fof(f588,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f351,f586]) ).

fof(f351,axiom,
    ! [X11,X25] :
      ( ~ c_InductTermi_OIT(X25)
      | c_InductTermi_OIT(c_Lambda_Olift(X25,X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

fof(f584,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f345,f582]) ).

fof(f345,axiom,
    ! [X36,X35,X30] : c_Lambda_OdB_OAbs(X30) != c_Lambda_OdB_OApp(X35,X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).

fof(f580,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f323,f578]) ).

fof(f323,axiom,
    ! [X0,X5,X25] : c_List_Olist_OCons(X5,X25,X0) != X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).

fof(f576,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f311,f574]) ).

fof(f311,axiom,
    ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

fof(f572,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f289,f570]) ).

fof(f570,plain,
    ( spl0_37
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f289,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f568,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f288,f566]) ).

fof(f566,plain,
    ( spl0_36
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f288,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f564,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f287,f562]) ).

fof(f562,plain,
    ( spl0_35
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f287,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f560,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f357,f558]) ).

fof(f558,plain,
    ( spl0_34
  <=> ! [X24] :
        ( ~ c_InductTermi_OIT(X24)
        | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X24)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f357,axiom,
    ! [X24] :
      ( ~ c_InductTermi_OIT(X24)
      | c_InductTermi_OIT(c_Lambda_OdB_OAbs(X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

fof(f556,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f331,f554]) ).

fof(f331,axiom,
    ! [X27,X30] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X30),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

fof(f552,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f307,f550]) ).

fof(f307,axiom,
    ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

fof(f548,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f299,f546]) ).

fof(f546,plain,
    ( spl0_31
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f299,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

fof(f544,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f275,f542]) ).

fof(f275,axiom,
    ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f540,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f335,f538]) ).

fof(f335,axiom,
    ! [X11,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

fof(f536,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f290,f534]) ).

fof(f290,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

fof(f532,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f265,f530]) ).

fof(f265,axiom,
    ! [X4] : c_Suc(X4) != X4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f528,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f353,f526]) ).

fof(f353,axiom,
    ! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

fof(f524,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f390,f521]) ).

fof(f390,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f519,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f389,f516]) ).

fof(f516,plain,
    ( spl0_24
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f389,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f514,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f388,f511]) ).

fof(f388,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f509,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f387,f506]) ).

fof(f506,plain,
    ( spl0_22
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f387,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f504,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f386,f501]) ).

fof(f501,plain,
    ( spl0_21
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f386,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f499,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f385,f496]) ).

fof(f496,plain,
    ( spl0_20
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f385,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f494,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f384,f491]) ).

fof(f491,plain,
    ( spl0_19
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f384,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f489,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f383,f486]) ).

fof(f383,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f484,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f382,f481]) ).

fof(f481,plain,
    ( spl0_17
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f382,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f479,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f381,f476]) ).

fof(f476,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f381,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f474,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f380,f471]) ).

fof(f471,plain,
    ( spl0_15
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f380,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f469,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f379,f466]) ).

fof(f466,plain,
    ( spl0_14
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f379,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f464,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f378,f461]) ).

fof(f378,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(f459,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f377,f456]) ).

fof(f377,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f454,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f376,f451]) ).

fof(f451,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f376,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(f449,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f375,f446]) ).

fof(f446,plain,
    ( spl0_10
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f375,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f444,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f374,f441]) ).

fof(f441,plain,
    ( spl0_9
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f374,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f439,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f373,f436]) ).

fof(f436,plain,
    ( spl0_8
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f373,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f434,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f372,f431]) ).

fof(f431,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f372,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(f429,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f371,f426]) ).

fof(f426,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f371,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(f424,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f370,f421]) ).

fof(f421,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f370,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f419,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f369,f416]) ).

fof(f416,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f369,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f414,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f360,f411]) ).

fof(f411,plain,
    ( spl0_3
  <=> c_InductTermi_OIT(v_u____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f360,axiom,
    c_InductTermi_OIT(v_u____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

fof(f409,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f356,f406]) ).

fof(f406,plain,
    ( spl0_2
  <=> c_InductTermi_OIT(v_ua______) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f356,axiom,
    c_InductTermi_OIT(v_ua______),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

fof(f404,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f368,f401]) ).

fof(f368,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL800-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 22:47:31 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (10867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39  % (10870)WARNING: value z3 for option sas not known
% 0.21/0.39  % (10871)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.39  % (10869)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.39  % (10868)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.39  % (10870)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.39  % (10872)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)
% 0.21/0.39  % (10874)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.39  % (10873)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.48  TRYING [3]
% 0.21/0.52  TRYING [1]
% 0.21/0.53  TRYING [2]
% 1.40/0.58  TRYING [1]
% 1.40/0.59  TRYING [2]
% 1.40/0.61  TRYING [3]
% 2.87/0.77  TRYING [4]
% 2.87/0.78  TRYING [3]
% 3.53/0.87  TRYING [4]
% 5.70/1.19  % (10872)First to succeed.
% 5.70/1.21  % (10872)Refutation found. Thanks to Tanya!
% 5.70/1.21  % SZS status Unsatisfiable for theBenchmark
% 5.70/1.21  % SZS output start Proof for theBenchmark
% See solution above
% 5.70/1.22  % (10872)------------------------------
% 5.70/1.22  % (10872)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.70/1.22  % (10872)Termination reason: Refutation
% 5.70/1.22  
% 5.70/1.22  % (10872)Memory used [KB]: 11279
% 5.70/1.22  % (10872)Time elapsed: 0.818 s
% 5.70/1.22  % (10872)Instructions burned: 2300 (million)
% 5.70/1.22  % (10872)------------------------------
% 5.70/1.22  % (10872)------------------------------
% 5.70/1.22  % (10867)Success in time 0.848 s
%------------------------------------------------------------------------------